### Numerical modelling of diffusion decomposition processes

A set of programs for the numerical simulation of the diffusion decomposition processes was developed by using simulation methods, kinetic and particle method. The complex has been validated on the model system Ni-Al by the growth of -phase separations. The results on the evolution of the distribution function and other characteristics of the ensemble, which in the zero volume fraction approximation are asymptotically in good agreement with the theory and the experiment, have been obtained. The peculiarity of the created program complex is the possibility of its adaptation to the description of the decomposition of multicomponent multiphase systems

### Critical phase in a class of 1D quasiperiodic models with exact phase diagram and generalized dualities

We propose a class of 1D quasiperiodic tight binding models that includes extended, localized and critical phases and analytically determine its phase diagram. Limiting cases of this class include the Aubry-Andr\'e model and the models of Refs. Phys. Rev. Lett. 114, 146601 and Phys. Rev. Lett. 104, 070601. Away from these limits, critical multifractal phases are found to extend over a tunable region of parameters. Such critical phases are of practical interest as they host non-trivial mobility edges without the need of implementing unbounded potentials required by previous proposals. This class of models illustrates the most general duality symmetry found so far. It extends previously encountered duality transformations, between extended and localized phases, to dual points within the critical phase. The crucial observation of this work is to recognize these models as a novel class of fixed-points of the renormalization group procedure proposed in arXiv:2206.13549. This allows to calculate the renormalized coefficients exactly and obtain a full analytical characterization of the phases of the infinite quasiperiodic system.

### Quasiclassical theory for antiferromagnetic metals

Antiferromagnetism can not, unlike ferromagnetism, be readily included in the quasiclassical Keldysh theory because of the rapid spatial variation of the magnetic order. The quasiclassical framework is useful because it separates the quantum effects occuring at length-scales comparable to the Fermi wavelength from other length-scales, and has successfully been used to study a wide range of phenomena involving both superconductivity and ferromagnetism. Starting from a tight-binding Hamiltonian, we develop quasiclassical equations of motion and boundary conditions which can, for instance, be used to describe antiferromagnetic order in the dirty limit.

### Light-driven C-H bond activation mediated by 2D transition metal dichalcogenides

C-H bond activation enables the facile synthesis of new chemicals. While C-H activation in short-chain alkanes has been widely investigated, it remains largely unexplored for long-chain organic molecules. Here, we report light-driven C-H activation in complex organic materials mediated by 2D transition metal dichalcogenides (TMDCs) and the resultant solid-state synthesis of luminescent carbon dots in a spatially resolved fashion. Through the first-principle calculations, we unravel that the defects and oxidized states in 2D TMDCs lead to efficient C-H activation and chemical reaction. Furthermore, we exploit the light-controlled point-and-shoot chemical reaction for versatile carbon dot patterning and optical encoding of encrypted information. Our results will shed light on 2D materials for C-H activation in a variety of organic compounds for applications in organic chemistry, photonic materials, and environmental remediation.

### Fractional quantum Hall effect at the filling factor $ν=5/2$

The fractional quantum Hall (FQH) effect at the filling factor $\nu=5/2$ was discovered in GaAs heterostructures more than 35 years ago. Various topological orders have been proposed as possible candidates to describe this FQH state. Some of them possess non-Abelian anyon excitations, an entirely new type of quasiparticle with fascinating properties. If observed, non-Abelian anyons could offer fundamental building blocks of a topological quantum computer. Nevertheless, the nature of the FQH state at $\nu=5/2$ is still under debate. In this chapter, we provide an overview of the theoretical background, numerical results, and experimental measurements pertaining to this special FQH state. Furthermore, we review some recent developments and their possible interpretations. Possible future directions toward resolving the nature of the $5/2$ state are also discussed.

### Drag force on cylindrical intruders in granular media: Experimental study of lateral vs axial intrusion and high grain-polydispersity effects

We report on experimentally measured drag force experienced by a solid cylinder penetrating a granular bed of glass beads including, specifically, a highly polydisperse sample with grain sizes in the range 1-100 {\mu}m. We consider both cases of lateral and axial intrusion in which the long axis of the cylinder is held horizontally and vertically, respectively. We explore different regimes of behavior for the drag force as a function of the penetration depth. In lateral intrusion, where the motion is effectively quasi-two-dimensional, we establish quantitative comparisons with existing theoretical predictions across the whole range of depths. In axial intrusion, we observe peculiar undulations in the force-depth profiles in a wide range of intrusion speeds and for different cylinder diameters. We argue that these undulations reflect general shear failure in the highly polydisperse sample and can be understood based on the ultimate bearing capacity theory on a semiquantitative level.

### Long-range order coexisting with long-range entanglement: Is Nd$_2$Sn$_2$O$_7$ the first Coulombic antiferromagnet with a visible emergent gauge photon?

Exotic state of matter could coexist with conventional orders such that the gauge fields and fractionalized excitations could prevail in a seemingly ordered state. By digging out and examining old experiments, we identify the pyrochlore Nd$_2$Sn$_2$O$_7$ as a Coulombic antiferromagnet. This novel and exotic state carries both antiferromagnetic order and emergent quantum electrodynamics with gapless gauge photon and fractionalized quasiparticles. The antiferromagnetic order and the gauge photon naturally explain the neutron diffraction result and the anomalously large $T^3$ specific heat, respectively. We propose the representative dynamical properties for the Coulombic antiferromagnet that can be examined by the inelastic neutron scattering measurements. If the experiment in Nd$_2$Sn$_2$O$_7$ can be repeated, Nd$_2$Sn$_2$O$_7$ might become the first Coulombic antiferromagnet with a visible emergent gauge photon and thus an unique system with both the long-range order and the long-range entanglement. We also expect this work to inspire interests in the search of exotic physics in ordered magnets.

### Surface roughness noise analysis and comprehensive noise effects on depth-dependent coherence time of NV centers in diamond

Noise is a detrimental issue for nitrogen-vacancy (NV) centers in diamond, causing line broadening and decreasing the coherence time (T2). Following our previous electric and magnetic field noise work, we investigate noise caused by the diamond surface roughness, which is a source for charge density fluctuations and incoherent photon scattering. We find that the varying surface charge density noise source is prevalent throughout the entire NV dynamical decoupling frequency range, while the photon scattering noise is almost negligible. Next, we combine the results from various noise sources to perform comprehensive analyses on T2 and how it varies with NV depth. At a given NV depth of 5 nm below a hydrogen- or fluorine-terminated surface, we find that these magnetic nuclei reduce the NV coherence time the most, followed by the surface electric field noise sources. The photon scattering and bulk magnetic field noise effects on T2 are weak compared to the varying charge density, electric dipole, and surface impurity noise. However, with oxygen surface termination, the surface electric field noise becomes comparable to the surface magnetic field noise. Our calculated values of T2,Hahn (few microseconds to ten microseconds) are in good agreement with the experimental values reported elsewhere. Finally, we calculate an anticipated signal-to-noise ratio (SNR) for NV AC magnetometry of external nuclear spins. In our simplified assessment, where some depth-dependent parameters (e.g. NV conversion efficiency) are held constant, we find that shallower NV layers should yield the best SNR, which is consistent with experimental findings.

### Mechanisms for Magnetic Skyrmion Catalysis and Topological Superconductivity

We propose an alternative route to stabilize magnetic skyrmion textures, which is free from the requirement of Dzyaloshinkii-Moriya interaction, magnetic anisotropy and the application of an external Zeeman field. Instead, it solely relies on time reversal symmetry (TRS) violation, and the emergence of flux in the ground state. We discuss scenarios that lead to a nonzero flux, and identify the possible magnetic ground states which become accessible in its presence. We focus on itinerant magnets with tetragonal symmetry, which preserve the full spin-rotational group but violate TRS. We demonstrate our mechanism for a concrete extended Dirac model, which can describe the protected surface states of a topological crystalline insulator. In addition, we investigate the topological phases obtained for the above extended Dirac model when two distinct magnetic skyrmion crystal ground states coexist with a conventional pairing gap. We find chiral topological superconducting phases, which harbor an integer number of chiral Majorana modes when line defects are present. Our mechanism opens alternative perspectives for engineering topological superconductivity in a minimal fashion. Evenmore, relaxing the stringent requirements to generate skyrmions, also promises to unlock new functional topological materials and devices which may be more compatible with electrostatic control than the currently explored skyrmion-Majorana platforms.

### Membrane viscosity signature in thermal undulations of curved fluid bilayers

Membrane viscosity is usually assumed to only affect short-wavelength undulations of lipid bilayers. Here, we show that fluctuation dynamics about a curved shape such as a quasi-spherical vesicle is sensitive to the membrane viscosity even at long wavelengths, if the Saffman-Debr\"uck length is larger than the radius of curvature. The theory predicts a relaxation rate of $\sim \ell^4$ for a spherical harmonic mode $\ell$, a drastic change from the classic result $\sim \ell^3$. Accordingly, the anomalous diffusion exponent governing the Dynamic Structure Factor (DSF) becomes 1/2 instead of the commonly used 2/3 [Zilman and Granek, Phys. Rev. Lett. (1996)]. Flickering spectroscopy of the shape fluctuations of giant vesicles made of phospholipid/cholesterol mixtures confirm the theoretical results and, for the first time, demonstrate the effect of membrane viscosity in the bilayer thermal undulations. The new DSF scaling implies that the data analysis in methods that utilize DSF of liposomes, e.g., neutron spin echo, need to be reassessed.

### Electrocatalytic Study for Hydrogen Evolution Reaction on MoS$_2$/BP and MoSSe/BP in Acidic Media

Molecular hydrogen (H$_2$) production by electrochemical hydrogen evolution reaction (HER) is being actively explored for non-precious-metal based electrocatalysts that are earth-abundant and low cost like MoS$_2$. Although it is acid-stable, its applicability is limited by catalytically inactive basal plane, poor electrical transport and inefficient charge transfer at the interface. Therefore, the present work examines its bilayer van der Waals heterostructure (vdW HTS). The second constituent monolayer Boron Phosphide (BP) is advantageous as an electrode material owing to its chemical stability in both oxygen and water environments. Here, we have performed first-principles based calculations under the framework of density functional theory (DFT) for HER in an electrochemical double layer model with the BP monolayer, MoS$_2$/BP and MoSSe/BP vdW HTSs. The climbing image nudged elastic band method (CI-NEB) has been employed to determine the minimum energy pathways for Tafel and Heyrovsky reactions. The calculations yield that Tafel reaction shows no reaction barrier. Thereafter, for Heyrovsky reaction, we have obtained low reaction barrier in the vdW HTSs as compared to that in the BP monolayer. Subsequently, we have observed no significant difference in the reaction profile of MoS$_2$/BP and MoSSe/BP vdW HTSs in case of high coverage (25 %) and 1/3 H$^+$ concentration (conc.). However, in the case of small coverage (11 %) and 1/3 H$^+$ conc., MoSSe/BP shows feasible Heyrovsky reaction with no reaction barrier. Finally, on comparing the coverages with 1/4 H$^+$ conc., we deduce high coverage with low conc. and low coverage with high conc. to be apt for HER via Heyrovsky reaction path.

### Atom Interferometric Imaging of Differential Potentials Using an Atom Laser

Interferometry is a prime technique for modern precision measurements. Atoms, unlike light, have significant interactions with electric, magnetic, and gravitational fields, making their use in interferometric applications particularly versatile. Here, we demonstrate atom interferometry to image optical and magnetic potential landscapes over an area exceeding $240 \mu m \times 600 \mu m$. The differential potentials employed in our experiments generate phase imprints in an atom laser that are made visible through a Ramsey pulse sequence. We further demonstrate how advanced pulse sequences can enhance desired imaging features, e.g. to image steep potential gradients. A theoretical discussion is presented that provides a semiclassical analysis and matching numerics.

### Rough diamond anvils: Steady microstructure, yield surface, and transformation kinetics in Zr

Study of the plastic flow and strain-induced phase transformations (PTs) under high pressure with diamond anvils is important for material and geophysics. We introduce rough diamond anvils and apply them to Zr, which drastically change the plastic flow, microstructure, and PTs. Multiple steady microstructures independent of pressure, plastic strain, and strain path are reached. Maximum friction equal to the yield strength in shear is achieved. This allows determination of the pressure-dependence of the yield strength and proves that omega-Zr behaves like perfectly plastic, isotropic, and strain path-independent immediately after PT. Record minimum pressure for alpha-omega PT was identified. Kinetics of strain-induced PT depends on plastic strain and time. Crystallite size and dislocation density in omega-Zr during PT depend solely on the volume fraction of omega-Zr.

### Screening and collective effects in randomly pinned fluids: A new theoretical framework

We propose a theoretical framework for the dynamics of bulk isotropic hard-sphere systems in the presence of randomly pinned particles and apply this theory to supercooled water to validate it. Structural relaxation is mainly governed by local and non-local activated process. As the pinned fraction grows, a local caging constraint becomes stronger and the long range collective aspect of relaxation is screened by immobile obstacles. Different responses of the local and cooperative motions results in subtle predictions for how the alpha relaxation time varies with pinning and density. Our theoretical analysis for the relaxation time of water with pinned molecules quantitatively well describe previous simulations. In addition, the thermal dependence of relaxation for unpinned bulk water is also consistent with prior computational and experimental data.

### Time-reversal symmetry breaking in charge density wave of CsV$_3$Sb$_5$ detected by polar Kerr effect

The Kagome lattice exhibits rich quantum phenomena owing to its unique geometric properties. Appealing realizations are the Kagome metals AV$_3$Sb$_5$ (A = K, Rb, Cs), where unconventional charge density wave (CDW) is intertwined with superconductivity and non-trivial band topology. Several experiments suggest that this CDW is a rare occurrence of chiral CDW characterized by orbital loop current. However, key evidences of loop current, spontaneous time-reversal symmetry-breaking (TRSB) and the coupling of its order parameter with the magnetic field remain elusive. Here, we investigate the CDW in CsV3Sb5 by magneto-optic polar Kerr effect with sub-microradian resolution. Under magnetic field, we observed a jump of the Kerr angle at the CDW transition. This jump is magnetic-field switchable and scales with field, indicating magneto--chirality coupling related to non-trivial band topology. At zero field, we found non-zero and field-trainable Kerr angle below CDW transition temperature, signaling spontaneous TRSB. Our results provide a crucial step to unveil quantum phenomena in correlated Kagome materials.

### The computational simulation of the reflection spectra of copper red glaze

Owing to the limitation of traditional analytical methods, the coloration mechanism of copper red glaze has been disputed in the academic field for a long time, which mainly focuses on whether the color agent is metallic copper nanoparticles or cuprous oxide (Cu2O) nanoparticles. Based on Mie scattering theory, this work calculated the reflection spectra of nanoparticles uniformly dispersed in transparent glaze with different types, diameters and volume fractions, then discussed the differences between the reflection spectra of metallic copper and cuprous oxide as scatters, calculated the corresponding L*a*b* values, and compared them with the experimental results. This work provides a feasible and convenient method to distinguish these two coloration mechanisms.

### Wide Effective Work-Function Tuning of Al/SiO$_2$/Si Junction Achieved with Graphene Interlayer at Al/SiO$_2$ Interface

The effective work-function of metal electrode is one of the major factors to determine the threshold voltage of metal/oxide/semiconductor junction. In this work, we demonstrate experimentally that the effective work-function of Aluminum (Al) electrode in Al/SiO$_2$/n-Si junction increases significantly by $\sim$1.04 eV with the graphene interlayer inserted at Al/SiO$_2$ interface. We also provide the device-physical analysis of solving Poisson equation when the flat-band voltage is applied to the junction, supporting that the wide tuning of Al effective work-function originates from the electrical dipole layer formed by the overlap of electron orbitals between Al and graphene layer. Our work suggests the feasibility of constructing the dual-metal gate CMOS circuitry just by using Al electrodes with area-specific underlying graphene interlayer.

### Driving force induced transition in thermal behavior of grain boundary migration in Ni

Grain boundaries (GBs) that show higher mobility at lower temperatures (i.e., the so-called nonthermally activated or non-Arrhenius GBs) have attracted significant interest in recent years. In this study, we use atomistic simulations to systematically investigate the effect of driving force on GB mobility based on a set of bicrystalline models in Ni. It is found that the thermal behavior of GB migration strongly depends on the temperature and the magnitude of driving forces. When the driving force is small, e.g., GB migration at the zero-driving force limit as induced solely by thermal fluctuations, the mobility of all GBs investigated in the current study shows a transition from thermally activated to non-thermally activated behavior when the temperature is increased. As the driving force increases, the transition temperature at which the mobility peaks would gradually decrease so that for some GBs only the non-thermally activated behavior would be detected. It is further revealed based on nudged elastic band (NEB) analysis that the transition temperature is linearly related to the energy barrier for migration in each GB, and the energy barrier is lowered as the driving force increases. Our work supports the previous theoretical model for GB migration based on both disconnection nucleation and the more recent one based on classical thermal activation. Furthermore, the current study can be used to improve both models by taking into account the influence of driving force with a simple fix to how the energy barrier for GB migration should be considered. It is expected that this work advances the current understanding of general GB migration and sheds some light on a unified theoretical framework in the near future.

### Nanoscale three-dimensional magnetic sensing with a probabilistic nanomagnet driven by spin-orbit torque

Detection of vector magnetic fields at nanoscale dimensions is critical in applications ranging from basic material science, to medical diagnostic. Meanwhile, an all-electric operation is of great significance for achieving a simple and compact sensing system. Here, we propose and experimentally demonstrate a simple approach to sensing a vector magnetic field at nanoscale dimensions, by monitoring a probabilistic nanomagnet's transition probability from a metastable state, excited by a driving current due to SOT, to a settled state. We achieve sensitivities for Hx, Hy, and Hz of 1.02%/Oe, 1.09%/Oe and 3.43%/Oe, respectively, with a 200 x 200 nm^2 nanomagnet. The minimum detectable field is dependent on the driving pulse events N, and is expected to be as low as 1 uT if N = 3 x 10^6.

### Structural and optical properties of micro-diamonds with SiV- color centers

Isolated, micro-meter sized diamonds are grown by micro-wave plasma chemical vapour deposition technique on Si(001) substrates. Each diamond is uniquely identified by markers milled in the Si substrate by Ga+ focused ion beam. The morphology and micrograin structure analysis indicates that the diamonds are icosahedral or bi-crystals. Icosahedral diamonds have higher (up to $\sigma_\mathrm{h}$ = 2.3 GPa), and wider distribution ($\Delta\sigma_\mathrm{h}$ = 4.47 GPa) of hydrostatic stress built up at the microcrystal grain boundaries, compared to the other crystals. The number and spectral shape of SiV- color centers incorporated in the micro-diamonds is analysed, and estimated by means of temperature dependent photoluminescence measurements, and Montecarlo simulations. The Montecarlo simulations indicate that the number of SiV- color centers is a few thousand per micro-diamond.

### Intrinsic Instabilities in Fermi Glass

In this paper, we study the effect of short-ranged interaction on disordered metals where the non-interacting single-particle eigenstates are all localized (Anderson Insulator). Through analysing the interaction matrix elements between different eigenstates of the non-interacting single-particle Hamiltonian carefully, we show that the Fermi Glass state is unstable towards formation of magnetic moments (for repulsive interaction) or local charge-2 bosons (for attractive interaction) in first order perturbation theory under very general conditions. Numerical simulations were performed to verify the above predictions. The disordered system is expected to become a ferromagnet for repulsive interaction and superconductor for attractive interaction when a self-consistent Hartree-Fock-Cooper theory is implemented.

### Spin-Hall Magnetoresistance in quasi-two-dimensional antiferromagnetic insulator/metal bilayer systems

We study temperature dependence of spin Hall magnetoresistance (SMR) in antiferromagnetic insulator (AFI)/metal bilayer systems. We calculate the amplitude of the SMR signal using the quantum Monte Carlo simulation and examine how the SMR depends on the amplitude of the spin, thickness of the AFI layer, and randomness of exchange interactions. Our results for simple quantum spin models provide a useful starting point for understanding of the SMR measurement for atomic layers of magnetic compounds.

### Exciton manifolds in highly ambipolar doped WS2

The disentanglement of single and many particle properties in 2D semiconductors and their dependencies on high carrier concentration is challenging to experimentally study by pure optical means. We establish an electrolyte gated WS2 monolayer field-effect structure capable to shift the Fermi level from the valence into the conduction band suitable to optically trace exciton binding as well as the single particle band gap energies in the weakly doped regime. Combined spectroscopic imaging ellipsometry and photoluminescence spectroscopies spanning large n- and p-type doping with charge carrier densities up to 10^14 cm-2 enable to study screening phenomena and doping dependent evolution of the rich exciton manifold whose origin is controversially discussed in literature. We show that the two most prominent emission bands in photoluminescence experiments are due to the recombination of spin-forbidden and momentum-forbidden charge neutral excitons activated by phonons. The observed interband transitions are redshifted and drastically weakened under electron or hole doping. This field-effect platform is not only suitable for studying exciton manifold but is also suitable for combined optical and transport measurements on degenerately doped atomically thin quantum materials at cryogenic temperatures.

### Zeeman effects on Yu-Shiba-Rusinov states

When the exchange interaction between the impurity spin and the spins of itinerant quasiparticles are strong or weak enough, the ground states for a magnetic impurity in a superconductor are the screened or free spins, respectively. In both cases, the lowest excited state is a bound state within the superconducting gap, known as the Yu-Shiba-Rusinov (YSR) state. The YSR state is spatially localized, energetically isolated, and fully spin-polarized, leading to applications such as functional scanning probes. While any application demands identifying whether the impurity spin is screened or free, a suitable experimental technique has been elusive. Here we demonstrate an unambiguous way to determine the impurity ground state using the Zeeman effect. We performed ultra-low temperature scanning tunneling spectroscopy of junctions formed between a Cu(111) surface and superconducting Nb tips decorated by single magnetic Fe atoms. Depending on the condition of the Fe adsorbate, the YSR peak in the spectrum either splits or shifts in a magnetic field, signifying that the Fe spin is screened or free, respectively. Our observations provide renewed insights into the competition between magnetism and superconductivity and constitute a basis for the applications of the YSR state.

### Scale free chaos in swarms

Swarms are examples of collective behavior of insects, which are singular among manifestations of flocking. Swarms possess strong correlations but no global order and exhibit finite-size scaling with a dynamic critical exponent $z \approx 1$. We have discovered a phase transition of the three-dimensional harmonically confined Vicsek model that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos that can be characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Susceptibility, correlation length, dynamic correlation function and largest Lyapunov exponent obey power laws. Their critical exponents agree with those observed in natural midge swarms, unlike values obtained from the order-disorder transition of the standard Vicsek model which confines particles by artificial periodic boundary conditions.

### Strain-induced pseudo-magnetic field in $α-{\cal T}_3$ lattice

We investigate the effects of a nonuniform uniaxial strain and a triaxial strain on the $\alpha-{\cal T}_3$ lattice. The analytical expressions of the pseudo-Landau levels (pLLs) are derived based on low-energy Hamiltonians, and are verified by tight-binding calculations. We find the pseudo-magnetic field leads to the oscillating density of states, and the first pLL is sublattice polarized, which is distributed on only two of the three sets of sublattices. For the nonuniform uniaxial strain, we show that pLLs become dispersive due to the renormalization of the Fermi velocity, and a valley polarized current emerges. Our results generalize the study of pseudo-magnetic field to the $\alpha-{\cal T}_3$ lattice, which will not only deepen the understanding of the intriguing effects of mechanical strains, but also provide theoretical foundation for possible experimental studies of the effects of strain on the $\alpha-{\cal T}_3$ lattice.

### Two-photon absorption in semiconductors: a multi-band length-gauge analysis

The simplest approach to deal with light excitations in direct-gap semiconductors is to model them as a two-band system: one conduction and one valence band. For such models, particularly simple analytical expressions are known to exist for the optical response such as multi-photon absorption coefficients. Here we show that generic multi-band models do not require much more complicated expressions. Our length-gauge analysis is based on the semiconductors Bloch equations in the absence of all scattering processes. In the evaluation, we focus on two-photon excitation by a pump-probe scheme with possibly non-degenerate and arbitrarily polarized configurations. The theory is validated by application to graphene and its bilayer, described by a tight-binding model, as well as bulk Zincblende semiconductors described by k.p theory.

### Dynamical Instability of 3d Stationary and Traveling Planar Dark Solitons

Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional Bose-Einstein condensates by quantitatively comparing theoretical analysis and associated numerical computations with our experimental results. Using fully 3d numerical simulations, we explore the existence, stability, and evolution dynamics of planar dark solitons, as well as their instability-induced decay products including solitonic vortices and vortex rings. In the trapped case and with no adjustable parameters, our numerical findings are in correspondence with experimentally observed coherent structures. Without a longitudinal trap, we identify numerically exact traveling solutions and quantify how their transverse destabilization threshold changes as a function of the solitary wave speed.

### SAT-UNSAT transitions of classical, quantum, and random field spherical antiferromagnetic Hopfield model

Here we study the fully connected spherical antiferromagnetic Hopfield model as a toy model of the convex continuous satisfaction problem. The model exhibits a sharp SAT-UNSAT transition at a certain point, where the system becomes isostatic: the number of degrees of freedom agrees with that of the constraints. The model is simple enough to investigate the scaling behavior near the SAT-UNSAT transition point without relying on the replica method. Furthermore, the simplicity of the model allows us to take into account the effects of the quantum fluctuation and random field. We found that the pure classical model, quantum model, and model with the random field have different critical exponents and thus belong to different universal classes.

### Shapes and dynamic regimes of an active fluid droplet under confinement

Active droplets are artificial microswimmers built from a liquid dispersion by microfluidic tools and showing self-propelled motion. These systems hold particular interest for mimicking biological phenomena, such as some aspects of cell locomotion and collective behaviors of bacterial colonies, as well as for the design of droplet-based biologically inspired materials, such as engineered tissues. Growing evidence suggests that geometrical confinement crucially affects their morphology and motility, but the driving physical mechanisms are still poorly understood. Here we study the effect of activity on a droplet containing a contractile fluid confined within microfluidic channels of various sizes. We find a surprising wealth of shapes and dynamic regimes, whose mechanics is regulated by a subtle interplay between contractile stress, droplet elasticity and microchannel width. They range from worm-like and fish-like shaped droplets displaying an oscillating behavior within wider channels to bullet-shaped droplets exhibiting rectilinear motion in narrower slits. Our findings support the view that geometrical confinement can provide a viable strategy to control and predict the propulsion direction of active droplets. It would be of interest to look for analogues of these motility modes in biological cells or in synthetic active matter.

### Theory of viscoelastic adhesion and friction

We present a novel theory of the adhesive contact of linear viscoelastic materials against rigid substrates moving at constant velocity. Despite the non-conservative behavior of the system, the closure equation of the contact problem can be rigorously formulated in the form of a local energy balance. In the case of adhesiveless contacts, this is equivalent to enforce the stationarity of the total energy stored into the viscoelastic material. However, in the presence of interfacial adhesion, the appearance of non-conservative terms leads to different values of the energy release rates G1 and G2 at the contact trailing and leading edges, respectively. Specifically, the present theory predicts a non-monotonic trend of G1 and G2 as function of the indenter velocity, as well as a very significant enhancement of hysteretic friction due to the coupling between adhesion and viscoelasticity, compared to the adhesiveless case. Both predictions are in very good agreement with existing experimental data.

### Toroflux: A counterpart of the Chandrasekhar-Kendall state in noncentrosymmetric superconductors

We demonstrate that superconductors with broken inversion symmetry support a family of stable, spatially localized configurations of the self-knotted magnetic field. These solutions, that we term "toroflux", are the superconducting counterparts of the Chandrasekhar-Kendall states (spheromaks) that appear in highly conducting, force-free astrophysical and nuclear-fusion plasmas. The superconducting torofluxes are solutions of superconducting models, in the presence of a parity breaking Lifshitz invariant associated with the $O$ point group symmetry. We demonstrate that a magnetic dipole or a ferromagnetic inclusion in the bulk of a noncentrosymmetric superconductor source finite-energy toroflux solutions.

### Harnessing the polymer-particle duality of ultra-soft nanogels to stabilise smart emulsions

Micro- and nanogels are widely used to stabilise emulsions and simultaneously implement their responsiveness to the external stimuli. One of the factors that improves the emulsion stability is the nanogel softness. Here, we study how the softest nanogels that can be synthesised with precipitation polymerisation of N-isopropylacrylamide (NIPAM), the ultra-low crosslinked (ULC) nanogels, stabilise oil-in-water emulsions. We show that ULC nanogels can efficiently stabilise emulsions already at low mass concentrations. These emulsions are resistant to droplet flocculation, stable against coalescence, and can be easily broken upon an increase in temperature. The resistance to flocculation of the ULC-stabilised emulsion droplets is similar to the one of emulsions stabilised by linear pNIPAM. In contrast, the stability against coalescence and the temperature-responsiveness closely resemble the one of emulsions stabilised by regularly crosslinked pNIPAM nanogels. The reason for this combination of properties is that ULC nanogels can be thought of as colloids in between flexible macromolecules and particles. As a polymer, ULC nanogels can efficiently stretch at the interface and cover it uniformly. As a regularly crosslinked nanogel particle, ULC nanogels protect emulsion droplets against coalescence by providing a steric barrier and rapidly respond to changes in external stimuli thus breaking the emulsion. This polymer-particle duality of ULC nanogels can be exploited to improve the properties of emulsions for various applications, for example in heterogeneous catalysis or in food science.

### Polarized neutron scattering study on the centrosymmetric skyrmion host material Gd2PdSi3

We have investigated magnetic structures of the centrosymmetrric skyrmion material Gd2PdSi3 by means of polarized neutron scattering near zero field with an isotope-160Gd-enriched single crystal. In a previous study, magnetic structures in Gd2PdSi3 at low temperatures were studied by resonant X-ray scattering measurements [T. Kurumaji et al. Science 365, 914 (2019)]. The present polarized neutron results confirm that the magnetic structure in zero field has elliptic screw-type magnetic modulation with a propagation vector of (q, 0, 0) with q ~ 0.14 and its equivalents. As the temperature increases, the system undergoes a magnetic phase transition while keeping the incommensurate q-vector of (q,0,0). We found that the thermally-induced phase has sinusoidal magnetic modulations with magnetic moments perpendicular both to the c axis and to the q-vector. We also investigate the spin-helicity degree of freedom in the ground state by polarized neutrons, revealing that the system contains equal fractions of the left-handed and right-handed screw-type orders as expected from the centrosymmetric crystal structure.

### Floquet states and optical conductivity of an irradiated two dimensional topological insulator

We study the topology of the Floquet states and time-averaged optical conductivity of the lattice model of a thin topological insulator subject to a circularly polarized light using the extended Kubo formalism. Two driving regimes, the off-resonant and on-resonant, and two models for the occupation of the Floquet states, the ideal and mean-energy occupation, are considered. In the ideal occupation, the real part of DC optical Hall conductivity is shown to be quantized while it is not quantized for the mean energy distribution. The optical transitions in the Floquet band structure depend strongly on the occupation and also the optical weight which consequently affect all components of optical conductivity. At high frequency regime, we present an analytical calculation of the effective Hamiltonian and also its phase diagram which depends on the tunneling energy between two surfaces. The topology of the system shows rich phases when it is irradiated by a weak on-resonant drive giving rise to emergence of anomalous edge states.

### Electric Circuit Simulation of Floquet Topological Insulators

We propose the simulation of every non-interacting time-periodic tight-binding Hamiltonian in electrical circuits with inductors and capacitors. First the time periodic Hamiltonian is mapped into a static Floquet Hamiltonian and so the time dimension is transformed into the Floquet dimension which in electric circuits is simulated as the additional dimension in space. However, the number of copies of the system which must be considered in this new dimension is controlled by the frequency and bandwidth. Furthermore, we show that the topological edge states (including anomalous edge states in the dynamical gap) can be detected in circuit by measuring the divergence of impedance between the nodes. Our results provide a simple and promising way to investigate and manipulate Floquet topological phases in electric circuits.

### Scaling theory of critical strain-stiffening in athermal biopolymer networks

Athermal biopolymer networks are disordered fibrous biomaterials abundant in living cells and tissues that feature strong rigidity scale separation between the bending and stretching response of the constituent fibers. Such networks -- that are generically underconstrained in terms of their degree of connectivity -- undergo a dramatic macroscopic stiffening transition when subjected to sufficiently large external strains, which in turn plays major roles in determining the mechanical stability and functionality of living systems. We present a complete scaling theory of the critical strain-stiffened state in terms of the small ratio between fiber bending and stretching/compression rigidities. We show that the small bending forces may be viewed as an isotropic singular perturbation applied to the stiff anisotropic backbone corresponding to fibers' stretching/compression. The critical state features quartic anharmonicity, from which a set of nonlinear scaling relations for various fundamental biophysical quantities are derived. These results, which are validated by highly accurate numerical simulations, are then used to derive scaling predictions for the macroscopic elastic modulus beyond the critical state, revealing a previously unidentified characteristic strain scale. We thus provide a comprehensive understanding of the strain-stiffening transition in athermal biopolymer networks.

### Brillouin propagation modes of cold atoms in dissipative optical lattices

An exact series expansion of the average velocity of cold atoms in dissipative optical lattices under probe driving, based on the amplitudes of the excited atomic density waves, is derived from the semiclassical equations for the phase space densities of the Zeeman ground-state sublevels. This expansion permits the identification of the precise contribution to the current of a propagating atomic wave for the specific driving, as well as providing the general threshold for the transition into the regime of infinite density for the average velocity.

### Low-energy Properties of Electrons and Holes in CuFeS$_2$

The antiferromagnetic semiconductor CuFeS$_2$ belongs to a magnetic symmetry class that is of interest for spintronics applications. In addition, its crystal lattice is compatible with Si, making it possible to integrate it with non-magnetic semiconducting structures. Therefore, we investigate this material by finding the effective $\boldsymbol{k}\cdot\boldsymbol{p}$ Hamiltonian for the electron- and hole bands. We base this description on \textit{ab initio} calculations and classify the electronic bands by their symmetry. As a result, we find that CuFeS$_2$ exhibits spin-polarized bands and an anomalous Hall effect. Finally, we suggest using cyclotron resonance to verify our proposed effective mass tensors at the conduction band minimum and valence band maximum.

### An exact chiral amorphous spin liquid

Topological insulator phases of non-interacting particles have been generalized from periodic crystals to amorphous lattices, which raises the question whether topologically ordered quantum many-body phases may similarly exist in amorphous systems? Here we construct a soluble chiral amorphous quantum spin liquid by extending the Kitaev honeycomb model to random lattices with fixed coordination number three. The model retains its exact solubility but the presence of plaquettes with an odd number of sides leads to a spontaneous breaking of time reversal symmetry. We unearth a rich phase diagram displaying Abelian as well as a non-Abelian quantum spin liquid phases with a remarkably simple ground state flux pattern. Furthermore, we show that the system undergoes a finite-temperature phase transition to a conducting thermal metal state and discuss possible experimental realisations.

### Activity-driven tissue alignment in proliferating spheroids

We extend the continuum theory of active nematic fluids to study cell flows and tissue dynamics inside multicellular spheroids, spherical, self-assembled aggregates of cells that are widely used as model systems to study tumour dynamics. Cells near the surface of spheroids have better access to nutrients and therefore proliferate more rapidly than those in the resource-depleted core. Using both analytical arguments and three-dimensional simulations, we find that the proliferation gradients result in flows and in gradients of activity both of which can align the orientation axis of cells inside the aggregates. Depending on environmental conditions and the intrinsic tissue properties, we identify three distinct alignment regimes: spheroids in which all the cells align either radially or tangentially to the surface throughout the aggregate and spheroids with angular cell orientation close to the surface and radial alignment in the core. The continuum description of tissue dynamics inside spheroids not only allows us to infer dynamic cell parameters from experimentally measured cell alignment profiles, but more generally motivates novel mechanisms for controlling the alignment of cells within aggregates which has been shown to influence the mechanical properties and invasive capabilities of tumors.

### Strong Connectivity in Real Directed Networks

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behaviour of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering -- a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes, and confirm our results on many real-world networks, including ecological, neural, trade and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. And we illustrate with example dynamics -- the SIS model, majority vote, Kuramoto oscillators and the voter model -- how a small number of edge deletions can utterly change dynamical processes in a wide range of systems.

### Solving nonequilibrium statistical mechanics by evolving autoregressive neural networks

Nonequilibrium statistical mechanics inherits the challenges of the equilibrium, including accurately describing the joint distribution of a large number of variables. It also poses new challenges as the joint distribution evolves over time. While a number of methods have been proposed, e.g., tensor networks for one-dimensional lattices, we lack a method for arbitrary finite time in higher dimensions. In this work, we propose a general approach to study the time evolution of nonequilibrium systems in statistical mechanics by autoregressive neural networks. Specifically, our method offers direct sampling and efficient computation of the normalized probabilities and dynamical partition functions, uncovering the dynamical phase transition over time. We apply the method to a prototype model of nonequilibrium statistical mechanics, the kinetically constrained models of structural glasses up to three dimensions. The obtained results reveal the phase diagram of the time and counting field, as well as the scaling relations. Our approach paves the way toward solving nonequilibrium statistical mechanics using tools in modern machine learning.

### Soft mechanical metamaterials with transformable topology protected by stress caching

Maxwell lattice metamaterials possess a rich phase space with distinct topological states featuring mechanically polarized edge behaviors and strongly asymmetric acoustic responses. Until now, demonstrations of non-trivial topological behaviors from Maxwell lattices have been limited to either monoliths with locked configurations or reconfigurable mechanical linkages. This work introduces a transformable topological mechanical metamaterial (TTMM) made from a shape memory polymer and based on a generalized kagome lattice. It is capable of reversibly exploring topologically distinct phases of the non-trivial phase space via a kinematic strategy that converts sparse mechanical inputs at free edge pairs into a biaxial, global transformation that switches its topological state. Thanks to the shape memory effect, all configurations are stable even in the absence of confinement or a continuous mechanical input. Topologically-protected mechanical behaviors, while robust against structural (with broken hinges) or conformational defects (up to ~55% mis-rotations), are shown to be vulnerable to the adverse effects of stored elastic energy from prior transformations (up to a ~70% reduction in edge stiffness ratios, depending on hinge width). Interestingly, we show that shape memory polymer's intrinsic phase transitions that modulate chain mobility can effectively shield a dynamic metamaterial's topological response (with a 100% recovery) from its own kinematic stress history, an effect we refer to as "stress caching".

### Probing local emission properties in InGaN/GaN quantum wells by scanning tunneling luminescence microscopy

Scanning tunneling electroluminescence microscopy is performed on a 3-nm-thick InGaN/GaN quantum well with x = 0.23 such that the main light emission occurs in the green. The technique is used to map the local recombination properties at a scale of ~10 nm and to correlate them with the surface topography imaged by scanning tunneling microscopy. A 500 nm x 500 nm area around a 150-nm large and 2.5-nm deep hexagonal defect is probed, revealing emission at higher energies close to the defect edges, a feature which is not visible in the macro-photoluminescence spectrum of the sample. Via a fitting of the local tunneling electroluminescence spectra, quantitative information on the fluctuations of the intensity, energy, width and phonon replica intensity of the different spectral contributions are obtained, revealing information about carrier localization in the quantum well. This procedure also indicates that carrier diffusion length on the probed part of the quantum well is approximately 40 nm.

### Cyclotron- and magnetoplasmon resonances in bilayer graphene ratchets

We report on a tunable - by magnetic field and gate voltage - conversion of terahertz radiation into a dc current in spatially modulated bilayer graphene. We experimentally demonstrate that the underlying physics is related to the so-called ratchet effect. Our key findings are the direct observation of a sharp cyclotron resonance in the photocurrent and the demonstration of two effects caused by electron-electron interaction: the plasmonic splitting of the resonance due to long-range Coulomb coupling and the partial suppression of its second harmonic due to fast interparticle collisions. We develop a theory which perfectly fits our data. We argue that the ratchet current is generated in the hydrodynamic regime of non-ideal electron liquid.

### The grammar of the Ising model: A new complexity hierarchy

How complex is an Ising model? Usually, this is measured by the computational complexity of its ground state energy problem. Yet, this complexity measure only distinguishes between planar and non-planar interaction graphs, and thus fails to capture properties such as the average node degree, the number of long range interactions, or the dimensionality of the lattice. Herein, we introduce a new complexity measure for Ising models and thoroughly classify Ising models with respect to it. Specifically, given an Ising model we consider the decision problem corresponding to the function graph of its Hamiltonian, and classify this problem in the Chomsky hierarchy. We prove that the language of this decision problem is (i) regular if and only if the Ising model is finite, (ii) constructive context free if and only if the Ising model is linear and its edge language is regular, (iii) constructive context sensitive if and only if the edge language of the Ising model is context sensitive, and (iv) decidable if and only if the edge language of the Ising model is decidable. We apply this theorem to show that the 1d Ising model and the Ising model on layerwise complete graphs are constructive context free, and the 2d Ising model, the all-to-all Ising model, and the Ising model on perfect binary trees are constructive context sensitive. We also provide a grammar for the 1d and 2d Ising model. This work is a first step in the characterisation of physical interactions in terms of grammars.

### Direct calculation of the planar NaCl-aqueous solution interfacial free energy at the solubility limit

Salty water is the most abundant electrolyte aqueous mixture on Earth, however, very little is known about the NaCl-saturated solution interfacial free energy. Here, we provide the first direct estimation of this magnitude for several NaCl crystallographic planes by means of the Mold Integration technique, a highly efficient computational method to evaluate interfacial free energies with anisotropic crystal resolution. Making use of the JC-SPC/E model, one of the most benchmarked force fields for NaCl/water solutions, we measure the interfacial free energy of four different planes, (100), (110), (111), and (11-2) with the saturated solution at normal conditions. We find high anisotropy between the different crystal orientations with values oscillating from 100 to 150 mJ/m2, being the average value of the distinct planes 137(20) mJ/m2. This value for the coexistence interfacial free energy is in reasonable agreement with previous extrapolations from nucleation studies. Our work represents a milestone in the computational calculation of interfacial free energies between ionic crystals and aqueous solutions.

### The importance of the interface for picosecond spin pumping in antiferromagnet-heavy metal heterostructures

Interfaces between heavy metals (HMs) and antiferromagnetic insulators (AFIs) have recently become highly investigated and debated systems in the effort to create spintronic devices able to function at terahertz frequencies. Such heterostructures have great technological potential because AFIs can generate sub-picosecond spin currents which the HMs can convert into charge signals. In this work we demonstrate an optically induced picosecond spin transfer at the interface between AFIs and Pt using time-resolved THz emission spectroscopy. We select two antiferromagnets in the same family of fluoride cubic perovskites, KCoF3 and KNiF3, whose magnon frequencies at the centre of the Brillouin zone differ by an order of magnitude. By studying their behaviour with temperature we correlate changes in the spin transfer efficiency across the interface to the opening of a gap in the magnon density of states below the N\'eel temperature. Our observations are reproduced in a model based on the spin exchange between the localized electrons in the antiferromagnet and the free electrons in Pt. These results constitute an important step in the rigorous investigation and understanding of the physics of AFIs/HMs interfaces on the ultrafast timescale.

### Majorana bound states in the presence of the half-smeared potential

The Majorana bound state can be realized in one dimensional chain, in form of two well localized and separated states at both ends of the chain. In this paper, we discuss the case when the potential is smeared at one end of the system. In our investigation, we assume the smearing in form of a quadratic function of position. We show that the smearing potential lead to the emergence of extra in-gap states, and effectively decrease the local gap (around the smeared potential). The Majorana states are still preserved in the system, however, their localization depend on the smearing. Moreover, the symmetric localization of the Majorana states from both side of the system is no longer preserved in the presence of the smearing potential.

### Thermoviscous Hydrodynamics in Non-Degenerate Dipolar Bose Gases

We present a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar Bosonic gases. Such systems present both $s$-wave and dipolar scattering, the latter of which results in anisotropic transport tensors of thermal conductivity and viscosity. This work presents an analytic derivation of the viscosity tensor coefficients, utilizing the methods established in [Wang et al., arXiv:2205.10465], where the thermal conductivities were derived. Taken together, these transport tensors then permit a comprehensive description of hydrodynamics that is now embellished with dipolar anisotropy. An analysis of attenuation in linear waves illustrates the effect of this anisotropy in dipolar fluids, where we find a clear dependence on the dipole orientation relative to the direction of wave propagation.

### Linking fluctuation and dissipation in spatially extended out-of-equilibrium systems

For systems in equilibrium at a temperature T, thermal noise and energy damping are related to T through the fluctuation-dissipation theorem (FDT). We study here an extension of the FDT to an out-of-equilibrium steady state: a micro-cantilever subject to a constant heat flux. The resulting thermal profile in this spatially extended system interplays with the local energy dissipation field to prescribe the amplitude of mechanical fluctuations. Using three samples with different damping profiles (localized or distributed), we probe this approach and experimentally demonstrate the link between fluctuations and dissipation. The thermal noise can therefore be predicted a priori from the measurement of the dissipation as a function of the maximum temperature of the micro-oscillator.

### A Green's function method for the two-dimensional frustrated spin-1/2 Heisenberg magnetic lattice

The magnon Hedin's equations are derived via the Schwinger functional derivative technique, and the resulting self-consistent Green's function method is used to calculate ground state spin patterns and magnetic structure factors for 2-dimensional magnetic systems with frustrated spin-1/2 Heisenberg exchange coupling. Compared to random-phase approximation treatments, the inclusion of a self-energy correction improves the accuracy in the case of scalar product interactions, as shown by comparisons between our method and exact benchmarks in homogeneous and inhomogeneous finite systems. We also find that for cross-product interactions (e.g. antisymmetric exchange), the method does not perform equally well, and an inclusion of higher corrections is in order. Aside from indications for future work, our results clearly indicate that the Green's function method in the form proposed here already shows potential advantages in the description of systems with a large number of atoms as well as long-range interactions.

### Modelling the processes of atom structure formation of a superconducting spin valve

The article considers the simulation of the formation of a multilayer nanocomposite, the combination of elements of which gives rise to the effect of a spin valve. The relevance and importance of the effects in the field of spintronics and related materials and devices are described. The composition and atomic structure of individual layers of the multilayer nanocomposite, as well as the composition and morphology of the interface of the nanocomposite layers are the object of research. A sample with a periodic superconductor - ferromagnetic structure consisting of more than 20 alternating layers of niobium and cobalt was analyzed as a sample. The deposition process took place under deep vacuum conditions. Modeling was performed by the molecular dynamics method using the potential of the modified submerged atom method. The formation of the layers was performed in the stacionar mode.

### Functional nanostructures superconductor-ferromagnet for spintronics

The work is devoted to the study of the processes of formation and analysis of the parameters of a functional nanostructure -- a superconducting spin valve, which is a multilayer structure consisting of ferromagnetic cobalt nanofilms separated by niobium superconductor films. The studies were carried out using molecular dynamics simulations. The atomic structure of individual nanolayers of the system is considered.

### Transport signatures of van Hove singularities in mesoscopic twisted bilayer graphene

Magic-angle twisted bilayer graphene exhibits quasi-flat low-energy bands with van Hove singularities close to the Fermi level. These singularities play an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. In this work, we study the correspondence of four-terminal conductance and the Fermi surface topology as a function of the twist angle, pressure, and energy in mesoscopic samples of small-angle twisted bilayer graphene. We establish a correspondence between features in the wide-junction conductance and the presence of van Hove singularities in the density of states. Moreover, we identify additional transport features, such as a large, pressure-tunable minimal conductance, conductance peaks coinciding with non-singular band crossings, and unusually large conductance oscillations as a function of the system size. Our results suggest that twisted bilayer graphene close the magic angle is a unique system featuring simultaneously large conductance due to the quasi-flat bands, strong quantum nonlinearity due to the van Hove singularities and high sensitivity to external parameters, which could be utilized in high-frequency device applications and sensitive detectors.

### Competing Incommensurate Spin Fluctuations and Magnetic Excitations in Infinite-Layer Nickelate Superconductors

The recently discovered infinite-layer nickelates show great promise in helping to disentangle the various cooperative mechanisms responsible for high-temperature superconductivity. However, lack of antiferromagnetic order in the pristine nickelates presents a challenge for connecting the physics of the cuprates and nickelates. Here, by using a quantum many-body Green's function-based approach to treat the electronic and magnetic structures, we unveil the presence of many two- and three-dimensional magnetic stripe instabilities that are shown to persist across the phase diagram of LaNiO$_2$. Our analysis indicates that the magnetic properties of the infinite-layer nickelates are closer to those of the doped cuprates which host inhomogeneous ground states rather than the undoped cuprates. The computed magnon spectrum in LaNiO$_2$ is found to contain an admixture of contributions from localized and itinerant carriers. The theoretically obtained magnon dispersion is in accord with the results of the corresponding RIXS experiments. Our study gives insight into the origin of inhomogeneity in the infinite-layer nickelates and their relationship with the cuprates.

### Role of spin-orbit coupling effects in rare-earth metallic tetra-borides : a first principle study

We have investigated the electronic structure of rare-earth tetraborides, $\textrm{RB}_{4}$, using first-principle electronic structure methods (DFT) implemented in Quantum Espresso (QE). In this article we have studied heather-to neglected strong spin-orbit coupling (SOC) effects present in these systems on the electronic structure of these system in the non-magnetic ground state. The calculations were done under GGA and GGA+SO approximations using ultrasoft pseudopotentials and fully relativistic ultrasoft pseudopotentials (for SOC case). Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) exchange-correlation functionals within the linearized plane-wave (LAPW) method as implemented in QE were used. The projected density of states consists of 3 distinct spectral peaks well below the Fermi energy and separated from the continuum density of states around the Fermi energy. The discrete peaks arises due to rare-earth $s$-orbital, rare-earth $p$ + B $p$ and B $p$-orbitals while the continuum arises due to hybridized B $p$, rare-earth $d$ orbitals. Upon inclusion of SOC the peak arising due to rare-earth $p$-orbitals gets split into two peaks corresponding to $j=0.5$ and $j=1.5$ configurations. In case of $\textrm{LaB}_{4}$, in the presence of SOC, spin-split $4f$ orbitals contributes to density of states at the Fermi level while the density of states at the Fermi level largely remains unaffected for all other materials under consideration.

### Single Mesoscopic Phononic Mode Thermodynamics

In recent decades, the laws of thermodynamics have been pushed down to smaller and smaller scales, within the field of stochastic thermodynamics and state-of-art experiments performed on mesoscopic systems. But these measurements concern mostly thermal properties of electrons and photons. Here we report on the measurements of thermal fluctuations of a single mechanical mode in-equilibrium with a heat reservoir. The device under study is a nanomechanical beam with a first flexure resonating at 3.8MHz, cooled down to temperatures in the range from 100mK to 400mK. The technique is constructed around a microwave opto-mechanical setup using a cryogenic High Electron Mobility Transistor, and is based on two parametric amplifications implemented in series: an in-built opto-mechanical 'blue-detuned' pumping plus a Traveling Wave Parametric Amplifier stage. We demonstrate our ability to resolve energy fluctuations of the mechanical mode in real-time up to the fastest relevant speed given by the mechanical relaxation rate. The energy probability distribution is then exponential, matching the expected Boltzmann distribution. The variance of fluctuations is found to be $(k_B T)^2$ with no free parameters. Our microwave detection floor is about 3 Standard Quantum Limit at 6GHz; the resolution of our fastest acquisition tracks reached about 100 phonons, and is related to the rather poor opto-mechanical coupling of the device ($g_0/2\pi\approx 0.5~$Hz). This result is deeply in the classical regime, but shall be extended to the quantum case in the future with systems presenting a much larger $g_0$ (up to $2\pi\times 250~$Hz), potentially reaching the resolution of a single mechanical quantum. We believe that it will open a new experimental field: phonon-based quantum stochastic thermodynamics, with fundamental implications for quantum heat transport and macroscopic mechanical quantum coherence.

### Structural properties of liquids in extreme confinement

We simulate a hard-sphere liquid in confined geometry where the separation of the two parallel, hard walls is smaller than two particle diameters. By systematically reducing the wall separation we analyze the behavior of structural and thermodynamic properties, such as inhomogeneous density profiles, structure factors, and compressibilities when approaching the two-dimensional limit. In agreement with asymptotic predictions, we find for quasi-two-dimensional fluids that the density profile becomes parabolic and the structure factor converges towards its two-dimensional counterpart. To extract the compressibility in polydisperse samples a perturbative expression is used which qualitatively influences the observed non-monotonic dependence of the compressibility with wall separation. We also present theoretical calculations based on fundamental-measure theory and integral-equation theory, which are in very good agreement with the simulation results.

### Finite temperature dynamics in gapped 1D models in the sine-Gordon family

The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Here we investigate the dynamics of generic, non-integrable systems belonging to the sine-Gordon family at finite temperature within the semiclassical approach. Focusing on time scales where the effect of nontrivial quasiparticle scatterings becomes relevant, we obtain universal results for the long-time behavior of dynamical correlation functions. We find that correlation functions of vertex operators behave neither ballistically nor diffusively but follow a stretched exponential decay in time. We also study the full counting statistics of the topological current and find that distribution of the transferred charge is non-Gaussian with its cumulants scaling non-uniformly in time.

### Intrinsic Josephson Effect and Horizons of Superconducting Spintronics

International Conference on Intrinsic Josephson Effect and Horizons of Superconducting Spintronics. The 12th International Conference on Intrinsic Josephson Effect and Horizons of Superconducting Spintronics, 22-25 September 2021, Chisinau, Moldova; Abstract Book, The editor Anatolie Sidorenko ; organizing committee Anatolie Sidorenko, Moldova; Alexander Golubov,Netherlands; Vladimir Krasnov,Sweden. Chisinau, 2021 F.E.-P. Tipografia Central. 87 p.

### Symmetries and zero modes in sample path large deviations

Sharp large deviation estimates for stochastic differential equations with small noise, based on minimizing the Freidlin-Wentzell action functional under appropriate boundary conditions, can be obtained by integrating certain matrix Riccati differential equations along the large deviation minimizers or instantons, either forward or backward in time. Previous works in this direction often rely on the existence of isolated minimizers with positive definite second variation. By adopting techniques from field theory and explicitly evaluating the large deviation prefactors as functional determinant ratios using Forman's theorem, we extend the approach to general systems where degenerate submanifolds of minimizers exist. The key technique for this is a boundary-type regularization of the second variation operator. This extension is particularly relevant if the system possesses continuous symmetries that are broken by the instantons. We find that removing the vanishing eigenvalues associated with the zero modes is possible within the Riccati formulation and amounts to modifying the initial or final conditions and evaluation of the Riccati matrices. We apply our results in multiple examples including a dynamical phase transition for the average surface height in short-time large deviations of the one-dimensional Kardar-Parisi-Zhang equation with flat initial profile.

### Microscopic Activated Dynamics Theory of the Shear Rheology and Stress Overshoot in Ultra-Dense Glass-Forming Fluids and Colloidal Suspensions

We formulate a microscopic, force-level, activated dynamics-based statistical-mechanical theory for the continuous startup nonlinear shear-rheology of ultra-dense glass-forming hard-sphere fluids and colloidal suspensions in the context of the ECNLE approach. Activated structural relaxation is described as a coupled local-nonlocal event involving caging and longer-range collective elasticity which controls the characteristic stress relaxation time. Theoretical predictions for the deformation-induced mobility enhancement, onset of relaxation acceleration at low values of stress, strain, or shear-rate, apparent power-law thinning of the steady-state structural relaxation time and viscosity, a non-vanishing activation barrier in the shear-thinning regime, an apparent Herschel-Bulkley form of the rate dependence of the steady-state shear stress, exponential growth of different measures of a dynamic yield or flow-stress with packing fraction, and reduced fragility and dynamic heterogeneity under deformation were previously shown to be in good agreement with experiment. The central new question addressed here is the defining feature of the transient response - the stress-overshoot. In contrast to the steady-state flow regime, understanding the transient response requires an explicit treatment of the coupled nonequilibrium evolution of structure, elastic modulus, and stress relaxation time. We formulate a new quantitative model for this aspect in a physically motivated and computationally tractable manner. Theoretical predictions for the stress-overshoot are shown to be in good agreement with experimental observations in the metastable ultra-dense regime of hard-sphere colloidal suspensions as a function of shear-rate and packing fraction, and accounting for deformation-assisted activated motion is crucial for both the transient and steady-state responses.

### Bootstrapped Dimensional Crossover of a Spin Density Wave

Quantum materials display rich and myriad types of magnetic, electronic, and structural ordering, often with these ordering modes either competing with one another or 'intertwining', that is, reinforcing one another. Low dimensional quantum materials, influenced strongly by competing interactions and/or geometric frustration, are particularly susceptible to such ordering phenomena and thus offer fertile ground for understanding the consequent emergent collective quantum phenomena. Such is the case of the quasi-2D materials R4Ni3O10(R=La, Pr), in which intertwined charge-and spin-density waves (CDW and SDW) on the Ni sublattice have been identified and characterized. Not unexpectedly, these density waves are largely 2D as a result of weak coupling between planes, compounded with magnetic frustration. In the case of R=Pr, however, we show here that exchange coupling between the transition metal and rare earth sublattices upon cooling overcomes both obstacles, leading to a dimensional crossover into a fully 3D ordered and coupled SDW state on both sublattices, as an induced moment on notionally nonmagnetic Pr3+ opens exchange pathways in the third dimension. In the process, the structure of the SDW on the Ni sublattice is irreversibly altered, an effect that survives reheating of the material until the underlying CDW melts. This 'bootstrapping' mechanism linking incommensurate SDWs on the two sublattices illustrates a new member of the multitude of quantum states that low-dimensional magnets can express, driven by coupled orders and modulated by frustrated exchange pathways.

### Anomalous Josephson effect and rectification in junctions between Floquet topological superconductors

We study Kitaev superconducting chain in which the chemical potential is periodically driven and a junction between two such Kitaev chains. Floquet states govern the dynamics of such systems. Starting from the ground state of the undriven system, we gradually switch on the periodic driving over a timescale $\tau$ and characterize the extent to which the single particle eigenstates of the undriven system get distributed among the Floquet states by calculating the inverse participation ratio. We find that when two superconductors not differing in phase of the pair potentials are driven by periodic potentials with different phases of the driving potentials, a net average current flows from one superconductor to the other. We term such a current anomalous current. Further, we study current phase relation in junctions between two periodically driven superconductors and find that the system exhibits nonequilibrium Josephson diode effect. We find that the current between two Floquet superconductors in absence of superconducting phase bias is maximum for difference in phases of driving $\phi=\pi/2$ and is large in the adiabatic limit ($\tau \gg T$, where $T$ is the period of driving potential) compared to sudden switching. We find that the magnitude of diode effect coefficient is maximum for $\phi=\pi/2$ and is lower in the adiabatic limit ($\tau\gg T$) compared to the case when the periodic driving is suddenly switched on. The Floquet Majorana end modes whenever present contribute significantly to the anomalous current and the diode effect.

### Phase dynamics in an AC driven multiterminal Josephson junction analogue

In the presence of an AC drive, multiterminal Josephson junctions exhibit the inverse AC Josephson effect, where the oscillations of the superconducting phase of each junction can lock onto one another or onto the external drive. The competition between these different phase locked states results in a complex array of quantized voltage plateaus whose stability strongly depend on the circuit parameters of the shunted junctions. This phase diagram cannot be explored with low temperature transport experiments alone, given the breadth of the parameter space, so we present an easily tunable analog circuit whose dynamical properties emulate those of a three terminal junction. We focus on the observation of the multiterminal inverse AC Josephson effect, and we discuss how to identify Shapiro steps associated with each of the three junctions as well as their quartet states. We only observe integer phase locked states in strongly overdamped networks, but fractional Shapiro steps appear as well when the quality factor of the junctions increases. Finally, we discuss the role of transverse coupling in the synchronization of the junctions.

### Structural relaxation, dynamical arrest and aging in soft-sphere liquids

We investigate the structural relaxation of a soft-sphere liquid quenched isochorically ($\phi=0.7$) and instantaneously to different temperatures $T_f$ above and below the glass transition. For this, we combine extensive Brownian dynamics simulations and theoretical calculations based on the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory. The response of the liquid to a quench generally consists of a sub-linear increase of the $\alpha$-relaxation time with system's age. Approaching the ideal glass-transition temperature from above ($T_f>T^a$) sub-aging appears as a transient process describing a broad equilibration crossover for quenches to nearly arrested states. This allows us to empirically determine an equilibration timescale $t^{eq}(T_f)$ that becomes increasingly longer as $T_f$ approaches $T^a$. For quenches inside the glass ($T_f\leq T^a$) the growth rate of the structural relaxation time becomes progressively larger as $T_f$ decreases and, unlike the equilibration scenario, $\tau_{\alpha}$ remains evolving within the whole observation time-window.These features are consistently found in theory and simulations with remarkable semi-quantitative agreement, and coincide with those revealed in the similar and complementary exercise [Phys. Rev. {\bf 96}, 022608 (2017)] that considered a sequence of quenches with fixed final temperature $T_f=0$ but increasing $\phi$ towards the hard-sphere dynamical arrest volume fraction $\phi^a_{HS}=0.582$. The NE-SCGLE analysis, however, unveils various fundamental aspects of the glass transition, involving the abrupt passage from the ordinary equilibration scenario to the persistent aging effects that are characteristic of glass-forming liquids. The theory also explains that, within the time window of any experimental observation, this can only be observed as a continuous crossover.

### Correlated topological pumping of interacting bosons assisted by Bloch oscillations

Thouless pumping, not only achieving quantized transport but also immune to moderate disorder, has attracted growing attention in both experiments and theories. Here, we explore how particle-particle interactions affect topological transport in a periodically-modulated and tilted optical lattice. Not limited to wannier states, our scheme ensures a dispersionless quantized transport even for initial Gaussian-like wave packets of interacting bosons which do not uniformly occupy a given band. This is because the tilting potential leads to Bloch oscillations uniformly sampling the Berry curvatures over the entire Brillouin zone. The interplay among on-site potential difference, tunneling rate and interactions contributes to the topological transport of bound and scattering states and the topologically resonant tunnelings. Our study deepens the understanding of correlation effects on topological states, and provides a feasible way for detecting topological properties in interacting systems.

### The Physics of Quantum Information

Rapid ongoing progress in quantum information science makes this an apt time for a Solvay Conference focused on The Physics of Quantum Information. Here I review four intertwined themes encompassed by this topic: Quantum computer science, quantum hardware, quantum matter, and quantum gravity. Though the time scale for broad practical impact of quantum computation is still uncertain, in the near future we can expect noteworthy progress toward scalable fault-tolerant quantum computing, and discoveries enabled by programmable quantum simulators. In the longer term, controlling highly complex quantum matter will open the door to profound scientific advances and powerful new technologies.

### Hawking radiation from acoustic black holes in hydrodynamic flow of electrons

Acoustic black holes are formed when a fluid flowing with subsonic velocities, accelerates and becomes supersonic. When the flow is directed from the subsonic to supersonic region, the surface on which the normal component of fluid velocity equals the local speed of sound acts as an acoustic horizon. This is because no acoustic perturbation from the supersonic region can cross it to reach the subsonic part of the fluid. One can show that if the fluid velocity is locally irrotational, the field equations for acoustic perturbations of the velocity potential are identical to that of a massless scalar field propagating in a black hole background. One, therefore, expects Hawking radiation in the form of a thermal spectrum of phonons. There have been numerous investigations of this possibility, theoretically, as well as experimentally, in systems ranging from cold atom systems to quark-gluon plasma formed in relativistic heavy-ion collisions. Here we investigate this possibility in the hydrodynamic flow of electrons. Resulting Hawking radiation in this case should be observable in terms of current fluctuations. Further, current fluctuations on both sides of the acoustic horizon should show correlations expected for pairs of Hawking particles.

### The quantum dynamic range of room temperature spin imaging

Magnetic resonance imaging of spin systems combines scientific applications in medicine, chemistry and physics. Here, we investigate the pixel-wise coherent quantum dynamics of spins consisting of a 40 by 40 micron sized region of interest implanted with nitrogen vacancy centers (NV) coupled to a nano-magnetic flake of $\mathrm{CrTe_2}$. $\mathrm{CrTe_2}$ is an in-plane van der Waals ferromagnet, which we can probe quantitatively by the NV electron's spin signal even at room temperature. First, we combine the nano-scale sample shapes measured by atomic force microscope with the magnetic resonance imaging data. We then map out the coherent dynamics of the colour centers coupled to the van der Waals ferromagnet using pixel-wise coherent Rabi and Ramsey imaging of the NV sensor layer. Next, we fit the pixel-wise solution of the Hamiltonian to the quantum sensor data. Combining data and model, we can explore the detuning range of the spin oscillation with a quantum dynamic range of over $\left|\Delta_{max}\right|= 60 { }\mathrm{MHz}$ in the Ramsey interferometry mode. Finally, we show the effect of the $\mathrm{CrTe_2}$ van der Waals magnet on the coherence of the NV sensor layer and measure a 70 times increase in the maximum frequency of the quantum oscillation going from the Rabi to the Ramsey imaging mode.

### Polarization-selective magneto-optical modulation

We study magneto-optical coupling in a ferrimagnetic sphere resonator made of Yttrium iron garnet. We find that the resonator can be operated in the telecom band as a polarization-selective optical modulator. Intermodulation gain can be employed in the nonlinear regime for amplification.

### Chaos and bi-partite entanglement between Bose-Joephson junctions

The entanglement between two weakly coupled bosonic Josephson junctions is studied in relation to the classical mixed phasespace structure of the system, containing symmetry-related regular islands separated by chaos. The symmetry-resolved entanglement spectrum and bi-partite entanglement entropy of the system's energy eigenstates are calculated and compared to their expected structure for random states that exhibit complete or partial ergodicity. The entanglement spectra of chaos-supported eigenstates match the microcanonical structure of a Generalized Gibbs Ensemble due to the existence of an adiabatic invariant that restricts ergodization on the energy shell. The symmetry-resolved entanglement entropy of these quasistochastic states consists of a mean-field maximum entanglement term and a fluctuation correction due to the finite size of the constituent subsystems. The total bi-partite entanglement entropy of the eigenstates correlates with their chaoticity. Island-supported eigenstates are macroscopic Schr\"odinger cat states for particles and excitations, with substantially lower entanglement.

### Magnetic domain scanning imaging using phase-sensitive THz-pulse detection

In our study, we determine the alignment of magnetic domains in a CoFeB layer using THz radiation. We generate THz-pulses by fs-laser-pulses in magnetized CoFeB/Pt heterostructures, based on spin currents. An LT-GaAs Auston switch detects the radiation phase-sensitively and allows to determine the magnetization alignment. Our scanning technique with motorized stages with step sizes in the sub-micrometer range, allows to image two dimensional magnetic structures. Theoretically the resolution is restricted to half of the wavelength if focusing optics in the far-field limit are used. By applying near-field imaging, the spatial resolution is enhanced to the single digit micrometer range. For this purpose, spintronic emitters in diverse geometric shapes, e.g. circles, triangles, squares, and sizes are prepared to observe the formation of magnetization patterns. The alignment of the emitted THz radiation can be influenced by applying unidirectional external magnetic fields. We demonstrate how magnetic domains with opposite alignment and different shapes divided by domain walls are created by demagnetizing the patterns using minor loops and imaged using phase sensitive THz radiation detection. For analysis, the data is compared to Kerr microscope images. The possibility to combine this method with THz range spectroscopic information of magnetic texture or antiferromagnets in direct vicinity to the spintronic emitter, makes this detection method interesting for much wider applications probing THz excitation in spin systems with high resolution beyond the Abbe diffraction limit, limited solely by the laser excitation area.

### Zeta-regularized Lattice Field Theory with Lorentzian background metrics

Lattice field theory is a very powerful tool to study Feynman's path integral non-perturbatively. However, it usually requires Euclidean background metrics to be well-defined. On the other hand, a recently developed regularization scheme based on Fourier integral operator $\zeta$-functions can treat Feynman's path integral non-pertubatively in Lorentzian background metrics. In this article, we formally $\zeta$-regularize lattice theories with Lorentzian backgrounds and identify conditions for the Fourier integral operator $\zeta$-function regularization to be applicable. Furthermore, we show that the classical limit of the $\zeta$-regularized theory is independent of the regularization. Finally, we consider the harmonic oscillator as an explicit example. We discuss multiple options for the regularization and analytically show that they all reproduce the correct ground state energy on the lattice and in the continuum limit. Additionally, we solve the harmonic oscillator on the lattice in Minkowski background numerically.

### Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models

We study characteristic, dynamic, and saturation regimes of the out-of-time-order correlation (OTOC) in the constant field Floquet system with and without longitudinal field. In the calculation of OTOC, we take local spins in longitudinal and transverse directions as observables which are local and non-local in terms of Jordan-Wigner fermions, respectively. We use the exact analytical solution of OTOC for the integrable model (without longitudinal field term) with transverse direction spins as observables and numerical solutions for other integrable and nonintegrable cases. OTOCs generated in both cases depart from unity at a kick equal to the separation between the observables when the local spins in the transverse direction and one additional kick is required when the local spins in the longitudinal direction. The number of kicks required to depart from unity depends on the separation between the observables and is independent of the Floquet period and system size. In the dynamic region, OTOCs show power-law growth in both models, the integrable (without longitudinal field) as well as the nonintegrable (with longitudinal field). The exponent of the power-law increases with increasing separation between the observables. Near the saturation region, OTOCs grow linearly with a very small rate.

### XPS core-level chemical shift by ab initio many-body theory

X-ray photoemission spectroscopy (XPS) provides direct information on the atomic composition and stoichiometry by measuring core electron binding energies. Moreover, according to the shift of the binding energy, so-called chemical shift, the precise chemical type of bonds can be inferred, which brings additional information on the local structure. In this work, we present a theoretical study of the chemical shift firstly by comparing different theories, from Hartree-Fock (HF) and density-functional theory (DFT) to many-body perturbation theory (MBPT) approaches like the GW approximation and its static version (COHSEX). The accuracy of each theory is assessed by benchmarking against the experiment on the chemical shift of the carbon 1s electron in a set of molecules. More importantly, by decomposing the chemical shift into different contributions according to terms in the total Hamiltonian, the physical origin of the chemical shift is identified as classical electrostatics.

### One-particle engine with a porous piston

We propose a variation of the classical Szilard engine that uses a porous piston. Such an engine requires neither information about the position of the particle, nor the removal and subsequent insertion of the piston when resetting the engine to continue doing work by lifting a mass against a gravitational field. Though the engine operates in contact with a single thermal reservoir, the reset mechanism acts as a second reservoir, dissipating energy when a mass that has been lifted by the engine is removed to initiate a new operation cycle.