Papers

WSe2 p-MOSFETs with Nb-doped WS2 contacts formed using atomic layer deposition are demonstrated. The devices are fabricated using a technique that aligns the contact metallization with the Nb-doped WS2 contacts using a selective oxidation process. Devices with source/drain spacing of 0.15 um have on-state current of 103 uA/um at VDS = -1 V at a channel carrier concentration of ~ 7.5 x 1012 cm-2. The results provide a promising CMOS-compatible pathway to create low-resistance contacts to 2D-channel transistors.

Through flat-folding, origami provides an extremely compact packaging strategy for deployable structures in aerospace, architecture, and robotics. However, origami's flat, volumeless facets limit the formation of smooth curvature, restricting its applicability in systems where smooth curved geometries are essential for performance, such as aerospace and electromagnetic communication systems. Here, we propose volumetric origami that preserves smooth curvature and an inverse design method that generates flat-foldable volumetric origami for given target curved surfaces. The flat-foldability enables arbitrarily prescribed compactness in volumetric origami folding, with its stowage efficiency governed by the number of cells and the target profile. The structural integrity and engineering feasibility of volumetric origami are validated through successful flight testing of a UAV equipped with flat-foldable volumetric origami wings replicating a target airfoil. Our approach bridges the gap between planar origami and the curvature requirements of engineering systems, expanding design freedom for curved structures under stringent spatial constraints.

We study the topology of the order parameter in the intermediate phase between the superconducting and time-reversal symmetry breaking transitions of a $p_x+ip_y$ superconductor under strain. The application of in-plane strain reduces the underlying crystal symmetry and lifts the degeneracy of the critical temperature between the $p_x$ and $p_y$ orbitals, resulting in a Dirac cone structure in the thermodynamic phase diagram. When the strain is varied adiabatically along a closed path enclosing the Dirac cone, the order parameter acquires a Berry phase of $\pi$, which originates from a half rotation of the superconducting gap function. This half rotation leaves a topological signature in the superfluid stiffness tensor, making it directly observable through the geometry of vortices and the upper critical field.

A necessary condition for understanding and predicting the properties of any material is knowledge of microscopic parameters which control these properties in a state of thermodynamic equilibrium. One can show (see, e.g., Ref.\,\cite{VK_book}), that in superconductors these parameters are the radius of the orbital motion of electrons bound in Cooper pairs $R_0$ and the radius of the field-induced currents $r_i$ caused by precession of the pairs; one more parameter, associated with $r_i$, is the number density of Cooper pairs $n_{cp}$. In this paper we report on the first measurements of these parameters in a type-II superconductor (niobium) by SANS (small-angle neutron scattering). Other approaches to measuring the microscopic parameters are considered. Our work suggests novel avenues for studying superconductivity, important for disclosing its mechanisms in superconductors of all kinds.

In crystalline solids, the electronic polarization follows the generalized Neumann's principle, under which all crystallographic point groups can, in principle, support ferroelectric polarization. However, in high-symmetry structures, polarization is constrained by symmetry operations and becomes quantized into discrete values. We demonstrate that this quantized polarization (QP) is not a mathematical artifact but a symmetry-protected invariant that encodes intrinsic information about a material's symmetry and electronic structure. Because of its discrete and non-continuous nature, when two materials with different QPs form an interface, their bulk polarization states cannot be connected adiabatically, compelling the system to develop pronounced interfacial responses: such as metallic states, bound charges, or strong lattice distortions. This theoretical framework provides a unified reinterpretation of classical systems such as the LaAlO$_3$/SrTiO$_3$ interface, revealing it as a prototypical case of QP mismatch. By establishing QP as a fundamental bulk invariant, our work uncovers a universal mechanism governing interfacial electronic phenomena and opens new pathways for the design of functional quantum materials through engineered polarization mismatch.

Organic photovoltaic (OPV) materials offer a promising path toward sustainable energy generation, but their development is limited by the difficulty of identifying high performance donor and acceptor pairs with strong power conversion efficiencies (PCEs). Existing design strategies typically focus on either the donor or the acceptor alone, rather than using a unified approach capable of modeling both components. In this work, we introduce a dual machine learning framework for OPV discovery that combines predictive modeling with generative molecular design. We present the Organic Photovoltaic Donor Acceptor Dataset (OPV2D), the largest curated dataset of its kind, containing 2000 experimentally characterized donor acceptor pairs. Using this dataset, we develop the Organic Photovoltaic Classifier (OPVC) to predict whether a material exhibits OPV behavior, and a hierarchical graph neural network that incorporates multi task learning and donor acceptor interaction modeling. This framework includes the Molecular Orbital Energy Estimator (MOE2) for predicting HOMO and LUMO energy levels, and the Photovoltaic Performance Predictor (P3) for estimating PCE. In addition, we introduce the Material Generative Pretrained Transformer (MatGPT) to produce synthetically accessible organic semiconductors, guided by a reinforcement learning strategy with three objective policy optimization. By linking molecular representation learning with performance prediction, our framework advances data driven discovery of high performance OPV materials.

Quantifying complexity in physical systems remains a fundamental challenge, and many proposed measures fail to capture the structural features that intuitive or theoretical considerations would demand. Among them, the Lopez-Ruiz-Mancini-Calbet (LMC) statistical complexity has been widely cited due to its simplicity and analytic tractability. Here, we examine the performance and limitations of the LMC measure in a controlled physical setting: a two-dimensional XY model studied through Monte Carlo simulations. By computing LMC complexity at each step of the system's relaxation dynamics, and directly comparing these values with the evolving dipole configurations, we show that LMC complexity systematically fails to identify states of high structural complexity. In particular, the measure often assigns maximal complexity to nearly equilibrated configurations while underestimating vortex-rich intermediate states. We further show that the time derivative of LMC complexity contains more meaningful dynamical information. We propose that future measures incorporate directionality and dynamical sensitivity to better reflect the emergence and decay of organization in nonequilibrium systems.

The issue of whether $d$-wave superconductivity (SC) occurs in the square-lattice Hubbard model with $U$ of order of the bandwidth has been one of the most debated issues to emerge from the study of high temperature SC. Here, we report variational results on eight-leg cylinders with next-nearest-neighbor hopping in the range $-0.5 t \leq t'\leq 0.25 t$ with $U = 8t$ and $12t$ and doped hole concentrations $\delta=1/12$ and $1/8$. For $t'\leq 0$, the ground-state appears to be a charge-density wave (CDW) of one sort or another with SC correlations that are extremely short-ranged. In contrast, in some cases, the local magnetic order has a correlation length greater than half the cylinder width - suggestive that magnetic order might also arise in the 2D limit. For $t'>0$, our results depend more strongly on boundary conditions (periodic vs antiperiodic), making it still harder to correctly guess whether SC or CDW correlations dominate in the 2D limit. These results were obtained employing matrix-product states with bond dimensions large enough that energy differences as small as $10^{-3}t$ per site can be resolved.

Debt recycling is a leveraged equity management strategy in which homeowners use accumulated home equity to finance investments, applying the resulting returns to accelerate mortgage repayment. We propose a novel framework to model equity and mortgage dynamics in presence of mortgage interest rates, borrowing costs on equity-backed credit lines, and tax shields arising from interest deductibility. The model is calibrated on three jurisdictions – Australia, Germany, and Switzerland – representing diverse interest rate environments and fiscal regimes. Results demonstrate that introducing positive interest rates without tax shields contracts success regions and lengthens repayment times, while tax shields partially reverse these effects by reducing effective borrowing costs and adding equity boosts from mortgage interest deductibility. Country-specific outcomes vary systematically, and rental properties consistently outperform owner-occupied housing due to mortgage interest deductibility provisions.

We study the coupled twin-diamond chain, a decorated one-dimensional Ising model motivated by the magnetic structure of $\mathrm{Cu}_{2}(\mathrm{TeO}_{3})_{2}\mathrm{Br}_{2}$. By applying an exact mapping to an effective Ising chain, we obtain the full thermodynamic description of the system through a compact transfer-matrix formulation. The ground-state analysis reveals five distinct phases, including two frustrated sectors with extensive degeneracy. These frustrated regions give rise to characteristic entropy plateaus and separate the ordered phases in the zero-temperature diagram. At low temperatures the model exhibits peculiar sharp yet continuous variations of entropy, magnetization, and response functions, reflecting clear signatures of pseudotransition behavior. The coupled twin-diamond chain thus provides an exactly solvable setting in which competing local configurations and internal frustration lead to pronounced dual pseudocritical features in one dimension.

Electric polarization in the absence of an externally applied electric field is a key property of polar materials, but the standard interpolation-based ab initio approach to compute polarization differences within the modern theory of polarization presents challenges for automated high-throughput calculations. Berry flux diagonalization [J. Bonini et. al, Phys. Rev. B 102, 045141 (2020)] has been proposed as an efficient and reliable alternative, though it has yet to be widely deployed. Here, we assess Berry flux diagonalization using ab initio calculations of a large set of materials, introducing and validating heuristics that ensure branch alignment with a minimal number of intermediate interpolated structures. Our automated implementation of Berry flux diagonalization succeeds in cases where prior interpolation-based workflows fail due to band-gap closures or branch ambiguities. Benchmarking with ab initio calculations of 176 candidate ferroelectrics, we demonstrate the efficacy of the approach on a broad range of insulating materials and obtain accurate effective polarization values with fewer interpolated structures than prior automated interpolation-based workflows. Our real-space heuristics that can predict gauge stability a priori from ionic displacements enable a general automated framework for reliable polarization calculations and efficient high-throughput screening of chemically and structurally diverse polar insulators. These results establish Berry flux diagonalization as a robust and efficient method to compute the effective polarization of solids and to accelerate the data-driven discovery of functional polar materials.

Carbon nanotube (CNT)-polymer composites are widely engineered using surface coatings and chemical treatments to improve interfacial bonding and load transfer. It has been suggested in the nanocomposite literature that nanotube curvature, in conjunction with surface functionalization such as polydopamine (PDA) coating, could serve as an additional control knob for tuning interfacial bonding and energy dissipation in polymer-CNT systems. While experimental and simulation studies have demonstrated the benefits of PDA functionalization, the fundamental mechanism by which nanotube curvature modulates interfacial energy flow and mechanical polarity remains unresolved. This gap is sharpened by a persistent paradox: identical PDA functionalization strengthens some CNT-polymer systems while weakening others, a curvature-dependent inconsistency that has remained unexplained. Here, we employ reactive molecular dynamics (ReaxFF) simulations to resolve how curvature and PDA functionalization jointly govern interfacial energy evolution in CNT-polyvinyl alcohol (PVA) nanocomposites. Our investigation reveals that curvature and PDA functionalization jointly produce opposite regimes of interfacial energy flow: high-curvature CNTs generate dissipative, frictional interphases, whereas low-curvature CNTs confine energy in rigid, cohesive shells. This polarity inversion originates from a curvature-induced transition in PDA adsorption geometry that transforms the interphase from an energy-releasing to an energy-storing configuration. These results establish curvature as a fundamental design parameter for engineering polymer-nanotube interfaces, offering a predictive route to tune interfacial energy flow, mechanical resilience, and transport properties beyond the limits of conventional chemical functionalization.

The single-layered perovskite Ca$_2$RuO$_4$, characterized by a 4$d^4$ electron configuration, has been studied from first principles using density functional theory (DFT) using the generalized gradient approximation, with inclusion of strong on-site Coulomb interactions and spin-orbit coupling (GGA+SO+$U$), in the framework of the fully relativistic, spin-polarized Dirac linear muffin-tin orbital (LMTO) band-structure method. This approach enabled a comprehensive investigation of the electronic structure of Ca$_2$RuO$_4$ through the modeling of relevant spectra obtained from synchrotron-based techniques widely used to probe electronic properties, with a primary focus on resonant inelastic X-ray scattering (RIXS) at the Ru $L_3$ and O $K$ edges. The calculated spectra were thoroughly analyzed with available experimental data reported in the literature. The good agreement between our results and experimental observations for Ca$_2$RuO$_4$ enables a conclusive interpretation of key features in the spectra obtained from the aforementioned techniques. Consequently, this enables us to describe its electronic properties and to establish a solid theoretical approach suitable for routine modeling of spectra, particularly from RIXS, aimed at characterizing the electronic structure and properties of similar or more complex strongly correlated, technologically relevant materials.

Floquet engineering severs as a forceful technique for uncovering high Chern numbers of quantum anomalous Hall (QAH) states with feasible tunability in high-order topologically insulating plumbene, which is readily accessible for experimental investigations. Under the irradiation of righthanded circularly polarized light, we predict a three-stage topological phase transition in plumbene, whether it is in a free-standing form or grown on h-BN. Initially, a metallic state evolves into a K(K')-valley-based QAH state with a Chern number of -8, which then decreases to -6 after the valley gap closes. Finally, a band inversion occurs at the $\Gamma$ point, resulting in a multichannel QAH state with C = -3. The trigonal warping model accounts for both K(K')-valley-based and $\Gamma$-pointbased QAH states. Additionally, growing plumbene on a non-van-der-Waals substrate eliminates the K(K')-valley-based topology, leaving only the $\Gamma$-point-based QAH state with C = +3. Our findings propose the tunability of various high Chern numbers derived from high-order topological insulators, aiming to advance the next-generation dissipationless electronic devices.

We study neural-network approximation of density functionals in a Banach-space setting. Since the exact continuum functionals are discontinuous in the natural density topology, we apply $p$-Moreau-Yosida regularization. We construct finite-rank ReLU networks that preserve convexity and nonnegativity, lie below the regularized functional, and approximate it uniformly on compact sets. For energies obtained by minimization over compact density sets, we account exactly for the energy shift caused by regularization and bound the remaining error by the localization on these compact sets and network approximation errors. We apply this framework to canonical and grand-canonical density-functional theory at fixed particle number and fixed mean particle number, respectively. We obtain uniform energy convergence on norm-compact classes of external potentials, including molecular Coulomb potentials. We illustrate our results through numerical experiments on a simple model system.

We show that continuous random walks (diffusion) in the Poincaré upper half-plane $\mathbb{H}^2 = \{(x,y)| y>0\}$ provide a unified description of three seemingly unrelated phenomena: (i) the non-analytic divergence of the correlation length at the Berezinskii–Kosterlitz–Thouless (BKT) transition; (ii) the emergence of a Lifshitz tail (LT) in the 1D statistics of rare events; and (iii) the appearance of Kardar–Parisi–Zhang (KPZ) scaling in the fluctuations of stretched random walks constrained above an impermeable disc. We adapt the renormalization-group (RG) analysis originally developed for the Schrödinger equation with mixed boundary conditions in a 2D conformally invariant potential to the spectral problem in $\mathbb{H}^2$, and identify the conditions under which BKT-type behavior emerges. We show that the same RG equations can be interpreted in terms of the statistics of random walks in the large-deviation regime through an instanton approach, leading to Lifshitz tails (LT) in the associated spectral problem. We further derive KPZ-type scaling for the fluctuations of stretched random walks near the boundary of a disc in $\mathbb{R}^2$ and emphasize the similarity of this behavior with the boundary fluctuations of paths in $\mathbb{H}^2$ analyzed using a WKB approach.

Random-matrix theory helps disentangle signal from noise in large data sets. We analyze rectangular $p \times q$ matrices $W = W_0 + M$ in which the noise $M$ generates a Marchenko-Pastur bulk, whereas the signal $W_0$ injects an extensive set of degenerate singular values. Keeping $\mathrm{rank}$ $W_0/q$ finite as $p,q \to \infty$, we show that the trace of the resolvent of $W^{\top} W$ obeys a quartic equation for one degenerate signal, yielding an exact spectral density, and derive explicit asymptotics in the strong-signal regime. We map out a detailed generalized Baik-Ben Arous-Péché (BBP) phase diagram and clarify how a finite density of spikes reshapes the bulk edges. We further derive a $1/3$-scaling law for the critical signal strength in terms of the rank ratio for rectangular matrices in the finite-to-extensive-rank crossover. Numerical simulations validate the theory and illustrate its relevance for high-dimensional inference tasks with multiple degenerate signals and more general signal distributions.

We develop a unified framework for Berezin integrals over Grassmann variables that establishes master identities for exponential quadratic fermionic forms and linear fermionic forms coupled to both bosonic and fermionic sources. The construction is rigorous for both real and complex fermions in arbitrary dimensions and remains well-defined even when the underlying matrices are singular. Our main mathematical results appear in two master theorems. Theorem 12 provides a comprehensive identity for Berezin integrals over Grassmann variables for real fermions with mixed bosonic-fermionic sources, applicable to any antisymmetric matrix. Its complex analogue, Theorem 13, yields corresponding determinant-based representations. Together, they serve as generating functionals for a wide range of combinatorial and physical models. Key applications include the dimer, monomer-dimer, matching, and almost-matching problems. We revisit the Kasteleyn theorem for planar dimers using Berezin integrals. We construct monomer-dimer systems through the Monobisyzexant (Mbsz) function, which generalizes the Hafnian to incorporate monomer contributions and admits a Pfaffian-sum representation for planar graphs (Theorem 5); and practical techniques for handling singular matrices via unitary block decomposition (Theorem 6) and spectral analysis. We further present explicit mappings between Hafnians and Pfaffians and their submatrix generalizations (Hafnianinhos and Pfaffianinhos); an alternative source-ordered Berezin integral representation for spanning trees and forests using complex bosonic sources that regularizes the Laplacian zero mode (Theorem 10). Overall, this work offers a flexible toolkit for the theoretical analysis and computational implementation of graph-based models and lattice field theories using Berezin integrals over Grassmann variables .

Lévy noise influences diverse non-equilibrium systems across scales, including quantum devices, active biological matter, and financial markets. While such noise is pervasive, its overall impact on activated transitions between metastable states remains unclear, despite prior studies of specific noise forms and scaling limits. In this work, we introduce a unified framework for Lévy noise defined by its finite intensity and independent stationary increments. By identifying the most probable transition paths as minimizers of a stochastic action functional, we derive analytical scaling laws for escape rates under weak noise, thereby extending the classical Arrhenius law. Our results demonstrate that Lévy noise universally enhances escape efficiency by reducing the effective potential barrier compared to Gaussian noise with equivalent intensity. Strikingly, even vanishingly weak Lévy noise can exponentially increase escape rates across a broad range of amplitude distributions. This phenomenon arises from discontinuous most probable transition paths, where escape occurs via finite jumps. We validate these paths through the cumulant-generating function, a path integral representation, the mean first passage time and numerical simulations. Our findings reveal fundamental distinctions in escape dynamics under thermal and athermal fluctuations, suggesting new strategies to optimize switching processes in metastable systems through engineering noise properties.

Two-dimensional (2D) nanochannels have emerged as a pivotal platform for exploring nanoscale hydrodynamics and electrokinetics. Conventional fabrication methods to make nanochannels often introduce polymer contamination and require lengthy processing, limiting device performance and scalability. Here we introduce the Mask & Stack method, employing silicon nitride stencil mask combined with dry transfer stacking to rapidly fabricate ultraclean vdW nanochannels within hours. This polymer-free approach preserves pristine interfaces, confirmed by atomic force microscopy and Raman spectroscopy, and yields nanochannel devices exhibiting reproducible ionic transport and long-term stability. The streamlined process is compatible with diverse 2D materials and promising for upscale production. Our method advances the fabrication of nanofluidic and 2D heterostructure devices, facilitating applications in quantum transport, photonics, energy harvesting, and sensing technologies requiring high-throughput, contamination-free heterostructure architectures.

Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. We introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and transform fractal dimensions. Starting from critical configurations, such as the O$(n)$ loop and fuzzy Potts models, successive coarse-graining generates a hierarchy of distinct yet critical generations. Using the conformal loop ensemble, we derive exact, generation-dependent fractal dimensions, which are quantitatively confirmed by large-scale Monte Carlo simulations. The evolutionary trajectory depends not only on the universality class of the initial state but also on whether it possesses a two-state critical structure, leading to different critical exponents starting from site and bond percolation. These results establish a general geometric mechanism for evolving fractal dimensions, in which scale invariance persists across generations.

Charge to spin (orbital) momentum conversion phenomena enclose great potential for advancing applications in spin/orbitronics. Although current-induced magnetic moment accumulation is crucial both for fundamental understanding and practical applications, direct quantifications are scarce. Optical polarization measurements, namely magneto-optical Kerr rotation (MOKE) ($\theta_K$), have been used to get direct evidence of magnetic accumulation perpendicular to a current flow density ($J$) in late transition metals (Pt) as well as in light transition elements (Ti, Cr), and used to conclude evidence of spin or orbital momentum accumulation. However, discrepancies of the reported $\theta_K/J$ values, exceeding one order of magnitude, together with early claims that conventional MOKE experiments were not a suitable tool, is prompting revisions of methods and results. Here, we report on a new methodology for MOKE measurements that solves known bottlenecks. We obtain a sensitivity of $(354 \pm 27)$ nV/nrad and use the designed protocol to measure $|\theta_K^S/J| = (7.92 \pm 1.94)$ nrad/$(10^7$ A/cm$^2)$ and $|\theta_K^P/J| = (6.89 \pm 1.74)$ nrad/$(10^7$ A/cm$^2)$ in a 50 nm thick Pt bar for S and P polarized incident light, respectively.The extracted value of $|\theta_K^S/J|$ is significantly smaller, about a 7-fold reduction, than previous results on a nominally identical device. Given that differences in the microstructure of Pt films cannot account for such large discrepancy, this implies that experimental procedures and models should be revised accordingly.

Two-terminal spintronic devices remain challenging to model under realistic operating conditions, where the interplay of complex electronic structures, correlation effects and bias-driven non-equilibrium dynamics may significantly impact charge and spin transport. Existing ab initio methods either capture bias-dependent transport but neglect dynamical correlations or include correlations but are restricted to equilibrium or linear-response regimes. To overcome these limitations, we present a framework for steady-state quantum transport, combining density functional theory (DFT), the non-equilibrium Greens' function (NEGF) method, and dynamical mean-field theory (DMFT). The framework is then applied to Cu/Co/vacuum/Cu and an Fe/MgO/Fe tunnel junction. In Co, correlations drive a transition from Fermi-liquid to non-Fermi-liquid behavior under finite bias, due to scattering of electrons with electron-hole pairs. In contrast, in the Fe/MgO/Fe junction, correlation effects are weaker: Fe remains close to equilibrium even at large biases. Nevertheless, inelastic scattering can still induce partly incoherent transport that modifies the device's response to the external bias. Overall, our framework provides a route to model spintronic devices beyond single-particle descriptions, while also suggesting new interpretations of experiments.

Glassy polymers are central to engineering applications, yet their viscoelastic response over broad frequency and temperature ranges remains difficult to characterize. We extend non-affine deformation theory by incorporating a time-dependent memory kernel within the Generalized Langevin Equation for atomistic non-affine motions, yielding frequency-dependent mechanical response. Applied to poly(methyl methacrylate) (PMMA), the method captures the shear modulus and relaxation spectrum across more than twenty decades in frequency, from hundreds of terahertz to the millihertz regime, thus bridging polymer mechanics from ordinary to extreme scales. Our predictions show quantitative consistency with independent estimates from oscillatory-shear molecular dynamics, Brillouin scattering, ultrasonic spectroscopy, Split-Hopkinson testing, and dynamic mechanical analysis (DMA), demonstrating a unified theoretical-computational route for multiscale characterization of polymer glasses.

The presence of defects strongly influences semiconductor behavior. However, predicting the electronic properties of defective materials at finite temperatures remains computationally expensive even with density functional theory due to the large number of atoms in the simulation cell and the multitude of thermally accessible configurations. Here, we present a neural network-based framework to investigate the electronic properties of defective semiconductors at finite temperatures efficiently. We develop an active learning approach that integrates two advanced equivariant graph neural networks: MACE for atomic energies and forces and DeepH-E3 for the electronic Hamiltonian. Focusing on representative point defects in GaAs, we demonstrate computational accuracy comparable to density functional theory at a fraction of the computational cost, predicting the temperature-dependent band gap of defective GaAs directly from larger scale molecular dynamics trajectories with an accuracy of few tens of meV. Our results highlight the potential of equivariant neural networks for accurate atomic-scale predictions in complex, dynamically evolving materials.

We present an exact, time-resolved theory for a two-dimensional chiral active Brownian particle (cABP) with translational inertia. Using a Laplace-transform moment hierarchy, we derive closed-form expressions for the mean velocity, velocity-orientation projections, velocity autocorrelation, mean-squared velocity, mean-squared displacement, and the fourth moment of velocity. These results agree quantitatively with simulations over all masses, activities, and chiralities. We show that the velocity autocorrelation factorizes into an inertial envelope and a chiral envelope. Despite rich transients in the velocity sector, the long-time positional diffusion equals the overdamped cABP value, independent of mass. From the steady mean-squared velocity, we define a kinetic temperature and a modified fluctuation-dissipation relation whose violation vanishes in two limits: large mass or large chirality, identifying chirality as an additional route to equilibrium-like behavior. The steady-state velocity excess kurtosis gives a phase map that exhibits a (Gaussian-like)-active(bimodal)-(Gaussian-like) re-entrance with mass; chirality confines activity and shrinks the active sector. A narrow positive-kurtosis window emerges at large mass and intermediate chirality, with analytic boundaries consistent with the heavy-mass asymptote.

Topological phases have been extensively studied primarily in crystalline systems with translational symmetry. Recent theoretical studies, however, have demonstrated the existence of topological phases in quasicrystals that are absent in crystals. Despite numerous experimental observations of topological phases in various crystalline systems, observing these phases without crystalline counterparts remains challenging due to very complex models. Here, we design a practically realizable tight-binding model with nearest-neighbor hopping on the Ammann-Beenker quasicrystalline lattice. This model respects eight-fold rotational and chiral symmetries, resulting in a higher-order topological phase with eight zero-energy corner modes that have no crystalline counterparts. We experimentally explore the topological phase in an acoustic quasicrystal. Surprisingly, we also discover symmetry-protected zero-energy modes near the center of the quasicrystal in a topologically trivial phase, a phenomenon not seen in crystals. We further experimentally observe these modes in a topologically trivial acoustic quasicrystal. Our work represents the first experimental observation of topological phases in quasicrystals without crystalline counterparts, paving the way for the study of exotic topological physics in quasicrystals.

We investigate a one-dimensional tight-binding model in which onsite potentials $\{\varepsilon_i\}$ exhibit power-law spatialcorrelations (with exponent $\alpha$) and the hopping amplitudes decay as $t_{ij}\sim |i-j|^{-\beta}$. This two-parameter family interpolates continuously between short-range Anderson-like disorder, correlated disorder with conventional hopping, and long-range hopping models with nontrivial delocalization tendencies. Using large-scale exact diagonalization, we construct a comprehensive phase map in the $(\alpha,\beta)$ plane by combining spectral statistics, density-of-states analysis, and energy-resolved localization indicators such as the participation ratio, single-particle entanglement entropy, level-spacing ratio $r$, and the ratio of the geometric to arithmetic density of states. From these observables we define phase-indicator functions that compactly quantify localization behavior across the spectrum. Our analysis reveals robust mobility edges and multiple regimes of spectral coexistence between localized, extended, resonant, and critical states. Finite-size scaling, implemented via an explicit smoothness-based cost function, enables extraction of critical exponents and delineation of transition lines across the $(\alpha,\beta)$ parameter space. To validate and complement these physics-based diagnostics, we employ a supervised autoencoder that learns high-level representations of eigenstate structure directly from raw features and reliably reproduces the phase classification defined by the indicator functions. Together, these approaches provide a coherent and internally consistent picture of the spectral transitions driven by correlated disorder and long-range hopping, establishing a unified framework for characterizing mobility edges in long-range one-dimensional systems.

In this paper, we formulate the real-space Chern number in a supercell framework. In this framework, the overlap matrix between two corners of the Brillouin zone (BZ) is derived from diagonalizing the real-space Hamiltonian with periodic boundary conditions. The path-ordered product of overlap matrices around the BZ boundary forms a Wilson loop, and defines the Chern number in real space. It is analytically shown that the real-space Chern number is quantized at integers for large enough systems and coincides with the Bott index used in the previous studies. The formulation is greatly simplified for the former so that it makes numerical computations more efficient. The real-space formula is used to numerically elucidate topological phases in a disordered Chern insulator. The Chern insulator is modeled by dimensional extension of the Rice-Mele model consisting of two sublattices, and is disordered by including a random onsite potential. As disorder strength increases, the nontrivial-to-trivial phase transition takes place for normal disorder with no sublattice polarization. By contrast, the phase diagram is almost unaffected by polarized disorder, indicating that nontrivial topology persists against disorder. These observations are supported by the linear conductance and the density of bulk states.

We accurately compute the RG exponents $Y_q$ of large $q$ fields at the $O(2)$ invariant fixed point in three dimensions. We build on an iterative approach that has been previously proposed and is implemented by using the worm algorithm. We simulate an improved XY model, that has next-to-next-to-nearest couplings in addition to nearest ones. In the worm update we incorporate weights, which allows us to obtain accurate results up to $q=64$. For example we get $Y_q=1.76370(12)$, $0.89167(23)$, and $-0.11203(34)$ for $q=2$, $3$, and $4$, respectively. The comparison with the large $q$ effective field theory gives an excellent agreement down to $q=4$ and provides accurate estimates of the parameters of the effective field theory.