Papers

While band topology is usually associated with the deterministic dynamics of a system, we show that it can instead reside in its fluctuations. Using a reciprocal lattice driven by nonequilibrium chiral active noise, we find that the displacement spectrum—which quantifies displacement fluctuations—admits bands with nonzero Chern numbers despite a Chern-trivial deterministic mechanics. A two-band valley theory captures the emergence of this topology through a Dirac mass inversion, a Haldane-type mechanism, or a quadratic band touching, depending on the relevant transition. Through the bulk–boundary correspondence, we find boundary-localized fluctuation modes that are distinct from the usual propagating mechanical edge states.

We formulate a minimal Landau theory for a charge-density wave (CDW) whose commensurability is defined with respect to a deformed lattice. The motivation is provided by recent observations on an isolated single NbS$_3$ chain, which exhibits a commensurate CDW state accompanied by a $6\%$ shrinkage of the lattice constant. A uniform stretch $a_0\to a_0(1+\varepsilon)$ changes the reciprocal lattice wave number to $G(\varepsilon)=G_0/(1+\varepsilon)$, so that an $N$-fold commensurate CDW has the wave number $Q_\mathrm{C}(\varepsilon)=G(\varepsilon)/N$, whereas the wave number $Q_\mathrm{IC}$ favored by the incommensurate instability remains fixed. We propose an amplitude-strain free energy for both $N=3$ and $N=4$, in which the CDW induces a finite uniform strain by relieving the mismatch between $Q_\mathrm{C}(\varepsilon)$ and $Q_\mathrm{IC}$. The mismatch is shared between the CDW and the lattice in a proportion set by their stiffness ratio; since the CDW stiffness grows with the CDW amplitude, the lattice takes up an increasing share of the mismatch as the CDW develops. Our results suggest a reexamination of lock-in theories and of strain-tuning experiments on density-wave systems.

We present a generalised tripartite Haldane model with a complex nearest neighbour hopping parameter. The total magnetic flux through the primitive unit cell, which consists of three hexagonal unit cells is zero, and thus the model has the structure of a loop-current model. We calculate topological phase diagrams of the Chern numbers as a function of the phases of the nearest and next-nearest neighbour hopping parameters for a fixed ratio of the magnitude of the hopping parameters. We show that, unlike the Haldane model, the topological phase diagram of this model is very complex, but some aspects can still be dealt with analytically. Furthermore, the Chern numbers of the topological phases are as large as $7$ in absolute value. The analysis is supported by explicit expressions for energy bands crossing at high symmetry points in the Brillouin zone, which show as linear phase boundaries in the phase diagram. We show that such lines explain many features in the topological phase diagrams. Finally, we analyse a few representative examples of the nature of level crossings away from high symmetry and their evolution with model parameters.

Integration of magnetic material with scalable microfluidic platforms can significantly improve the throughput and precision in biotechnology processes. In this work we have developed a new magnetic platform based on printed circuit board (PCB) technology. Cobalt-Platinum (CoPt) micromagnets are electroplated on copper pads with an arbitrary footprint on a Kapton substrate to enable generation of different magnetic field gradients. The magnets are characterized by XRD and VSM, before and after thermal annealing. The ordered L10 phase appear in XRD results after annealing at 600 {\deg}C, and VSM results show around six times increase for in-plane magnetic remanence from 0.24T to 1.4T. The near equiatomic ratios of Co:Pt is confirmed by EDX observations. The performance of these magnets is experimentally validated by trapping magnetic nanoparticles in microfluidic channels. These results are in excellent agreement with FEA models presented in COMSOL Multiphysics.

The rapid growth of generative AI has intensified the need for efficient heat dissipation in large-scale data centers. To control heat flow, thermal metamaterials with layered structures have been widely used, which impart the anisotropic properties of thermal conductivities. However, the conventional effective medium approximation (EMA) often fails to provide accurate predictions in systems with a high thermal conductivity contrast between adjacent layers embedded in a background medium. Here, we generalize the EMA by introducing two corrective coefficients that extend its validity to regimes where the conventional EMA was previously inapplicable, i.e., high-contrast thermal metamaterials with the background medium. Notably, one of these coefficients that we proposed has the same mathematical form as the Fresnel reflection coefficient in optics. This allows us to interpret the "reflection-like" behavior of heat flow as it penetrates adjacent layers with high thermal contrast. Our findings suggest that heat diffusion, traditionally viewed as a purely dissipative process, can be understood intuitively through the framework of ray optics.

In recent years, all-optical writing and switching of valley polarization in two-dimensional semiconductors has been demonstrated on femtosecond timescales. Reading this polarization out on the same timescale, carrier by carrier, has so far remained out of reach. Employing semiconductor Bloch equation simulations of monolayer MoS$_2$, we show that attosecond transient absorption closes this gap by turning the Mo $4p$ semicore edge into a quantitative valley polarimeter. We find that pump-enabled core-to-valence absorption probes the holes while core-to-conduction bleaching probes the electrons, so that a single spectrum identifies each carrier by its photoabsorption energy. The hole channel, Pauli-blocked in equilibrium, emerges background-free. Its circular dichroism reverses sign with the pump helicity, and its normalized magnitude is proportional to the valley polarization. Finally, we show that scanning the probe delay clocks the few-femtosecond write in real time. Thus, attosecond core-level dichroism is a carrier-sensitive, quantitative probe of the creation and evolution of valley polarization.

Competing and coupled spin and charge interactions in quantum materials lead to a variety of ordered states where local configurations preferentially influence the long-range order. When these interactions are finely balanced in energy, disorder and fluctuations play an outsized role. Raman scattering is particularly well-suited to revealing the underlying physics in such situations because of its sensitivity to local environments and ability to reveal overall symmetries. We perform angle-resolved Raman polarization measurements on single crystals of the correlated, layered magnet, \ce{Sr2IrO4}, where the Mott insulating ground state arises from strong spin-orbit coupling. We characterize the symmetries of both the phonon and magnon modes through comprehensive measurements in both the $ab$-plane and out-of-plane geometries from 10 to 700 cm$^{-1}$, and trace the evolution of these modes in both configurations to 12 GPa in a diamond anvil cell with perforated diamonds. Pressure does not significantly alter the lattice as the phonon modes shift linearly under compression, but at the same time the magnon modes become position dependent and spread over a range of wavenumbers. We attribute this magnetic heterogeneity to pressure-enhanced variations in the weak interlayer interactions, which may locally favor competing magnetic stacking configurations, and compare our experimental results to the predictions of linear spin wave calculations. Our results demonstrate that Raman-active magnons amplify $\mu$eV-scale interactions responsible for ground-state selection into easily measurable spectral changes.

When a plane polarized Gaussian beam of light is incident on a surface, upon reflection it splits into right and left circularly polarized beams that are spatially separated in the direction perpendicular to the plane of incidence. This is known as the photonic spin-Hall effect (PSHE). In this work, we show that the centroid shift, which is the intensity weighted average of the shifts of the right and the left circularly polarized beams directly probes the optical Hall conductivity, which carries the essential information about the topological properties of the system. We show that the centroid shift as a function of the frequency of light has a unique sign structure depending on whether the system is in a time-reversal symmetry broken band topological phase or a trivial phase. Thus, the PSHE may serve as an unambiguous and a non-invasive probe to detect time-reversal symmetry broken band topological phases.

We study the equilibrium phase behavior of a fluid confined in a slit made from two patterned walls. Shearing the walls frustrates the fluid, due to a competition between capillary condensation and interface delocalization, forcing the formation of bridging phases with different pinning properties. This leads to an unusually rich phase diagram, displaying first-order and continuous phase transitions, depending sensitively on the slit width and shear. Generalized Kelvin equations determine the phase boundaries, while the bridging phases are characterized by large correlation lengths, predictions for which are tested using a microscopic density functional model.

The usual WKB analysis for quantum tunneling applies when the tunneling action is large, as it is for tall, wide potential barriers. In contrast we analyze tunneling when the action is small, as it is for tunneling across a tall, thin barrier. We develop a perturbative analysis where the control parameter is the inverse of the area under the potential barrier and apply our technique to several examples in $1+1$ dimensions. In resonant situations for bound particles we find that the tunneling probability grows with time as $\propto t^2$, while in non-resonant situations it grows linearly with time. We evaluate not only the tunneling probability but also the time-dependent tunneling wavefunction for a particle that escapes to infinity, i.e. from a quasi-bound state to the continuum.

Learning a quantum system's Hamiltonian is crucial for understanding and controlling its dynamics and has recently become a topic of widespread interest. To understand the learning protocol's error tolerances, i.e. its stability in the presence of inevitable errors, this work utilizes tensor network techniques to emulate Hamiltonian learning workflows at scale and with noise. Specifically, we employed a Hamiltonian learning technique based on approximate stationary states which are constructed using matrix product tools. We provide analytic bounds on the Hamiltonian learning estimation errors and perform numerical simulations that highlight learning error's stability under two families of errors. Using our workflow, we are able to scale up the protocol and learn mixed-field Ising model Hamiltonians of an $N=300$ site spin chain. By simulating the protocol at large scale, and empirically studying its practical limitations, our analysis of how errors affect the Hamiltonian learning process provides valuable lessons for future experiments. We conclude by discussing the avenues our work opens as well as future work that can support Hamiltonian learning experiments.

Centrosymmetric 1T-MX$_2$ monolayers(MLs) have attracted considerable attention owing to their intriguing transport properties and potential technological applications arising from the interplay among quantum geometry, electronic band structure, and band-gap characteristics. Despite this rich physics, a comprehensive microscopic tight-binding(TB) description that simultaneously captures these properties remains insufficiently established, while first-principles approaches can be computationally demanding for systematic investigations across different materials and perturbations. Here, we develop a transferable eleven-band Slater-Koster TB description of ML 1T-MX$_2$ TMDs and use it to establish a connection among their microscopic electronic structure, quantum geometry, and optical response. The model is constructed in an orthogonal orbital basis from the crystal geometry and symmetry-constrained SK parameters, with material-specific parametrizations obtained from DFT calculations for ML ZrS$_2$ and HfS$_2$. The resulting geometry-based Hamiltonian accurately describes the low-energy electronic structures and provides a natural framework for extending the analysis to the broader isostructural 1T-MX$_2$ family. We find that the pristine MLs possess a finite quantum metric, with the dominant contribution concentrated in the two highest occupied bands owing to the small near-gap energy separation and strong metal-chalcogen $p$-$d$ hybridization. Furthermore, we verify the interband $f$-sum rule, which directly relates the integrated optical spectral weight to the Brillouin-zone-averaged quantum metric. Our results establish optical spectral weight as an experimentally accessible probe of the quantum geometry of occupied Bloch states and provide a unified microscopic framework for connecting electronic structure, quantum geometry, and measurable optical responses across the 1T-MX$_2$ family.

We propose a theoretical scheme for realizing a tunable nonreciprocal Goos-Hänchen shift (GHS) in a hybrid cavity magnomechanical system. The setup consists of a rotating yttrium iron garnet sphere embedded in a microwave cavity, with magnetic-dipole and magnetostrictive interactions mediating magnon-photon and magnon-phonon couplings, respectively. Owing to the Barnett effect, the magnon frequency acquires a rotation-induced shift whose sign can be reversed by changing the direction of the bias magnetic field. We show that the output probe spectrum exhibits a Fano resonance, while the associated GHS responds asymmetrically to opposite field directions, providing a controllable mechanism for nonreciprocal beam shifts. The magnon-photon and magnon-phonon interactions are found to affect the GHS in opposite ways, while the cavity length offers an additional degree of tunability. These results provide a route toward magnetically reconfigurable microwave photonic devices and sensitive detection of Barnett-induced effective fields.

Herbertsmithite is a prototypical candidate quantum spin liquid (QSL), believed to feature a long-range entangled ground state and deconfined fractionalised spinon excitations. Confirmation of these properties has been hindered by the presence of magnetic impurities (spin-1/2 Cu2+ spins substituted onto non-magnetic Zn2+ sites). Recently these impurities were reconceptualised as 'witnesses' of the QSL, inheriting long-range interactions and entanglement mediated by the QSL spinons, leading to spin glass formation amongst witnesses below 260 mK. Here we present a full theoretical account of this idea. Despite having only one free parameter (the witness-kagome spin coupling), our model captures the full range of experimental data, including: the formation of a spin glass amongst witnesses; the frequency and temperature dependence of the magnetic noise; a sharp peak in the DC magnetic susceptibility as a function of temperature; and the static neutron scattering structure factor at 2 K. Both candidate QSLs (Z2 and U(1)) give similar agreement with all data; however, our model predicts a qualitative difference between the Z2 and U(1) neutron scattering intensities below 260 mK, providing a long-sought definitive test to distinguish the two cases. We also predict phase diagrams as a function of temperature and witness concentration, finding a phase transition to different long-range ordered witness states for Z2 and U(1) at high concentration.

Unlike second-order phase transitions, a first-order transition has a stage, in which a system is trapped in a metastable state. The decay of this state leads to abundant excitations over the ground state. We present a field theory for kinetics of defects emerging during quantum annealing computations. This theory predicts several power laws for the error generation rate during quantum annealing either though or near the first-order phase transition. Sharp changes between the power exponents are predicted for continuous parameter changes. Observation of this behavior would be a signature of first-order critical points and could help identify and avoid them for better computations. The driven Lipkin-Meshkov-Glick model (LMGm) serves as the minimal model of interacting Ising spins that demonstrates this behavior.

Recently, it was shown that additional material constants of strain gradient elasticity (SGE) can be identified for brittle and quasi-brittle materials based on the analysis of experimental data on the crack size effect. In the present paper, we perform precise numerical simulations within SGE and derive regression relations for processing experimental data from standard fracture mechanics tests under pure Mode I loading conditions (CCT, SENT, SENB). We consider the simplified SGE, whose constitutive relations contain a single length scale parameter $\ell$ in addition to the classical elastic constants. We show that, for brittle materials, this parameter can be explicitly identified as $\ell \approx 0.362 (K_{Ic}/\sigma_{ult})^2$. This identification ensures that the fracture loads predicted by classical linear elastic fracture mechanics (LEFM) and by the simplified SGE coincide for relatively long Mode I cracks. However, within the simplified SGE, these fracture loads are evaluated from the nonsingular stress field using the maximum principal stress criterion. For quasi-brittle materials, we derive regression relations that describe the non-classical size effect on strength. This effect is usually treated within nonlinear fracture mechanics but can be naturally captured by SGE. Examples of identification of the length scale parameter $\ell$ based on the established relations and the experimental data for chopped fiber composites and for porous and dense quasi-brittle ceramics are presented.

Artificial intelligence (AI) is redefining the landscape of polymer science. Although numerous AI applications have been introduced in this field, the roles of polymer encoding strategies and different applications of AI models in polymer design remain insufficiently understood. Here, we build upon the foundation of polymer databases to critically examine the performance and applicability of current encoding strategies across different use cases. We then focus on two major AI application domains, property prediction and inverse design, to evaluate the strengths, weaknesses and suitable scenarios for various model architectures. Finally, we emphasize the significance of the online platforms for promoting data accessibility and accelerating the migration from experience-based discovery toward AI-driven innovation in polymer science and engineering. Through these discussions, we aim to provide practical guidance for future research and development in AI-assisted polymer design.

Artificial spin ices (ASIs) are decorations of single domain nanomagnets on geometric lattices allowing for study of magnetic interactions on easily varied lattice geometries. We extend the study of ASIs on single rhomb tilings by simulating an ASI with the aperiodic hexagonal $H_{\frac{1}{2}\frac{1}{2}}$ tiling as the base structure, and the periodic dice lattice for additional comparison. Using a point dipole metropolis Monte Carlo approach, we cool our arrays of nanoislands to form a low energy configuration, assessing individual vertex excitations as identified through complementary micromagnetic simulations. Using the energy and charge landscape of final spin states, we propose a potential ground state spin configuration for the aperiodic system.

The fabrication of highly ordered laser-induced periodic surface structures (LIPSS) on thin metallic films is dictated, predomaninatly, by a synergy of periodic electromagnetic energy deposition and complex fluid dynamics. In this work, we present a combined experimental and theoretical study on the formation of ultra-regular LIPSS on 32-nm-thick Au films using a double-pulse femtosecond laser scheme. We demonstrate that for thin films, the excitation of coupled Surface Plasmon Polaritons (SPPs) at both interfaces dictates the initial energy distribution. On the othe hand, the final morphology is greatly influenced by hydrodynamical processes. Interestingly, due to the low electron-phonon coupling of Au and the high thermal confinement of the thin film, single-pulse irradiation leads to uncontrolled hydrodynamic instabilities a non uniform topographies. Thus, we demonstrate that a double-pulse approach with an optimized interpulse delay ({\Delta}{\tau}=1.2 ns) effectively controls the melt duration and viscosity, suppressing complex fluid motion and promoting the growth of highly ordered arrays. These structures support narrow surface lattice resonances (SLRs) suitable for high-sensitivity plasmonic biosensing.

Though quantum computing naturally offers an advantage for simulations of real-time quantum systems, implementing Imaginary-Time Evolution (ITE) is comparatively more difficult. Nevertheless, quantum implementations of ITE are useful both in cases where classical implementations have associated sign problems, and also as an exact method of preparing eigenstates on quantum computers. In this work we present an algorithm to obtain ITE of a generic quantum Hamiltonian by performing analytic continuation of measured real-time correlation functions. We present simulations and demonstrations on IBM quantum hardware of 1D Fokker-Planck equations for classical diffusion process and imaginary-time evolution of integrated correlation functions in 1D quantum mechanical scattering as examples to demonstrate the effectiveness of the method.

Nonlinear multiphoton conversion processes are theoretically and experimentally challenging systems in quantum optics and related areas. These phenomena bring remarkable quantum properties and can be of fundamental relevance in quantum information and computation applications. Based on recent experimental advances and the possible uses in generalized three-photon squeezing, we investigate degenerate three-photon parametric down-conversion generated inside a cavity fed by a classical pump. In addition, we consider that the process is stimulated by a coherent driving mode and subjected to dissipation by spontaneous emission of the cavity. A treatment using phase-space methods and stochastic differential equations is applied and the stability conditions of its steady states are found. We find that the system does not exhibit multistability, instead it has a limited parameter region leading to a single stable steady branch, alongside multiple unstable branches. Focusing on the stable steady states and linearizing the dynamics around them, we calculate the spectral densities of the quadrature variables. We identify and characterize the squeezing of three-photon down-conversion. Moreover, since the quasi-probability differential equations of the higher-order multiphoton processes have higher-order derivatives, hindering their mapping into stochastic differential equations, we make use of a positive Wigner function approach to calculate two-dimensional spectral densities associated with three-time correlation functions, with the goal of studying non-Gaussian properties of the system.

We show that the conventional multipolar Hamiltonian is qualitatively modified when the photonic vacuum breaks inversion or time-reversal symmetry. By explicitly applying the Power-Zienau-Woolley transformation, we derive the resulting multipolar Hamiltonians for two idealized chiral photonic environments: a spatial-chiral vacuum, which breaks inversion symmetry, and a temporal-chiral vacuum, which breaks time-reversal symmetry. In the spatial-chiral case, the transformation generates an inversion-breaking self-energy, whereas in the temporal-chiral case it produces an additional Zeeman-like energy. Using a trapped hydrogen-like atom and a charged harmonic oscillator in cavities as minimal examples, we show that these symmetry-dependent terms lead to characteristic spectral shifts. Our work provides a general framework for describing light-matter interactions in chiral quantum electrodynamics and identifying the associated symmetry-dependent effects on cavity-embedded atoms, molecules, and quantum materials.

We identify different regimes of quantum state transfer in long-range coupled spin-$\frac{1}{2}$ systems, where naturally occurring power-law interactions enable rapid, high-fidelity transfer with minimal engineering. Across a broad range of interaction profiles, from effectively nearest-neighbour coupling to Coulomb interactions, we show how long-range connectivity fundamentally reshapes the mechanisms underlying information propagation within such systems. For effectively short-range interactions, transfer follows familiar ballistic transfer dynamics: an initially localised excitation spreads across many eigenmodes concentrated within the approximately linear region of the spectrum, enabling robust wavepacket motion. In contrast, increasing long-distance interactions via lowering the power-law exponent $\alpha$ ($\alpha=1-2$) drives a striking transformation, where the initial state becomes confined to progressively fewer eigenmodes, ultimately reducing the dynamics to the coherent participation of only a few states corresponding to the highest eigenenergies. This spectral localization gives rise to emergent long-range oscillations between distant sites, revealing a distinct – and faster – transfer mechanism arising from the intrinsic structure of long-range quantum interactions rather than from full-system engineering pathways.

We present an efficient method for computing the real-space propagators (lattice Green's functions) of any tight-binding Hamiltonian in the presence of a Fermi sea with carrier concentration $x$. The method is valid for any lattice, dispersion, and dimension, provided the corresponding $x=0$ propagators are known. We show that suitable combinations of the finite-$x$ particle-addition propagators have a real or imaginary part trivially related to their $x=0$ counterpart, while the remaining part follows from a Kramers-Kronig relation that can be evaluated for all energies at once using the fast Fourier transforms. The computational cost is therefore independent of the dimensionality, unlike that of direct Brillouin-zone integration. The particle-removal propagators follow from general identities. We validate the method against direct integration for hypercubic lattices in one, two, and three dimensions, and use the 2D square lattice to illustrate how the shape of the Fermi surface is imprinted on the spatial structure of the propagators. In particular, at energies far outside the band, the propagator maps converge to the Fraunhofer diffraction pattern whose aperture is the unoccupied part of the Brillouin zone.

Electron-doped strontium titanate has emerged as a prototypical quantum ferroelectric metal. It provides a fertile ground to explore how ferroelectric instability intertwined with itinerant electrons creates quantum phenomena, including unconventional superconductivity. Despite extensive studies, the microscopic origin of the ferroelectric transition remains unsettled, with distinct interpretations based on displacive mechanism driven by soft mode and order-disorder alignment of local dipoles. In particular, the local dipoles form nanoscale, spatially heterogeneous clusters, termed polar nanoregions, posing a significant challenge for probing or manipulating them. Here, using rotational anisotropy second harmonic generation, a symmetry-resolved probe, we quantify the orientational statistics of polar nanoregions in dilute electron-doped Sr$_{0.95}$Ba$_{0.05}$Ti$_{1-x}$Nb$_x$O$_3$. By tracking the alignment and meltdown of polar nanoregions in thermal cycles, we unambiguously demonstrate the order-disorder nature of the ferroelectric transition. We further show that, above transition temperature, femtosecond optical fields enable deterministic control of otherwise disordered polar nanoregions, realizing reversible write and readout of polar textures on ultrafast timescales. Our findings provide new insight into ferroelectric instability and establish an all-optical route of controlling polar metal systems where conventional electrical approaches are not feasible.

Molecular self-assembly on solid surfaces has been the subject of extensive research, motivated by both fundamental and technological interests. On the fundamental side, these studies seek to elucidate the mechanisms governing molecular self-assembly and the resulting surface structures. From an applied perspective, they provide a route toward controlling surface reactions and engineering molecular electronic devices. Here, based on first-principles density functional theory calculations, we present a comprehensive study of self-assembled molecular wires (MWs), composed of graphyne (GY(1D)) and graphdiyne (GYD(1D))-like structures, adsorbed on Au(111), Ag(111), and Al(111) surfaces. Our total-energy calculations reveal that non-aligned MW arrays are energetically preferred on all three metal substrates. The GY(1D) and GYD(1D) molecular wires interact with the metal surfaces through van der Waals (vdW) forces, while their molecular orbitals do not contribute to the formation of metallic interface states. Simulated X-ray photoelectron spectroscopy (XPS) spectra reveal that the C 1s spectral features of the molecular wires are largely preserved upon adsorption, while the absolute binding energies undergo a substantial downshift that is nearly independent of the metal substrate, indicating that metallic screening effects dominate the adsorption-induced core-level shifts. Electronic band-structure calculations further show that the semiconducting character of the molecular wires is retained, resulting in vdW metal-semiconductor heterostructures in which the semiconducting component consists of one-dimensional semiconducting channels. These findings demonstrate that self-assembled graphyne- and graphdiyne-based molecular wires on metal surfaces provide a promising platform for the realization of low-dimensional molecular electronic devices.

We formulate a non-Abelian theory of network compatibility in which dynamical transformations reside on the links. Gauge covariance follows from the freedom to choose local representation frames, while plaquette holonomies quantify the incompatibility of closed-loop transformations. For an SU(2) model on the complete simplicial 2-complex with quenched random plaquette couplings, parallel-tempering simulations reveal a continuous disorder-driven phase transition characterized by the network compatibility $M_P$. As the disorder strength approaches the critical value, the compatibility drops rapidly to a value that decreases with system size, while the frustration energy of the network sharply rises. Moreover, analysis of connected replica-overlap width provides no evidence for thermodynamic replica-symmetry breaking. Instead, the high-disorder regime sustains a nearly constant integrated adjacent correlation as the system size increases. Therefore, rather than a frozen gauge glass or a featureless disordered “gas” phase, dense topological frustration produces a non-glassy correlated gauge liquid in which individual pair correlations are geometrically diluted while a finite integrated correlation survives.

Ferroelectrics enable large charge doping of two-dimensional overlayers, but the coexistence of switching and nonswitching charge dynamics complicate electro-optical analysis. Here, we investigate the optoelectronic response of a ferroelectric/graphene device under 365 and 530 nm illumination, disentangling effects on ferroelectric dipole alignment from extrinsic current pathways. Graphene acts as a high-gain sensor, amplifying subtle polarization dynamics into a pronounced resistance difference. By resolving switching and nonswitching channels in dark and illuminated conditions, we reveal a competition between photovoltaic charge screening and defect-assisted excitation that governs device electrostatics. Above-band gap illumination generates free carriers that induce leaky ferroelectric hysteresis and suppress the graphene resistance ratio between opposite remanent polarization states from 290% to 15% due to dynamic photovoltaic charge screening. In contrast, 530 nm illumination primarily induces charge redistribution in ferroelectrics via defect-state excitation, leading to a significantly weaker suppression of the resistance variation of graphene. These results establish practical guidelines for selecting photon energy and intensity to either preserve remanent polarization while tuning channel doping or deliberately reconfigure polarization through optical programming.

We consider a Su-Schrieffer-Heeger(SSH)-type trimer model with next-nearest-neighbor(NNN) interaction and balanced loss-gain(BLG) to study the combined effect of lattice symmetries, topology, non-hermiticity and general boundary conditions(GBC)on the existence of flat band and the nature of Bulk-Boundary correspondence(BBC). We derive the necessary and sufficient conditions for the existence of an entirely real spectrum under the periodic boundary condition(PBC). The exact expressions for the compact localized states(CLS) and energy eigenvalues corresponding to flat bands are derived analytically under the PBC. We establish topological phase transitions(TPT) for PT-symmetry and pseudo-chiral symmetry through the computation of the Zak phase and sub-lattice Zak phase, respectively. The Hamiltonian under the open boundary condition(OBC) is studied numerically, and edge states are observed in the topologically non-trivial phase, thereby establishing the non-hermitian BBC. The CLS exists in both bulk and the boundary for systems having only pseudo-chiral symmetry, and an additional PT-symmetry destroys the CLS at the boundary. We generalize a known formalism to study the same Hamiltonian under GBC, and derive analytic expressions for the energy and eigenstates for a class of boundary conditions in parametric ranges which admit flat band under the PBC. The edge states for these boundary conditions, including the OBC, are obtained analytically in the topologically non-trivial phase, thereby establishing BBC. The non-hermitian skin effect(NHSE) is seen in the model with reciprocal bulk interaction and strongly non-reciprocal boundary terms. The winding number based on spectral topology is computed analytically.

We introduce an incidence-based random walk on the edges of a random two-dimensional simplicial complex with a complete $1$-skeleton and independently retained triangular faces. The dynamics combine two transport channels, one mediated by vertices and the other by triangular faces, through an effective transition operator controlled by a mixing parameter $q$. This construction isolates the effects of higher-order connectivity without modifying the underlying pairwise support of the walk. We characterize the model through structural observables, spectral relaxation, stationary localization, and first-passage transport. Our results show that partial face retention generates heterogeneous higher-order connectivity, giving rise to a pronounced transport bottleneck at intermediate face densities. In this regime, the second-largest eigenvalue modulus, the inverse participation ratio of the stationary distribution, and the mean first-passage time all exhibit non-monotonic behavior, reaching their largest values at intermediate face densities. The corresponding first-passage-time distributions reveal an enhanced probability of unusually long trajectories. Together, these results establish a simple framework for investigating how heterogeneous higher-order connectivity reshapes spectral and transport properties beyond pairwise network dynamics.