### Gauge protection in non-Abelian lattice gauge theories

Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-Abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization that non-Abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength $V$, which when sufficiently large leads to the emergence of an \textit{adjusted} gauge theory with the same local gauge symmetry up to least a timescale $\propto\sqrt{V/V_0^3}$. Thereafter, a \textit{renormalized} gauge theory dominates up to a timescale $\propto\exp(V/V_0)/V_0$ with $V_0$ a volume-independent energy factor, similar to the case of faulty Abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in exact diagonalization, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and NISQ devices.

### Optical Direct Write of Dolan-Bridge Junctions for Transmon Qubits

We characterize highly coherent transmon qubits fabricated with a direct-write photolithography system. Multi-layer evaporation and oxidation allows us to tune the Josephson energy by reducing the effective tunneling area and increasing the barrier thickness. Surface treatments before resist application and again before evaporation reduce the occurrence of strongly-coupled two-level system fluctuators, resulting in high coherence devices. With optimized surface treatments we achieve energy relaxation $T_1$ times in excess of 80 $\mu$s for three dimensional transmon qubits with Josephson junction lithographic areas of 2 $\mu\mathrm{m}^2$.

### Fock-space landscapes across the many-body localisation transition

We explore the Fock-space landscape of eigenstates across the many-body localisation (MBL) transition in a disordered, interacting quantum spin-1/2 chain. Eigenstate expectation values of spatially local observables, which distinguish an MBL phase from an ergodic one, can be represented in terms of eigenstate amplitudes on the Fock space. Motivated by this, we introduce and study spatial correlations on the Fock space. From these, a correlation length emerges, which is found to vary discontinuously across the MBL transition; and is intimately connected to the discontinuous jump in the multifractal exponents characterising the Fock-space wavefunctions. Exploiting the direct connection between the local observables and Fock-space correlations, we show that the discontinuity in the lengthscale also implies discontinuous behaviour of the local observables across the transition. The scaling behaviour of this lengthscale, which is closely connected to that of the inverse participation ratios, shows that the nature of the MBL transition is consistent with it being Kosterlitz-Thouless like, as predicted by recent phenomenological theories. Finally, we also show how correlation functions on the Fock space reveal the inhomogeneities in eigenstate amplitudes on the Fock space in the MBL phase.

### 1D Majorana fermions and supersymmetry in quantum wires

One-dimensional Majorana modes can be obtained as boundary excitations of topologically nontrivial two-dimensional topological superconductors. Here, we propose instead the bottom-up creation of one-dimensional, counterpropagating, and dispersive Majorana modes as bulk excitations of a periodic chain of partially-overlapping, zero-dimensional Majorana modes in proximitized quantum nanowires via periodically-modulated magnetic fields. These dispersive one-dimensional Majorana modes can be either massive or massless. Massless Majorana modes are pseudohelical, having opposite Majorana pseudospin, and realize emergent quantum mechanical supersymmetry. The experimental fingerprint of massless Majorana modes and supersymmetry is the presence of a finite zero-bias peak, which is generally not expected for Majorana modes with a finite overlap and localized at a finite distance. Moreover, slowly varying magnetic fields can induce adiabatic pumping of Majorana modes, which can be used as a dynamically probe of topological superconductivity.

### Quantum phase transition dynamics in the two-dimensional transverse-field Ising model

The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior in the vicinity of quantum phase transitions (QPTs). It is now well understood for one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by fundamental differences of the associated QPTs and their underlying conformal field theories. In this work, we take the first steps towards exploring the QKZM in two dimensions. We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods. As a central result, we quantify universal QKZM behavior close to the QPT. However, upon traversing further into the ferromagnetic regime, we observe deviations from the QKZM prediction. We explain the observed behavior by proposing an {\it extended QKZM} taking into account spectral information as well as phase ordering. Our work provides a starting point towards the exploration of dynamical universality in higher-dimensional quantum matter.

### Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields

In condensed matter systems, zero-dimensional or one-dimensional Majorana modes can be realized respectively as the end and edge states of one-dimensional and two-dimensional topological superconductors. In this $\textit{top-down}$ approach, $(d-1)$-dimensional Majorana modes are obtained as the boundary states of a topologically nontrivial $d$-dimensional bulk. In a $\textit{bottom-down}$ approach instead, $d$-dimensional Majorana modes in a $d$-dimensional system can be realized as the continuous limit of a periodic lattice of coupled $(d-1)$-dimensional Majorana modes. We illustrate this idea by considering one-dimensional proximitized superconductors with spatially-modulated potential or magnetic fields. The ensuing inhomogenous topological state exhibits one-dimensional counterpropagating Majorana modes with finite dispersion, and with a Majorana gap which can be controlled by external fields. In the massless case, the Majorana modes have opposite Majorana polarizations and pseudospins, are conformally invariant, and realize emergent quantum mechanical supersymmetry.

### Spatio-temporal Spread of Fermi-edge Singularity as Time Delayed Interaction and Impact on Time-dependent RKKY Type Coupling

Fermi-edge singularity and Anderson's orthogonality catastrophe are paradigmatic examples of non-equilibrium many-body physics in conductors, appearing after a quench is created by the sudden change of a localised potential. We investigate if the signal carried by the quench can be used to transmit a long ranged interaction, reminiscent of the RKKY interaction, but with the inclusion of the full many-body propagation over space and time. We calculate the response of a conductor to two quenches induced by localised states at different times and locations. We show that building up and maintaining coherence between the localised states is possible only with finely tuned interaction between the localised states and the conductor. This puts bounds to the use of time controlled RKKY type interactions and may limit the speed at which some quantum gates could operate.

### Discrete Quantum Geometry and Intrinsic Spin Hall Effect

We show that the quantum geometry of the Fermi surface can be numerically described by a 3-dimensional discrete quantum manifold. This approach not only avoids singularities in the Fermi sea, but it also enables the precise computation of the intrinsic Hall conductivity resolved in spin, as well as any other local properties of the Fermi surface. The method assures numerical accuracy when the Fermi level is arbitrarily close to singularities, and it remains robust when Kramers degeneracy is protected by symmetry. The approach is demonstrated by calculating the anomalous Hall and spin Hall conductivities of a 2-band lattice model of a Weyl semimetal and a full-band ab-initio model of zincblende GaAs.

### Electronic Structure of the Bond Disproportionated Bismuthate Ag$_2$BiO$_3$

We present a comprehensive study on the silver bismuthate Ag$_2$BiO$_3$, synthesized under high-pressure high-temperature conditions, which has been the subject of recent theoretical work on topologically complex electronic states. We present X-ray photoelectron spectroscopy results showing two different bismuth states, and X-ray absorption spectroscopy results on the oxygen $K$-edge showing holes in the oxygen bands. These results support a bond disproportionated state with holes on the oxygen atoms for Ag$_2$BiO$_3$. We estimate a band gap of $\sim$1.25~eV for Ag$_2$BiO$_3$ from optical conductivity measurements, which matches the band gap in density functional calculations of the electronic band structure in the non-symmorphic space group $Pnn2$, which supports two inequivalent Bi sites. In our band structure calculations the disproportionated Ag$_2$BiO$_3$ is expected to host Weyl nodal chains, one of which is located $\sim$0.5~eV below the Fermi level. Furthermore, we highlight similarities between Ag$_2$BiO$_3$ and the well-known disproportionated bismuthate BaBiO$_3$, including breathing phonon modes with similar energy. In both compounds hybridization of Bi-$6s$ and O-$2p$ atomic orbitals is important in shaping the band structure, but in contrast to the Ba-$5p$ in BaBiO$_3$, the Ag-$4d$ bands in Ag$_2$BiO$_3$ extend up to the Fermi level.

### Swirling and snaking, 3D oscillatory bifurcations of vesicle dynamics in microcirculation

Vesicles are soft elastic bodies with distinctive mechanical properties such as bending resistance, membrane fluidity, and their strong ability to deform, mimicking some properties of biological cells. While previous three-dimensional (3D) studies have identified stationary shapes such as slipper and axisymmetric ones, we report a complete phase diagram of 3D vesicle dynamics in a bounded Poiseuille flow with two more oscillatory dynamics, 3D snaking and swirling. 3D snaking is characterized by planar oscillatory motion of the mass center and shape deformations, which is unstable and leads to swirling or slipper. Swirling emerges from supercritical pitchfork bifurcation. The mass center moves along a helix, the preserved shape rolls on itself and spins around the flow direction. Swirling can coexist with slipper.

### Oxidation of 2D electrenes: structural transition and the formation of half-metallic channels protected by oxide layers

Based on first-principles calculations we performed a systematic study of the structural stability, and the electronic properties of oxidized $A_2B$, electrenes. Initially, we have considered one-side fully oxidized $A_2B$, single layer electrenes (O/$A_2B$), with $A$= Ba, Ca, Sr, Y, and $B$= As, N, P, C. We show that the hexagonal lattice of the pristine host is no longer the ground state structure in the oxidized systems. Our total energy results reveal an exothermic structural transition from hexagonal to tetragonal (h $\rightarrow$ t) geometry, resulting in layered tetragonal structures [($A$O$AB$)$^{\rm t}$]. Phonon spectra calculations show that the ($A$O$AB$)$^{\rm t}$, systems are dynamically stable for $A$= Ba, Ca, Sr, and $B$= N [($A$O$A$N)$^{\rm t}$]. In the sequence, we have examined the surface oxidation of bilayer systems [O/($A_2\text{N})_2$/O], with $A$= Ca, Sr, Ba, where we have also found an exothermic h $\rightarrow$ t transition to a dynamically stable layered tetragonal phase [$(A$O($A$N)$_2$$AO)^{\rm t}]. Further electronic structure calculations of reveal the formation of half-metallic bands spreading through the AN layers. These findings indicate that (AOAN)^{\rm t}, and (AO(AN)_2$$A$O)$^{\rm t}$, are quite interesting platforms for application in spintronics; since the half-metallic channels along the $A$N and $(A\text{N})_2$ layers (core) are protected against the environment conditions by oxidized $A\text{O}$ sheets (cover shells).

### Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: Experiments, theory and numerical tests

We study experimentally, numerically and theoretically the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius $R_{\text tol}$, a target at a distance $L$ from an initial position in the presence of resetting. The reset position is Gaussian distributed with width $\sigma$. We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first-passage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean first-passage time as a function of the resetting period/rate for different target distances (values of the ratios $b=L/\sigma$) and target size ($a=R_\text{tol}/L$). We find an interesting phase transition at a critical value of $b$, both in one and two dimensions. The details of the calculations as well as experimental setup and limitations are discussed.

### Optical response and band structure of LiCoO2 including electron-hole interaction effects

The optical response functions and band structures of LiCoO$_2$ are studied at different levels of approximation, from density functional theory (DFT) in the generalized gradient approximation (GGA) to quasiparticle self-consistent QS$GW$ (with $G$ for Green's function and $W$ for screened Coulomb interaction) without and with ladder diagrams (QS$G\hat W$) and the Bethe Salpeter Equation (BSE) approach. The QS$GW$ method is found to strongly overestimate the band gap and electron-hole or excitonic effects are found to be important. They lower the quasiparticle gap by only about 11~\% but the lowest energy peaks in absorption are found to be excitonic in nature. The contributions from different band to band transitions and the relation of excitons to band-to-band transitions are analyzed. The excitons are found to be strongly localized. A comparison to experimental data is presented.

### Topological Magnetic Hysteresis in Single Crystals of CeAgSb2 Ferromagnet

Closed-topology magnetic domains are usually observed in thin films and in an applied magnetic field. Here we report the observation of rectangular cross-section tubular ferromagnetic domains in thick single crystals of CeAgSb2 in zero applied field. Relatively low exchange energy, small net magnetic moment, and anisotropic in-plane crystal electric fields lower the domain wall energy and allow for the formation of the closed-topology patterns. Upon cycling the magnetic field, the domain structure irreversibly transforms into a dendritic open-topology pattern. This transition between closed and open topologies results in a "topological magnetic hysteresis" - the actual hysteresis in magnetization, not due to the imperfections and pinning, but due to the difference in the pattern morphology. Similar physics was suggested before in pure type-I superconductors and is believed to be a generic feature of other nonlinear multi-phase systems in the clean limit.

### Influence of grain bidispersity on dense granular flow in a two dimensional hopper

Discrete element method is conducted to investigate the bidisperse dense granular flow having big and small grains in a two dimensional hopper. A half-circular dynamical force arch is observed above the outlet and Beverloo's law is verified to describe the relationship between flow rate and outlet size. The bidisperse flow can reach the maximum flow rate when a small fraction of big grains is added into the monodisperse flow with only small grains. The distributions of contact force, packing fraction and grain velocity indicate that the flow properties in the hopper are closely related to the local flow characteristics of the key area which almost overlaps with the force arch. The interior packing structures, i.e., ordered arrangement for monodisperse flow and disordered arrangement for bidisperse flow, play a dominant role in the flow pattern transition from mass flow to funnel flow. The earlier occurrence of the transition can effectively increase the grain velocity and therefore improve the flow rate.

### Reduced density matrix approach to ultracold few-fermion systems in one dimension

The variational determination of the two-fermion reduced density matrix is described for trapped, ultracold few-fermion systems in one dimension with equal spin populations. This is accomplished by formulating the problem as a semi-definite program, with the two-fermion reduced density matrix being subject to the D, Q, G, T1, and T2 $N$-representability conditions. The ground-state energies of $N=2,4$, and $8$ fermion systems are found by utilising an augmented Lagrangian method for semi-definite programming. The ground-state energies are found to match extremely well to those determined by full-configuration interaction and coupled-cluster calculations. This demonstrates the utility of the reduced density matrix approach to strongly correlated, ultracold few-fermion systems.

### Diamond anvil cell with boron-doped diamond heater for high-pressure synthesis and in-situ transport measurements

Temperature and pressure are essential parameters in the synthesis, evaluation, and application of functional materials. This study proposes the addition of a heating function to a high-pressure diamond anvil cell (DAC) with in-situ measurement probes. The proposed DAC allows for simultaneous control of temperature and pressure within the sample space and can be used to synthesize functional materials under extreme conditions. The various components, namely the heater, thermometer, and measurement probes, were fabricated with a boron-doped diamond epitaxial film and could be used repeatedly. The developed DAC was used to successfully conduct the high-pressure annealing of La(O,F)BiS$_{2}$ single crystal and the high-pressure synthesis of EuFBiS$_{2}$ superconductors. The proposed technique shows promise for further exploration of superconductors to broaden the research field.

### Finite temperature mean-field theory with intrinsic non-hermitian structures for Bose gases in optical lattices

We reveal a divergent issue associated with the mean-field theory for Bose gases in optical lattices constructed by the widely used straightforward mean-field decoupling of the hopping term, where the corresponding mean-field Hamiltonian generally assumes no lower energy bound once the spatial dependence of the mean-field superfluid order parameter is taken into account. Via a systematic functional integral approach, we solve this issue by establishing a general finite temperature mean-field theory that can treat any possible spatial dependence of the order parameter without causing the divergent issue. Interestingly, we find the theory generally assumes an intrinsic non-hermitian structure that originates from the indefiniteness of the hopping matrix of the system. Within this theory, we develop an efficient approach for investigating the physics of the system at finite temperature, where properties of the system can be calculated via straightforward investigation on the saddle points of an effective potential function for the order parameter. We illustrate our approach by investigating the finite temperature superfluid transition of Bose gases in optical lattices. Since the underlying finite temperature mean-field theory is quite general, this approach can be straightforwardly applied to investigate the finite temperature properties of related systems with phases possessing complex spatial structures.

### Clean vs Dirty: Anisotropic Scattering Caused by Apical Oxygen Vacancies in Overdoped Cuprates

There is a hot debate on the anomalous behavior of superfluid density $\rho_s$ in overdoped La$_{2-x}$Sr$_x$CuO$_4$ films in recent years. Its linear temperature dependence $\rho_s(0)-\rho_s(T)\propto T$ infers the superconductors are clean, but the zero temperature value $\rho_s(0)\propto T_c$ is a hallmark of the dirty limit in the Bardeen-Cooper-Schrieffer (BCS) framework (Bozovic et al., 2016). In this work, we show that the apical oxygen vacancies can lead to an anisotropic scattering rate $\Gamma_d\cos^2(2\theta)$, which can explain the above two linear scalings simultaneously, and thus provides a plausible solution to this clean-dirty paradox. Furthermore, by analyzing the optical conductivity, it may also explain the missing'' Drude weight upon doping as reported in the THz experiment (Mahmood et al., 2019). Therefore, we conclude that the superconducting states of the overdoped cuprates are consistent with the disordered BCS theory.

### Tilted Dirac cone effects and chiral symmetry breaking in a planar four-fermion model

We analyze the chiral symmetry breaking in a planar four-fermion model with non-null chemical potential, temperature and including the effect of the tilt of the Dirac cone. The system is modeled with a $(2+1)$-dimensional Gross-Neveu-like interaction model in the context of the generalized Weyl Hamiltonian and its phase structure is studied in the meanfield and large-$N$ approximations. Possible applications of the results obtained, e.g., in connection to graphene, are discussed. We also discuss the effect of an external magnetic field applied to the system, which can give rise to the appearance of the anomalous Hall effect and that is expected to arise in connection with two-dimensional Weyl and Dirac semimetals.

### Extraordinary $π$-Electron Superconductivity Emerging from a Quantum Spin Liquid

Quantum spin liquids (QSLs), in which spins are highly entangled, have been considered a groundwork for generating exotic superconductivity.Despite numerous efforts, superconductivity emerging from QSLs has been unrealized in actual materials due to the difficulties in stabilizing QSL states with metallic conductivity.Recently, an organic compound, $\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$, with a nearly regular triangular lattice of molecular dimers was recognized as a candidate for doped QSLs. In this study, we report an unusual superconducting phase of $\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$: unexpectedly large ratios of the upper critical field to the critical temperature $H_{\rm c2}$/$T_{\rm c}$ in fields not only parallel but also perpendicular to the two-dimensional conducting layers and a very wide region of fluctuating superconductivity above $T_{\rm c}$.Our results reveal that these peculiarities arise from strong electron correlations and possible quantum criticality unique to the doped QSL state, leading to a heavy mass of itinerant carriers and a large superconducting energy gap.

### Formation of high temperature Majorana macroscopic states with fractional entropy and conductance

Quantum thermodynamics is a promising route to unambiguous detections of Majorana bound states. Being fundamentally different from quantum transport, this approach reveals unique Majorana thermodynamic behavior and deepens our insight into Majorana quantum transport itself. Here we demonstrate that a nanoscopic system with topological superconductors produces a remarkable accumulation of Majorana macroscopic states in wide ranges of Majorana tunneling phases by means of increasing its temperature $T$. Revealing this physical behavior is twofold beneficial. First, it significantly reduces the dependence of the entropy on the tunneling phases which become almost irrelevant in experiments. Second, the fractional Majorana entropy $S_M^{(2)}=k_B\ln(2^\frac{3}{2})$ may be observed at very high temperatures, up to $T\approx 0.1$ K, which substantially facilitates experiments. Analyzing quantum transport, we predict that when the temperature increases, the above thermodynamic behavior will induce an anomalous increase of the linear conductance from vanishing values up to the unitary fractional Majorana plateau $G_M=e^2/2h$ extending to very high temperatures.

### 3D analysis of a strain gradient plasticity material reinforced by elastic particles

A 3D unit cell model containing eight different spherical particles embedded in a homogeneous strain gradient plasticity (SGP) matrix material is presented. The interaction between particles and matrix is controlled by an interface model formulated within the higher order SGP theory used. Strengthening of the particle reinforced material is investigated in terms of the increase in macroscopic yield stress. The results are used to validate a closed form strengthening relation proposed by the authors, which suggests that the increase in macroscopic yield stress is governed by the interface strength times the total surface area of particles in the material volume.

### Cavity Magnonics

Cavity magnonics deals with the interaction of magnons - elementary excitations in magnetic materials - and confined electromagnetic fields. We introduce the basic physics and review the experimental and theoretical progress of this young field that is gearing up for integration in future quantum technologies. Much of its appeal is derived from the strong magnon-photon coupling and the easily-reached nonlinear regime in microwave cavities. The interaction of magnons with light as detected by Brillouin light scattering is enhanced in magnetic optical resonators, which can be employed to manipulate magnon distributions. The cavity photon-mediated coupling of a magnon mode to a superconducting qubit enables measurements in the single magnon limit.

### Unveiling critical stripy state in the triangular-lattice SU(4) spin-orbital model

By combining the density matrix renormalization group (DMRG) method with Gutzwiller projected wave functions, we provide clear evidence that the ground state of the SU(4) Kugel-Khomskii spin-orbital model on the triangular lattice is a critical stripy state. This state preserves SU(4) symmetry, but spontaneously breaks translational symmetry by doubling the unit cell along one of the lattice vector directions. Our DMRG results indicate that the fluctuating stripes are critical and the central charge of each stripe is $c=3$, in agreement with the SU(4)$_1$ Wess-Zumino-Witten conformal field theory. Furthermore, we find that this critical stripy state is well described by a Gutzwiller projected wave function with an emergent parton Fermi surface. All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.

### Plasticity of an extra-strong nanocrystalline stainless steel controlled by the "dislocation-segregation'' interaction

We study three structurally different states of nanocrystalline 316 steel and show that the state, where boundaries containing excess concentration of alloying elements are combined with mobile dislocations in grain interiors, allows maintaining extraordinarily high strength and remarkably enhanced plasticity. Underlying mechanisms featuring interaction between the segregations and mobile dislocations are discussed.

### Solid-Liquid Composites for Soft Multifunctional Materials

Soft materials with a liquid component are an emerging paradigm in materials design. The incorporation of a liquid phase, such as water, liquid metals, or complex fluids, into solid materials imparts unique properties and characteristics that emerge as a result of the dramatically different properties of the liquid and solid. Especially in recent years, this has led to the development and study of a range of novel materials with new functional responses, with applications in topics including soft electronics, soft robotics, 3D printing, wet granular systems and even in cell biology. Here we provide a review of solid-liquid composites, broadly defined as a material system with at least one, phase-separated liquid component, and discuss their morphology and fabrication approaches, their emergent mechanical properties and functional response, and the broad range of their applications.

### Improving spatial resolution of scanning SQUID microscopy with an on-chip design

Scanning superconducting quantum interference device microscopy (sSQUID) is currently one of the most effective methods for direct and sensitive magnetic flux imaging on the mesoscopic scale. A SQUID-on-chip design allows integration of field coils for susceptometry in a gradiometer setup which is very desirable for measuring magnetic responses of quantum matter. However, the spatial resolution of such a design has largely been limited to micrometers due to the difficulty in approaching the sample. Here, we used electron beam lithography technology in the fabrication of the 3D nano-bridge-based SQUID devices to prepare pick-up coils with diameters down to 150 nm. Furthermore, we integrated the deep silicon etching process in order to minimize the distance between the pick-up coil and the wafer edge. Combined with a tuning-fork-based scanning head, the sharpness of the etched chip edge enables a precision of 5 nm in height control. By scanning measurements on niobium chessboard samples using these improved SQUID devices, we demonstrate sub-micron spatial resolutions in both magnetometry and susceptometry, significantly better than our previous generations of nano-SQUIDs. Such improvement in spatial resolution of SQUID-on-chip is a valuable progress for magnetic imaging of quantum materials and devices in various modes.

### Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions

We consider theoretically a $1D$-semiconducting wire with strong Rashba interaction in proximity with $s$-wave superconductor, driven into topological phase by external magnetic field. Additionally, we take into account on-site Coulomb interactions inside the wire. The system is modelled by a tight binding Hamiltonian with Rashba hopping term and induced $s$-wave superconductivity. Calculations are performed utilizing recursive Green's function method, and Coulomb interactions are treated selfconsistently within Hubbard $I$ approximation. For the Hubbard levels residing within $p$-wave superconducting gap, particle-hole symmetric four-resonance structure develops in the density of states, apart from Majorana resonance. One pair of particle-hole symmetric resonances is created by the discrete $II$-Hubbard levels of the particular site, and the second pair of Hubbard sub-bands originates from recursive summation over the sites of the wire. Quantum interference between both types of pairs of states creates in-gap charge-conjugated Fano resonances with opposite asymmetry factors. We demonstrate that when quantum interference is dominated by two-particle tunneling, the Majorana resonance is strongly diminished, while it is not altered when single-particle tunneling dominates in interference process. We also discuss some consequences for experimental distinction of true Majorana states, and show that on-site Coulomb interactions support the appearance of topological phase.

### Similarity of particle systems using an invariant root mean square deviation measure

Determining whether two particle systems are similar is a common problem in particle simulations. When the comparison should be invariant under permutations, orthogonal transformations, and translations of the systems, special techniques are needed. We present an algorithm that can test particle systems of finite size for similarity and, if they are similar, can find the optimal alignment between them. Our approach is based on an invariant version of the root mean square deviation (RMSD) measure and is capable of finding the globally optimal solution in $O(n^3)$ operations where $n$ is the number of three-dimensional particles.

### Squeeze-film effect on atomically thin resonators in the high-pressure limit

The resonance frequency of membranes depends on the gas pressure due to the squeeze-film effect, induced by the compression of a thin gas film that is trapped underneath the resonator by the high frequency motion. This effect is particularly large in low-mass graphene membranes, which makes them promising candidates for pressure sensing applications. Here, we study the squeeze-film effect in single layer graphene resonators and find that their resonance frequency is lower than expected from models assuming ideal compression. To understand this deviation, we perform Boltzmann and continuum finite-element simulations, and propose an improved model that includes the effects of gas leakage and can account for the observed pressure dependence of the resonance frequency. Thus, this work provides further understanding of the squeeze-film effect and provides further directions into optimizing the design of squeeze-film pressure sensors from 2D materials.

### Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion

The elusive nature of localized integrals of motion (or l-bits) in disordered quantum systems lies at the core of some of their most prominent features, i.e. emergent integrability and lack of thermalization. Here, we study the quench dynamics of a one-dimensional model of spinless interacting fermions in a quasi-periodic potential with a localization-delocalization transition. Starting from an unentangled initial state, we show that in the strong disorder regime an important subset of the $l$-bits can be explicitly identified with strongly localized two-level systems, associated with particles confined on two lattice sites. The existence of such subsystems forming an ensemble of nearly free l-bits is found to dominate the short-time dynamics of experimentally relevant quantities, such as the Loschmidt echo and the particle imbalance. We investigate the importance of the choice of the initial state by developing a second quench protocol, starting from the ground-state of the model at different initial disorder strengths and monitoring the quench dynamics close to the delicate ETH-MBL transition regime.

### Brain, Rain and Forest Fires -- What is critical about criticality: In praise of the correlation function

We present a brief review of power laws and correlation functions as measures of criticality and the relation between them. By comparing phenomenology from rain, brain and the forest fire model we discuss the relevant features of self-organisation to the vicinity about a critical state. We conclude that organisation to a region of extended correlations and approximate power laws may be behaviour of interest shared between the three considered systems.

### Graphene FET on diamond for high-frequency electronics

Transistors operating at high frequencies are the basic building blocks of millimeter-wave communication and sensor systems. The high velocity and mobility of carriers in graphene can open way for ultra-fast group IV transistors with similar or even better performance than can be achieved with III-V based semiconductors. However, the progress of high-speed graphene transistors has been hampered due to fabrication issues, influence of adjacent materials, and self-heating effects. Here, we report a graphene field-effect transistor (FET) on a diamond substrate, with a $f_{max}$ up to 54 GHz for a gate length of 500 nm. The high thermal conductivity of diamond provides an efficient heat-sink, and its relatively high optical-phonon energy improves saturation velocity of carriers in the graphene channel. Moreover, we show that graphene FETs on diamond, with different gate lengths, exhibit excellent scaling behavior. These results indicate that graphene FETs on diamond technology can reach sub-terahertz frequency performance.

### Fingerprints of possible even-parity superconducting states in Sr$_2$RuO$_4$ detected by planar tunneling spectroscopy

After more than 25 years of research, three even-parity superconducting states -- the $d+id$-wave, $d+ig$-wave, and $s+id$-wave states -- have emerged as leading candidates for the superconducting states of Sr$_2$RuO$_4$. In the present work, we propose a tunneling spectroscopy experiment for distinguishing among these three superconducting states. The key component of our proposal is that we examine the conductance spectra of normal-metal/Sr$_2$RuO$_4$ junctions with various angles between the junction interface and the crystal axis of the Sr$_2$RuO$_4$. The angle dependence of the conductance spectra shows a unique pattern in each superconducting state, which can function as a fingerprint for verifying the pairing symmetry of Sr$_2$RuO$_4$.

### Phonon-induced pairing in quantum dot quantum simulator

Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context we study the phase diagram of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. Our study shows that this system thus constitutes a relevant example of a correlated system that could be studied by experimental realization.

### Coexistence of Ferroelectric-like Polarization and Dirac-like Surface State in TaNiTe5

By combining angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), piezoresponse force microscopy (PFM) and first-principles calculations, we have studied the low-energy band structure, atomic structure and charge polarization on the surface of a topological semimetal candidate TaNiTe5. Dirac-like surface states were observed on the (010) surface by ARPES, consistent with the first-principles calculations. On the other hand, PFM reveals a switchable ferroelectric-like polarization on the same surface. We propose that the noncentrosymmetric surface reconstruction observed by STM could be the origin of the observed ferroelectric-like state in this novel material. Our findings provide a new platform with the coexistence of ferroelectric-like surface charge distribution and novel surface states.

### Convergence of time-averaged observables towards their steady values for Markov trajectories with application to Skew-Detailed-Balance Lifted-Markov processes

Among the Markov chains breaking detailed-balance that have been proposed in the field of Monte-Carlo sampling in order to accelerate the convergence towards the steady state with respect to the detailed-balance dynamics, the idea of 'Lifting' consists in duplicating the configuration space into two copies $\sigma=\pm$ and in imposing directed flows in each copy in order to explore the configuration space more efficiently. The skew-detailed-balance Lifted-Markov-chain introduced by K. S. Turitsyn, M. Chertkov and M. Vucelja [Physica D Nonlinear Phenomena 240 , 410 (2011)] is revisited for the Curie-Weiss mean-field ferromagnetic model, where the dynamics for the magnetization is closed. The typical convergence properties and the large deviations at various levels for empirical time-averaged observables are analyzed and compared with their detailed-balance counterparts, both for the discrete extensive magnetization $M$ and for the continuous intensive magnetization $m=\frac{M}{N}$ for large system-size $N$.

### Direct detection of odd-frequency superconductivity via time- and angle-resolved photoelectron fluctuation spectroscopy

We propose a measurement scheme to directly detect odd-frequency superconductivity via time- and angle-resolved photoelectron fluctuation spectroscopy. The scheme includes two consecutive, non-overlapping probe pulses applied to a superconducting sample. The photoemitted electrons are collected in a momentum-resolved fashion. Correlations between signals with opposite momenta are analyzed. Remarkably, these correlations are directly proportional to the absolute square of the time-ordered anomalous Green's function of the superconductor. This setup allows for the direct detection of the "hidden order parameter'' of odd-frequency pairing. We illustrate this general scheme by concretely analyzing the signal for the prototypical case of two-band superconductors, which are known to exhibit odd-frequency pairing under certain conditions.

### Anomalous spin waves in CsFeCl$_{3}$ and RbFeCl$_{3}$

We investigate magnetic excitations in the $S=1$ easy-plane type triangular antiferromagnets CsFeCl$_{3}$ and RbFeCl$_{3}$ through a combination of inelastic neutron scattering measurements and spin-wave theory calculations based on an established exchange-coupling Hamiltonian. We show that in either material the model falls short of providing an adequate description of the measured intensities and for RbFeCl$_{3}$ even fails to reproduce the measured dispersion relation. The most striking discrepancy is a very anisotropic azimuthal intensity distribution in the acoustic spin wave branches in the long-wavelength limit, which is incompatible with spin wave theory on a fundamental level. The observed anomalies are attributed to long-range dipolar interactions.

### Emergence of near-boundary segregation zones in face-centered cubic multi-principal element alloys

Grain boundaries have been shown to dramatically influence the behavior of relatively simple materials such as monatomic metals and binary alloys. The increased chemical complexity associated with multi-principal element alloys is hypothesized to lead to new grain boundary phenomena. To explore the relationship between grain boundary structure and chemistry in these materials, hybrid molecular dynamics/Monte Carlo simulations of a faceted {\Sigma}11 <110> tilt boundary, chosen to sample both high- and low-energy boundary configurations, are performed in face-centered cubic CrFeCoNiCu and CrFeCoNi equiatomic alloys. Unexpected enrichment of Fe is discovered in the face-centered cubic regions adjacent to the interface and found to be correlated with a structurally-distinct region of reduced atomic volume. Comparison with the boundary of the same type in monatomic Cu demonstrates that altered near-boundary regions exist in simpler systems as well, with the chemical complexity of the multi-principal element alloys highlighting its existence and importance.

### Singularities in the acoustic Casimir pressure as a function of reflectivities

We study the acoustic Casimir pressure between imperfectly reflecting plates immersed in various isotropic noise backgrounds. For flat as well as narrowly peaked noise spectra, the force tends to strong repulsion as the plate separation tends to zero, in contrast to the case of perfect reflectors. We uncover and analyze the associated singular behavior as the product of the reflection coefficients approaches 1, obtaining in the process expressions for the pressure resulting from arbitrary power-law spectra.

### Theory of superconductivity due to Ngai's mechanism in lightly doped SrTiO3

We develop a theory of superconducting pairing in low-density Strontium titanate due to quadratic coupling of electron density to soft transverse optical phonons. It leads to static attractive potential between electrons which decay length scales inversely with soft optical gap. For low electron densities attraction between electrons is local and transition temperature Tc was found. The Tc(n) dependence in agreement with experimental data for low doping was calculated. Next, we show that suppression of Tc by hydrostatic pressure and strong increase of Tc due to isotop substitution are explained within our theory.

### Synthesis of Murunskite Single Crystals: A Bridge Between Cuprates and Pnictides

Numerous contemporary investigations in condensed matter physics are devoted to high temperature (high-$T_c$ ) cuprate superconductors. Despite its unique effulgence among research subjects, the enigma of the high-$T_c$ mechanism still persists. One way to advance its understanding is to discover and study new analogous systems. Here we begin a novel exploration of the natural mineral murunskite, K$_2$FeCu$_3$S$_4$, as an interpolation compound between cuprates and ferropnictides, the only known high-$T_c$ superconductors at ambient pressure. Because in-depth studies can be carried out only on single crystals, we have mastered the synthesis and growth of high quality specimens. Similar to the cuprate parent compounds, these show semiconducting behavior in resistivity and optical transmittance, and an antiferromagnetic ordering at 100 K. Spectroscopy (XPS) and calculations (DFT) concur that the sulfur 3$p$ orbitals are partially open, making them accessible for charge manipulation, which is a prerequisite for superconductivity in analogous layered structures. DFT indicates that the valence band is more cuprate-like, while the conduction band is more pnictide-like. With appropriate doping strategies, this parent compound promises exciting future developments.

### Diffraction and interference with run-and-tumble particles

Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well, e.g. for producing waves in the telegraph process. Here, we use a wave function to drive their propulsion and tumbling. Such quantum-active motion realizes a jittery motion of Dirac electrons (as in the famous Zitterbewegung): the Dirac electron is a run-and-tumble particle, where the tumbling is between chiralities. We visualize the trajectories in diffraction and double slit experiments for electrons. In particular, that yields the time-of-arrival statistics of the electrons at the screen. Finally, we observe that away from pure quantum guidance, run-and-tumble particles with suitable spacetime-dependent parameters produce an interference pattern as well.

### Defects and phase formation in non-stoichiometric LaFeO$_3$: a combined theoretical and experimental study

The defect chemistry of perovskite compounds is directly related to the stoichiometry and to the valence states of the transition metal ions. Such relations are of high interest as they offer the possibility to influence the catalytic activity of perovskites for the application in solid-oxide fuel- and electrolyser cells. Combining theoretical and experimental approaches, we explore the feasibility of actively manipulating the valence state of Fe and the concentration of point defects by synthesizing non-stoichiometric LaFeO$_3$ (LFO). In the theoretical part, formation energies and concentrations of point defects were determined as a function of processing conditions by first-principles DFT+U calculations. Based on the DFT+U results, significant compositional deviations from stoichiometric LFO cannot be expected by providing rich or poor conditions of the oxidic precursor compounds (Fe$_2$O$_3$ and La$_2$O$_3$) in a solid-state processing route. In the experimental part, LFO was synthesized with a targeted La-site deficiency. We analyze the resulting phases in detail by X-ray diffraction and dedicated microscopy methods, namely scanning electron microscopy (SEM) and (scanning) transmission electron Microscopy ((S)TEM) in combination with energy dispersive X-ray spectroscopy (EDS) and electron energy-loss spectrometry (EELS). Instead of a variation of the La/Fe ratio, a mixture of two phases, Fe$_2$O$_3$/LaFeO$_3$, was observed resulting in an invariant charge state of Fe, which is in line with the theoretical results. We discuss our findings with respect to partly differing assumptions made in previously published studies on this material system.

### Lethe-DEM : An open-source parallel discrete element solver with load balancing

Approximately $75 \%$ of the raw material and $50 \%$ of the products in the chemical industry are granular materials. The Discrete Element Method (DEM) provides detailed insights of phenomena at particle scale and it is therefore often used for modeling granular materials. However, because DEM tracks the motion and contact of individual particles separately, its computational cost increases non-linearly $O(n_p\log(n_p))$ -- $O(n_p^2)$ depending on the algorithm) with the number of particles ($n_p$). In this article, we introduce a new open-source parallel DEM software with load balancing: Lethe-DEM. Lethe-DEM, a module of Lethe, consists of solvers for two-dimensional and three-dimensional DEM simulations. Load-balancing allows Lethe-DEM to significantly increase the parallel efficiency by $\approx 25 - 70 \%$ depending on the granular simulation. We explain the fundamental modules of Lethe-DEM, its software architecture, and the governing equations. Furthermore, we verify Lethe-DEM with several tests including analytical solutions and comparison with other software. Comparisons with experiments in a flat-bottomed silo, wedge-shaped silo, and rotating drum validate Lethe-DEM. We investigate the strong and weak scaling of Lethe-DEM with $1 \leq n_c \leq 192$ and $32 \leq n_c \leq 320$ processes, respectively, with and without load-balancing. The strong-scaling analysis is performed on the wedge-shaped silo and rotating drum simulations, while for the weak-scaling analysis, we use a dam break simulation. The best scalability of Lethe-DEM is obtained in the range of $5000 \leq n_p/n_c \leq 15000$. Finally, we demonstrate that large scale simulations can be carried out with Lethe-DEM using the simulation of a three-dimensional cylindrical silo with $n_p=4.3 \times 10^6$ on 320 cores.

### Optical Response from Charge-Density Waves in Weyl Semimetals

The study of charge-density wave (CDW) distortions in Weyl semimetals has recently returned to the forefront, inspired by experimental interest in materials such as (TaSe4)2I. However, the interplay between collective phonon excitations and charge transport in Weyl-CDW systems has not been systematically studied. In this paper, we examine the longitudinal electromagnetic response due to collective modes in a Weyl semimetal gapped by a quasi one-dimensional charge-density wave order, using both continuum and lattice regularized models. We systematically compute the contributions of the collective modes to the linear and nonlinear optical conductivity of our models, both with and without tilting of the Weyl cones. We discover that, unlike in a single-band CDW, the gapless CDW collective mode does not contribute to the conductivity unless the Weyl cones are tilted. Going further, we show that the lowest nontrivial collective mode contribution to charge transport with untilted Weyl cones comes in the third-order conductivity, and is mediated by the gapped amplitude mode. We show that this leads to a sharply peaked third harmonic response at frequencies below the single-particle energy gap. We discuss the implications of our findings for transport experiments in Weyl-CDW systems.

### Excitonic effects on the third-order nonlinear optical properties of solids: Theory and application

We present a many-body Bethe-Salpeter equation eigenstates based sum-over-states method to calculate the linear and nonlinear optical properties of solids. Excitonic and local field effects are included in the calculations. As applications, we calculate the one-photon absorption, third harmonic generation, degenerate four-wave mixing spectra of solid C60 fullerene. The overall agreement between the theoretical and experimental results is very good for all three calculated spectra. By comparisons with the independent particle approximation based sum-over-states method, we show that excitonic effects mix the independent particle transition peaks to new excitonic ones. The position and intensity of spectral peaks are modified significantly. By tracing the sum-over-states progress, we determine the type of nonlinear polarization resonances for the characteristic peaks of third harmonic generation process, which may clear up a discrepancy in two experimental results.

### Attraction from frustration in ladder systems

We analyze the formation of multi-particle bound states in ladders with frustrated kinetic energy in two component bosonic and two component fermionic systems. We focus on the regime of light doping relative to insulating states at half-filling, spin polarization close to 100 percent, and strong repulsive interactions. A special feature of these systems is that the binding energy scales with single particle tunneling $t$ rather than exchange interactions, since effective attraction arises from alleviating kinetic frustration. For two component Fermi systems on a zigzag ladder we find a bound state between a hole and a flipped spin (magnon) with a binding energy that can be as large as $0.6t$. We demonstrate that magnon-hole attraction leads to formation of clusters comprised of several holes and magnons and expound on antiferromagentic correlations for the transverse spin components inside the clusters. We identify several many-body states that result from self-organization of multi-particle bound states, including a Luttinger liquid of hole-magnon pairs and a density wave state of two hole - three magnon composites. We establish a symmetry between the spectra of Bose and Fermi systems and use it to establish the existence of antibound states in two component Bose mixtures with SU(2) symmetric repulsion on a zigzag ladder. We also consider Bose and Fermi systems on a square ladder with flux and demonstrate that both systems support bound states. We discuss experimental signatures of multi-particle bound states in both equilibrium and dynamical experiments. We point out intriguing connections between these systems and the quark bag model in QCD.

### Two particles on a chain with disordered interaction: Localization and dissociation of bound states and mapping to chaotic billiards

We consider two particles hopping on a chain with a contact interaction between them. At strong interaction, there is a molecular bound state separated by a direct gap from a continuous band of atomic states. Introducing weak disorder in the interaction, the molecular state becomes Anderson localized. At stronger disorder, part of the molecular band delocalizes and dissociates due to its hybridization to the atomic band. We characterize these different regimes by computing the density of states, the inverse participation ratio, the level-spacing statistics and the survival probability of an initially localized state. The atomic band is best described as that of a rough billiard for a single particle on a square lattice that shows signatures of quantum chaos. In addition to typical chaotic states'', we find states that are localized along only one direction. These separatrix states'' are more localized than chaotic states, and similar in this respect to scarred states, but their existence is due to the separatrix iso-energy line in the interaction-free dispersion relation, rather than to unstable periodic orbits.

### Emission of particles from a parametrically driven condensate in a 1D lattice

Motivated by recent experiments, we calculate particle emission from a Bose-Einstein condensate trapped in a single deep well of a one-dimensional (1D) lattice when the interaction strength is modulated. In addition to pair emission, which has been widely studied, we observe single-particle emission. Within linear response, we are able to write closed-form expressions for the single-particle emission rates, and reduce the pair emission rates to one-dimensional integrals. The full nonlinear theory of single-particle emission is reduced to a single variable integro-differential equation, which we numerically solve.

### Molecular beam epitaxy of single-crystalline bixbyite (In$_{1-x}$Ga$_x$)$_2$O$_3$ films ($x \leq 0.18$): Structural properties and consequences of compositional inhomogeneity

In this work, we show the heteroepitaxial growth of single-crystalline bixbyite (In$_{1-x}$Ga$_x$)$_2$O$_3$ films on (111)-oriented yttria-stabilized zirconia substrates using plasma-assisted molecular beam epitaxy under various growth conditions. A pure In$_2$O$_3$ buffer layer between the substrate and (In$_{1-x}$Ga$_x$)$_2$O$_3$ alloy is shown to result in smoother film surfaces and significantly improved crystallinity. Symmetric out-of-plane 2$\theta - \omega$ x-ray diffraction scans show a single (111) crystal orientation and transmission electron microscopy confirms the single-crystallinity up to $x = 0.18$ and only slight film quality deterioration with increasing Ga content. Partially relaxed layers are demonstrated via reciprocal space mapping with lattice parameters fitting well to Vegard's law. However, the Ga cations are not evenly distributed within the films containing nominally $x > 0.11$: inclusions with high Ga density up to $x = 0.50$ are observed within a "matrix" with $x \approx 0.08$. The cubic bixbyite phase is preserved, in both the "matrix" and the inclusions. Moreover, for $x \geq 0.11$, both the Raman phonon lines as well as the optical absorption onset remain nearly constant. Hard x-ray photoelectron spectroscopy measurements also indicate a widening of the band gap and exhibit similar saturation of the Ga 2p core level position for high Ga contents. This saturation behavior of the spectroscopic properties further supports the limited Ga incorporation into the "matrix" of the film.

### Computational Optimization of MnBi to Enhance Energy Product

High energy density magnets are preferred over induction magnets for many applications, including electric motors used in flying rovers, electric vehicles, and wind turbines. However, several issues related to cost and supply with state-of-the-art rare-earth-based magnet necessities development of high-flux magnets containing low cost, earth-abundant materials. Here, we demonstrate the possibility of tuning magnetization and magnetocrystalline anisotropy of one of the candidate materials, MnBi, by alloying it with foreign elements. By using the density functional theory in the high-throughput fashion, we consider the possibility of alloying MnBi with all possible metal and non-metal elements in the periodic table and found that MnBi-based alloys with Pd, Pt, Rh, Li, and O are stable against decomposition to constituent elements and have larger magnetization, energy product compared and magnetic anisotropy compared to MnBi We consider the possibility of these elements occupying half and all of the available empty sites. Combined with other favorable properties of MnBi, such as high Curie temperature and earth abundancy of constituents elements, we envision the possibility of MnBi-based high-energy-density magnets.

### Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric

Among non-Hermitian systems, pseudo-Hermitian phases represent a special class of physical models characterized by real energy spectra and by the absence of non-Hermitian skin effects. Here, we show that several pseudo-Hermitian phases in two and three dimensions can be built by employing $q$-deformed matrices, which are related to the representation of deformed algebras. Through this algebraic approach we present and study the pseudo-Hermitian version of well known Hermitian topological phases, raging from two-dimensional Chern insulators and time-reversal-invariant topological insulators to three-dimensional Weyl semimetals and chiral topological insulators. We analyze their topological bulk states through non-Hermitian generalizations of Abelian and non-Abelian tensor Berry connections and quantum metric. Although our pseudo-Hermitian models and their Hermitian counterparts share the same topological invariants, their band geometries are different. We indeed show that some of our pseudo-Hermitian phases naturally support nearly-flat topological bands, opening the route to the study of pseudo-Hermitian strongly-interacting systems. Finally, we provide an experimental protocol to realize our models and measure the full non-Hermitian quantum geometric tensor in synthetic matter.

### Gate-tunable Veselago Interference in a Bipolar Graphene Microcavity

The relativistic charge carriers in monolayer graphene can be manipulated in manners akin to conventional optics (electron-optics): angle-dependent Klein tunneling collimates an electron beam (analogous to a laser), while a Veselago refraction process focuses it (analogous to an optical lens). Both processes have been previously investigated, but the collimation and focusing efficiency have been reported to be relatively low even in state-of-the-art ballistic pn-junction devices. These limitations prevented the realization of more advanced quantum devices based on electron-optical interference, while understanding of the underlying physics remains elusive. Here, we present a novel device architecture of a graphene microcavity defined by carefully-engineered local strain and electrostatic fields. We create a controlled electron-optic interference process at zero magnetic field as a consequence of consecutive Veselago refractions in the microcavity and provide direct experimental evidence through low-temperature electrical transport measurements. The experimentally observed first-, second-, and third-order interference peaks agree quantitatively with the Veselago physics in a microcavity. In addition, we demonstrate decoherence of the interference by an external magnetic field, as the cyclotron radius becomes comparable to the interference length scale. For its application in electron-optics, we utilize Veselago interference to localize uncollimated electrons and characterize its contribution in further improving collimation efficiency. Our work sheds new light on relativistic single-particle physics and provides important technical improvements toward next-generation quantum devices based on the coherent manipulation of electron momentum and trajectory.

### Prethermal Dynamical Localization and the Emergence of Chaos in a Kicked Interacting Quantum Gas

While ergodicity is a fundamental postulate of statistical mechanics and implies that driven interacting systems inevitably heat, ergodic dynamics can be disrupted by quantum interference. Despite a quarter-century of experimental studies, the effect of many-body interactions on the resulting dynamically localized state has remained unexplored. We report the experimental realization of a tunably-interacting kicked quantum rotor ensemble using a Bose-Einstein condensate in a pulsed optical lattice. We observe a prethermal localized plateau, which survives for hundreds of kicks, followed by interaction-induced anomalous diffusion. Echo-type time reversal experiments establish the role of interactions in destroying reversibility, and a mapping to kicked spin models illustrates connections to many-body dynamical localization in spin chains. These results demonstrate a dynamical transition to many-body quantum chaos, and illuminate and delimit possibilities for globally protecting quantum information in interacting driven quantum systems.

### Intertwined states at finite temperatures in the Hubbard model

Significant advances in numerical techniques have enabled recent breakthroughs in the study of various properties of the Hubbard model - a seemingly simple, yet complex model of correlated electrons that has been a focus of study for more than half a century. In particular, it captures the essence of strong correlations, and is believed to possess various emergent, low energy states and collective excitations characteristic of cuprate high-temperature superconducting materials. While a thorough review of all activity is not possible here, we have focused the discussion on our recent work using unbiased, numerically exact, brute force", finite temperature quantum Monte Carlo methods. Our various studies reveal a rich variety of quantum liquid crystal phases, and complementary transport properties, which answer some questions, but certainly raise others concerning strange metal" behavior and the ultimate fate of quasiparticles in the Hubbard model.

### Quantum Gases in Optical Boxes

Advances in light shaping for optical trapping of neutral particles have led to the development of box traps for ultracold atoms and molecules. These traps have allowed the creation of homogeneous quantum gases and opened new possibilities for studies of many-body physics. They simplify the interpretation of experimental results, provide more direct connections with theory, and in some cases allow qualitatively new, hitherto impossible experiments. Here we review progress in this emerging field.

### Higher-order topological insulators from $3Q$ charge bond orders on hexagonal lattices: A hint to kagome metals

We show that unconventional boundary phenonema appear in the $3Q$ charge bond orders on hexagonal lattices. At the saddle points with Van Hove singularity, the $3Q$ orders can develop at three nesting momenta. An insulator can develop from the bond modulations, where the $\text{C}_6$ symmetry is respected. On the kagome lattice, in-gap corner states arise and carry fractional corner charges $2e/3$. Such corner phenomena originates from the corner filling anomaly and indicates a higher-order topological insulator. Despite subtle issues of unit cells, the in-gap corner states also appear on the triangular lattice. The honeycomb lattice does not support anomalous corner states, while in-gap edge states are manifest. We discuss possible indications to the experimentally observed charge bond orders in kagome metals $\text{AV}_3\text{Sb}_5$ with $\text{A}=\text{K},\text{Rb},\text{Cs}$. With layer stacking along the out-of-plane direction, the corner states may constitute the hinge states with fractional charges.

### On the training of sparse and dense deep neural networks: less parameters, same performance

Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial compression of the parameter space. This latter scales by definition with the number of computing neurons. The classification scores, as measured by the displayed accuracy, are however inferior to those attained when the learning is carried in direct space, for an identical architecture and by employing the full set of trainable parameters (with a quadratic dependence on the size of neighbor layers). In this Letter, we propose a variant of the spectral learning method as appeared in Giambagli et al {Nat. Comm.} 2021, which leverages on two sets of eigenvalues, for each mapping between adjacent layers. The eigenvalues act as veritable knobs which can be freely tuned so as to (i) enhance, or alternatively silence, the contribution of the input nodes, (ii) modulate the excitability of the receiving nodes with a mechanism which we interpret as the artificial analogue of the homeostatic plasticity. The number of trainable parameters is still a linear function of the network size, but the performances of the trained device gets much closer to those obtained via conventional algorithms, these latter requiring however a considerably heavier computational cost. The residual gap between conventional and spectral trainings can be eventually filled by employing a suitable decomposition for the non trivial block of the eigenvectors matrix. Each spectral parameter reflects back on the whole set of inter-nodes weights, an attribute which we shall effectively exploit to yield sparse networks with stunning classification abilities, as compared to their homologues trained with conventional means.

### Regularization of Mixture Models for Robust Principal Graph Learning

A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can be modeled as a graph structure acting like a topological prior for the Gaussian clusters turning the problem into a maximum a posteriori estimation. Parameters of the model are iteratively estimated through an Expectation-Maximization procedure making the learning of the structure computationally efficient with guaranteed convergence for any graph prior in a polynomial time. We also embed in the formalism a natural way to make the algorithm robust to outliers of the pattern and heteroscedasticity of the manifold sampling coherently with the graph structure. The method uses a graph prior given by the minimum spanning tree that we extend using random sub-samplings of the dataset to take into account cycles that can be observed in the spatial distribution.

### Quantum Monte Carlo studies with microscopic two- and three-body interactions of a trimer scaling function

We present an energy scaling function to predict, in a specific range, the energy of bosonic trimers with large scattering lengths and finite range interactions, which is validated by quantum Monte Carlo calculations using microscopic Hamiltonians with two- and three-body potentials. The proposed scaling function depends on the scattering length, effective range, and a reference energy, which we chose as the trimer energy at unitarity. We obtained the scaling function as a limit cycle from the solution of the renormalized zero-range model with effective range corrections. We proposed a simple parameterization of the energy scaling function. Besides the intrinsic interest in theoretical and experimental investigations, this scaling function allows one to probe Efimov physics with only the trimer ground-states, which may open opportunities to identify Efimov trimers whenever access to excited states is limited.

### Drive-induced nonlinearities of cavity modes coupled to a transmon ancilla

High-Q microwave cavity modes coupled to transmon ancillas provide a hardware-efficient platform for quantum computing. Due to their coupling, the cavity modes inherit finite nonlinearity from the transmons. In this work, we theoretically and experimentally investigate how an off-resonant drive on the transmon ancilla modifies the nonlinearities of cavity modes in qualitatively different ways, depending on the interrelation among cavity-transmon detuning, drive-transmon detuning and transmon anharmonicity. For a cavity-transmon detuning that is smaller than or comparable to the drive-transmon detuning and transmon anharmonicity, the off-resonant transmon drive can induce multiphoton resonances among cavity and transmon excitations that strongly modify cavity nonlinearities as drive parameters vary. For a large cavity-transmon detuning, the drive induces cavity-photon-number-dependent ac Stark shifts of transmon levels that translate into effective cavity nonlinearities. In the regime of a weak transmon-cavity coupling, the cavity Kerr nonlinearity relates to the third-order nonlinear susceptibility function $\chi^{(3)}$ of the driven ancilla. This susceptibility function provides a numerically efficient way of computing the cavity Kerr particularly for systems with many cavity modes controlled by a single transmon. It also serves as a diagnostic tool for identifying undesired drive-induced multiphoton resonance processes. Lastly, we show that by judiciously choosing the drive amplitude, a single off-resonant transmon drive can be used to cancel the cavity self-Kerr nonlinearity as well as inter-cavity cross-Kerr. This provides a way of dynamically correcting the cavity Kerr nonlinearity during bosonic operations or quantum error correction protocols that rely on the cavity modes being linear.

### Differential models for the Anderson dual to bordism theories and invertible QFT's

In this paper, we construct new models for the Anderson duals $(I\Omega^G)^*$ to the stable tangential $G$-bordism theories and their differential extensions. The cohomology theory $(I\Omega^G)^*$ is conjectured by Freed and Hopkins \cite{Freed:2016rqq} to classify deformation classes of possibly non-topological invertible quantum field theories (QFT's). Our model is made by abstractizing certain properties of invertible QFT's, thus supporting their conjecture.

### Solving the Bose-Hubbard model in new ways

We introduce a new method for analysing the Bose-Hubbard model for an array of bosons with nearest neighbor interactions. It is based on a number-theoretic implementation of the creation and annihilation operators that constitute the model. One of the advantages of this approach is that it facilitates computation with arbitrary accuracy, enabling nearly perfect numerical experimentation. In particular, we provide a rigorous computer assisted proof of quantum phase transitions in finite systems of this type. Furthermore, we investigate properties of the infinite array via harmonic analysis on the multiplicative group of positive rationals. This furnishes an isomorphism that recasts the underlying Fock space as an infinite tensor product of Hecke spaces, i.e., spaces of square-integrable periodic functions that are a superposition of non-negative frequency harmonics. Under this isomorphism, the number-theoretic creation and annihilation operators are mapped into the Kastrup model of the harmonic oscillator on the circle. It also enables us to highlight a kinship of the model at hand with an array of spin moments with a local anisotropy field. This identifies an interesting physical system that can be mapped into the model at hand.

### Polaron models with regular interactions at strong coupling

We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau--Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.

### Beaming Elastic and SERS Emission from Bent-Plasmonic Nanowire on a Mirror Cavity

We report on the experimental observation of beaming elastic and surface enhanced Raman scattering (SERS) emission from a bent-nanowire on a mirror (B-NWoM) cavity. The system was probed with polarization resolved Fourier plane and energy-momentum imaging to study the spectral and angular signature of the emission wavevectors. The out-coupled elastically scattered light from the kink occupies a narrow angular spread. We used a self-assembled monolayer of molecules with a well-defined molecular orientation to utilize the out-of-plane electric field in the cavity for enhancing Raman emission from the molecules and in achieving beaming SERS emission. Calculated directionality for elastic scattering and SERS emission were found to be 16.2 and 12.5 dB respectively. The experimental data were corroborated with three-dimensional numerical finite element and finite difference time domain based numerical simulations. The results presented here may find relevance in understanding coupling of emitters with elongated plasmonic cavities and in designing on-chip optical antennas.

### Quantum Entanglement of Free Particles

The Schrodinger equation is solved for many free particles and their quantum entanglement is studied via correlation analysis. Converting the Schrodinger equation in the Madelung hydrodynamic-like form, the quantum mechanics is extended to open quantum systems by adding Ohmic friction forces. The dissipative evolution confirms correlation decay over time, but a new integral of motion is discovered, being appropriate for storing everlasting quantum information.

### A Finite Energy-Momentum Tensor for the $φ^3$ theory in $6$ dimensions

Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite operators of low dimension, then do this with traceless tensor operators. We then express the bare energy momentum tensor in terms of the renormalised composite operators, with some terms having divergent coefficients. We subtract these away and obtain a manifestly finite energy tensor. The subtracted terms are transverse, so this does not affect the conservation of the energy momentum tensor. The trace of this finite improved energy momentum tensor vanishes at the fixed point indicating conformal invariance. Interestingly it is not RG-invariant except at the fixed point, but can be made RG invariant everywhere by further addition of transverse terms, whose coefficients vanish at the fixed point.

### HVPE growth of corundum-structured $α$-Ga$_2$O$_3$ on sapphire substrates with $α$-Cr$_2$O$_3$ buffer layer

Gallium oxide films were grown by HVPE on (0001) sapphire substrates with and without ${\alpha}-Cr_{2}O_{3}$ buffer produced by RF magnetron sputtering. Deposition on bare sapphire substrates resulted in a mixture of ${\alpha}-Ga_{2}O_{3}$ and ${\epsilon}-Ga_{2}O_{3}$ phases with a dislocation density of about $2{\cdot}10^{10} cm^{-2}$. The insertion of ${\alpha}-Cr_{2}O_{3}$ buffer layers resulted in phase-pure ${\alpha}-Ga_{2}O_{3}$ films and a fourfold reduction of the dislocation density to $5{\cdot}10^{9} cm^{-2}$.

### Poisson-Dirichlet asymptotics in condensing particle systems

We study measures on random partitions, arising from condensing stochastic particle systems with stationary product distributions. We provide fairly general conditions on the stationary weights, which lead to Poisson-Dirichlet statistics of the condensed phase in the thermodynamic limit. The Poisson-Dirichlet distribution is known to be the unique reversible measure of split-merge dynamics for random partitions, which we use to characterize the limit law. We also establish concentration results for the macroscopic phase, using size-biased sampling techniques and the equivalence of ensembles to characterize the bulk distribution of the system.

### Quantum error as an emergent magnetic field

We investigate the effect of quantum errors on a monitored Brownian Sachdev-Ye-Kitaev (SYK) model featuring a measurement-induced phase transition that can be understood as a symmetry-breaking transition of an effective $Z_4$ magnet in the replica space. The errors describe the loss of information about the measurement outcomes and are applied during the non-unitary evolution or at the end of the evolution. In the former case, we find that this error can be mapped to an emergent magnetic field in the $Z_4$ magnet, and as a consequence, the symmetry is explicitly broken independent of the measurement rate. R\'enyi entropies computed by twisting boundary conditions now generate domain walls even in the would-be symmetric phase at a high measurement rate. The entropy is therefore volume-law irrespective of the measurement rate. In the latter case, the error-induced magnetic field only exists near the boundary of the magnet. Varying the magnetic field leads to a pinning transition of domain walls, corresponding to error threshold of the quantum code prepared by the non-unitary SYK dynamics.

### Full counting statistics of Schwinger pair production and annihilation

We study the probability distribution of the number of particle and antiparticle pairs produced via the Schwinger effect when a uniform but time-dependent electric field is applied to noninteracting scalars or spinors initially at a thermodynamic equilibrium. We derive the formula for the characteristic function by employing techniques in mesoscopic physics, reflecting a close analogy between the Schwinger effect and mesoscopic tunneling transports. In particular, we find that the pair production in a medium is enhanced (suppressed) for scalars (spinors) due to the Bose stimulation (Pauli blocking). Furthermore, in addition to the production of accelerated pairs by the electric field, the annihilation of decelerated pairs is found to take place in a medium. Our formula allows us to extract the probability distributions in various situations, such as those obeying the generalized trinomial statistics for spin-momentum resolved counting and the bidirectional Poisson statistics for spin-momentum unresolved counting.

### Quasi-solid-state sodium-ion hybrid capacitors enabled by UiO-66@PVDF-HFP multifunctional separators: selective charge transfer and high safety

The practical application of sodium-ion hybrid capacitors is limited by their low energy densities resulted from the kinetics mismatch between cathodes and anodes, and the fire safety related to the flammable electrolyte-separator system. Hence, we report a rational design of metal-organic frameworks (MOFs, UiO-66) modified PVDF-HFP separator. High tensile strength and dimensional thermal stability of the separator reduce the risk of electrode short circuit caused by the separator deformation. MCC test demonstrates a reduction of 75% in peak heat release rate (pHRR), indicating an enhanced fire-resistant property of the separator. This is due to the transformation of UiO-66 into ZrO2 accompanied by the consumption of oxygen and the formation of the barrier char that suppresses further heat release. Quasi-solid-state electrolyte prepared based on this separator presents an enhanced ionic conductivity of 2.44 mS*cm-1 and Na-ion transference number of 0.55, which are related to the high porosity ( >70%) and electrolyte uptake (~ 320%) of the separator. Moreover, the open metal sites of UiO-66 can capture PF6- and consequently liberate the Na+ for faster migration, thus reducing the kinetics mismatch between cathodes and anodes. Such multifunctional separator enables the quasi-solid-state Na-ion hybrid capacitor to achieve high energy density (182 Wh*kg-1 @31 W*kg-1) and power density (5280 W*kg-1 @22 Wh*kg-1), as well as excellent cyclic stability (10000 cycles @1000 mA*g-1). Keywords: Quasi-solid-state; PVDF-HFP; Metal-organic frameworks; Dimensional thermal stability; Fire safety; Selective charge transfer