Papers

Foundation machine-learning interatomic potentials cover broad configurational and chemical spaces, but their reliability can vary across the atomic environments encountered during a simulation. Here we introduce the calibrated Mahalanobis (CALM) extrapolation grade $\gamma$, a piecewise differentiable per-atom quantity integrated into GRACE foundation models and evaluated alongside energies and forces in a single model pass. We define $\gamma$ from nearest-cluster Mahalanobis distances in latent feature space, setting $\gamma=1$ from the training-distance distribution separately for each element and cluster. Controlled tests show that a normalized random projection of the invariant many-body basis detects structural and chemical extrapolation. On different foundation datasets, OMat24 and SMAX, $\gamma$ correlates with atomic force errors and separates structures with different error distributions. The CALM grade adds percent-level computational cost, and its spatial gradient guides uncertainty-biased data collection toward configurations with larger absolute force errors.

Superconductor and two-dimensional hole gas heterostructures are promising platforms for quantum devices, but their intrinsic properties, e.g., unconventional pairings, are hard to access experimentally. Here, we show that the in-plane-field dependence of the superfluid stiffness and spin susceptibility exhibits nonanalyticities encoding the induced gap structure in the hole gas. Additionally, Fourier harmonics of the stiffness tensor's field-angle dependence, accessible via kinetic-inductance measurements, provide fingerprints of unconventional pairing and cubic Rashba coupling.

We present an analytical study of impurity-induced density correlations in interacting one-dimensional Luttinger liquids using the Unified Field Bosonization Technique (UFBT). Unlike conventional approaches that treat impurities perturbatively, UFBT incorporates localized impurities exactly at the free-fermion level while treating interactions non-perturbatively. Closed analytical expressions for fermionic Green functions and density-density correlation functions are obtained for strongly inhomogeneous systems, enabling a unified description of the impurity-induced $2k_F$ Friedel oscillations and the $4k_F$ Wigner-crystal like correlations. The corresponding scaling behaviour is derived analytically, revealing a crossover in the dominant long-distance correlations at $g=1/3$: Friedel correlations dominate for $g>1/3$, whereas Wigner-crystal like correlations become dominant for $g<1/3$, corresponding to the regime of sufficiently strong repulsive interactions. A reflection-coupled harmonic analysis is developed to account for the left-right mixing induced by impurity backscattering and to consistently reproduce the resulting density correlations. The spinless limit is also obtained as a direct reduction of the spinful formulation. These results provide an analytically controlled framework for describing impurity-induced and interaction-driven density correlations in strongly inhomogeneous one-dimensional quantum systems.

Measures of non-stabilizerness (“magic”) of a quantum evolution quantify how hard it is to simulate on a classical computer. A natural question is how to extract information about magic from physical correlators, for example at finite temperature or in the ground state. In this paper we show how to measure magic using out-of-time-order correlators evaluated in an arbitrary state. For every full-rank state, and in particular for every Gibbs state, the resulting quantity vanishes if and only if the evolution is Clifford. We establish its basic properties, relate it to the stabilizer entropy of the Choi state, and prove that, even with a single fixed probe operator, it gives a lower bound on the number of $T$ gates needed to implement the dynamics in any circuit architecture.

A variety of disordered materials, including jammed particulate systems and crumpled paper, can be trained to exhibit memory of a cyclic strain amplitude. Only recently, however, have questions emerged around the whether random driving can impart similar training. Here, we employ x-ray photon correlation spectroscopy to study a fractal nanoparticle gel trained via either deterministic cyclic shear or random shear bounded by strain amplitudes $-\gamma_t$ and $+\gamma_t$. Both types of training lead to microstructural reversibility, with a slower and more irregular training for the random protocol. In both cases, the shear induces redistribution of internal stress in the gel with corresponding irreversible strain displacements whose magnitudes decrease during training. Finally, we show that memory of the random driving can be read out and quantified using a standard protocol.

Exploring exotic quantum phases of matter at room temperature represents a frontier challenge in modern physics. The supersolid phase, uniquely merging crystalline order with frictionless superfluid flow, stands among the most intriguing macroscopic quantum phenomena. However, all previous demonstrations of supersolidity, whether in ultracold atomic gases or III-V semiconductor-based polariton systems, have been strictly confined to cryogenic temperatures. Here, we report the observation of room-temperature supersolids in photonic-crystal polariton condensates. By integrating a room-temperature-stable perovskite semiconductor with a dispersion-engineered photonic-crystal waveguide, we create a polariton condensate with multi-mode dispersion landscapes and pronounced parametric nonlinearities. Above a critical condensation density, the interacting condensates spontaneously break continuous translational symmetry, creating a non-rigid supersolid phase that simultaneously exhibits emergent crystalline order and global quantum coherence. This work establishes a room-temperature platform for investigating quantum hydrodynamics and developing coherent quantum simulation devices.

Planar parity-preserving tensor networks (ppTNs) admit a fermionic formulation in which the Gaussian, efficiently contractible limit is deformed by local interactions. We investigate how many-body methods can be used to analyze such contractions in a minimal two-parameter ppTN. Its contraction is simultaneously an interacting fermionic partition function, a loop gas, a deformed toric-code norm, and a quartic Ising model, allowing the same phase diagram to be approached with complementary tools. At its center lies a `topological island', characterized beyond the Gaussian limit by a boundary-twist $\mathbb Z_2$ indicator that reduces to Chern-number parity and admits a loop-winding interpretation under duality. Fermionic perturbation theory predicts the interacting phase boundaries, tensor-network numerics establish their critical behavior, and the loop and spin descriptions reveal a self-dual line with a $c=1$ four-state-Potts multicritical fixed point.

We identify a route to altermagnetism driven by entropy upon heating and demonstrate it in a minimal square-lattice antiferromagnet. An exchange modulation is entropically favored because the resulting momentum-dependent magnon splitting increases the magnon entropy, thereby lowering the free energy and favoring altermagnetism. We derive an instability criterion for this exchange-modulated state, predict its temperature-driven reentrant behavior, and show that its overlap with Néel order defines a finite-temperature altermagnetic phase. Variational spin-wave theory, spin–lattice Monte Carlo, and cluster diagonalization establish the entropy-driven instability and its coexistence with magnetic order. The resulting state supports a transverse spin conductivity. The mechanism provides a route to thermally induced altermagnetism in compensated magnets coupled to sufficiently soft physical modes.

Beyond a critical Toner–Tu drive, bacterial turbulence exhibits universal statistics, including a parameter-independent energy spectrum $E(k)\sim k^{-3/2}$. We show that the same universal state can be reached not only by increasing activity, but also by strengthening nonlinear advection, weakening nonlinear saturation, or tuning the Swift–Hohenberg instability. Motivated by the competition between these processes, we identify the independent dimensionless groups governing the dynamics and construct a Reynolds-like control parameter from them. A single critical value, calibrated from the known activity-controlled transition, predicts the onset of universality along the other parameter routes and collapses them onto a common threshold. These results identify a dynamical organizing parameter for the onset of universal active turbulence and provide a Reynolds-like measure for the Toner–Tu–Swift–Hohenberg universality class.

The Scrooge ensemble associated with a density matrix $\rho$ is the maximally random ensemble whose average density matrix is $\rho$. It has attracted growing interest for its applications to quantum many-body dynamics and quantum information. The intrinsic statistical properties of the Scrooge ensembles are encoded in their higher-order moments, yet they are nontrivial to analyze and prepare for they feature a non-polynomial Haar integrand, blocking direct use of Haar integration machinery. Existing physical mechanisms to sample multiple copies of states from the Scrooge ensembles, meanwhile, typically require costly postselection, rendering them inefficient for large system size. In this work, we develop efficient and accurate methods for analyzing and implementing Scrooge moments. We first introduce a polynomial approximation to the Scrooge $k$-th moments whose error is tunable down to a threshold that improves from inverse polynomial to exponential in $1/||\rho||_\infty$ over previous results. Building on our approximation, we then give the first efficient quantum algorithm that estimates observable expectation values using $\widetilde{\mathcal{O}}(k^3/\epsilon^5)$ copies of $\rho$ for any target error $\epsilon$ above this threshold. We further provide a construction of a block encoding of the Scrooge $k$-th moment when the preparation circuit of $\rho$ is known. Of independent interest could be a key subroutine in our algorithms, which efficiently implements projection onto the $k$-fold symmetric subspace for $\rho^{\otimes k}$ using $\mathcal{O}(k^3/\epsilon^2)$ samples of $\rho$, avoiding the naive $k!$ postselection cost of such a projection. These results provide new tools for both the theoretical analysis and practical prediction of properties of Scrooge ensembles, with potential applications to quantum many-body dynamics and quantum information processing.

We study the problem of optimally placing a large number of small absorbing traps to minimize the mean first-passage time (MFPT) of particles diffusing in a heterogeneous medium with space-dependent diffusivity $D(x)$ and prescribed initial particle distribution $\omega(x)$. In two and three dimensions we identify two distinct regimes, depending on how strongly the trap ensemble depletes the particles. In the weak trapping regime (fewer traps) the optimal trap density $\rho$ is the arithmetic average $\rho = \frac12(\mu+\omega)$ of the normalized inverse diffusivity $\mu \propto 1/D$ and the initial particle distribution $\omega$. In the strong trapping regime (more traps), it is proportional to their geometric average, $\rho \propto \sqrt{\mu \omega}$. We revisit the classical Green's function approach and show that it applies to weak trapping only; in 2D this requires the trap size to be exponentially small in the number of traps, so that most applications of interest fall in the strong trapping regime instead. We therefore develop a homogenization approach that captures both regimes. A special choice of initial particle distribution is $\omega \propto 1/D$, which corresponds to the equilibrium particle distribution in the absence of traps according to the Itô interpretation. In this case we show that the optimal trap distribution is the stationary particle distribution itself, regardless of the trapping strength, and this makes the MFPT constant throughout the domain; the same trap distribution also minimizes the worst-case capture time. Finally, in one dimension we find instead $\rho\propto\left(\mu \omega\right) ^{1/3}$, and a similar analysis covers space-dependent drift and thin domains of variable cross-section. Direct numerical optimization confirms the analytical results.

Helical trilayer graphene (HTG) has emerged as a highly tunable moire quantum material that hosts strong electronic correlations and nontrivial band topology. However, the atomic-scale lattice structure and local electronic properties have remained largely unexplored. Here we present a comprehensive real-space study of HTG using a combination of scanning near-field optical microscopy and low-temperature scanning tunneling microscopy. We directly image supermoire lattice relaxation, revealing large triangular domains separated by sharp domain walls, as well as stripe domains connected by smoothly varying boundaries. Atomic-scale spectroscopy uncovers flat bands with a honeycomb electronic texture and one-dimensional boundary states confined to domain walls. By systematically varying the twist angle, we identify a magic angle of approximately 1.9{\deg}, substantially larger than the 1.6 degree predicted by theory. Our results establish a direct microscopic link between lattice relaxation and flat bands in HTG.

Machine learning interatomic potentials (MLIPs) are essential components for accelerating simulation-driven materials design. Data-efficient MLIP training relies on data-selection strategies that maximize structural diversity while limiting computationally expensive first-principles calculations. A key challenge in such strategies is evaluating structural similarity, which involves a trade-off between retaining information on individual atomic environments and reducing computational cost. Here, we propose similarity evaluation methods that achieve both representational fidelity and computational efficiency. Our method represents each structure using a small set of characteristic atomic environments identified by k-medoids clustering and computes pairwise similarity through optimal matching between these representatives or their distributions. Molecular benchmarks demonstrate that our method is approximately 50 times faster than the baseline method while also more clearly distinguishing structures with different chemical compositions. Similarity-based data-selection benchmarks demonstrate that our methods improve the data efficiency and stability of force prediction in MLIPs.

We investigate the field-dependent low-energy thermodynamics of the distorted triangular quantum antiferromagnet $\mathrm{Cu}_3(\mathrm{OH})_4(\mathrm{HCO}_2)_2$ using a sector-resolved Superblock Diagonalization Method (SBDM) supplemented by a transfer-matrix treatment of weakly coupled layers. The strong exchange hierarchy, dominated by the Cu1–Cu1 intradimer coupling $J_2=150\,\mathrm{K}$, separates a high-energy dimer sector from a much softer magnetic manifold formed predominantly by the Cu2 moments. In the 24-site cluster, sixteen Cu1 spins form the strongly bound sector while eight Cu2 spins remain magnetically active; polarization of these eight spins gives $S^z=4$ compared with $S^z_{\rm sat}=12$, providing a direct microscopic origin for the one-third magnetization scale. The finite-temperature thermodynamics reveals a non-monotonic field evolution of the low-energy scale: the dominant $C/T$ feature softens with increasing field, reaches a minimum near the field region around $2\,\mathrm{T}$, and subsequently hardens as the low-temperature magnetization approaches $M_{\rm sat}/3$. Temperature and field sweeps thus expose a common field-induced spectral reconstruction, while the strongly reduced entropy reflects the restricted number of thermally active degrees of freedom below the dimer excitation scale. Our results identify strong-dimer-induced reduction of the active magnetic Hilbert space, followed by field-driven reorganization of the residual spin sector, as the common microscopic origin of the one-third magnetic response and the non-monotonic low-temperature thermodynamics.

Progress in information processing relies on spintronics, where magnetic states serve as efficient carriers for data storage and transfer. In this work, we theoretically study magnon propagation in a bilayer composed of a ferro-magnet and an antiferromagnet. For this purpose, we probe the spin Seebeck effect by introducing a spatially varying temperature profile. This generates a local magnon excitation and a continuous magnon flux from hot to cold regions which we quantify through the resulting non-equilibrium magnon accumulation. Based on the chirality of these modes, we identify specific constraints for magnon modes traveling either from the ferromagnet into the antiferromagnet or vice versa. A key finding is the observation of a thermally triggered spin current in the antiferromagnet, a phenomenon typically absent in bulk antiferromagnets that obey time-reversal symmetry. These results provide important insights into the design of heterostructures for magnonic chirality-selective spin transport.

We introduce a simple reaction-network model of a quorum-sensing population that couples the cell density $x$ to the signal density $w$. In the four-channel cell-signal network studied here, scaling signal production and removal by the same factor $r$ leaves all deterministic equilibria, and their stability types, unchanged. Nevertheless, we show that $r$ shifts the quasipotential barrier $\Delta V(r)$ for rare transitions towards extinction, and thus, under metastable exit assumptions, the mean time to reach a fixed neighbourhood of the extinction state on the exponential scale $e^{N\Delta V(r)}$. We compute the barrier by minimization of the path action with the signal retained as a fluctuating coordinate, and we compare it with exact stochastic simulation of population-threshold crossing times regressed in $N$. Over a range of $r$, the minimum-action barriers satisfy $\Delta V(r)=\Delta V_\infty+O(1/r)$, where $\Delta V_\infty$ is obtained by eliminating the signal first. At $r=1$, the barrier is 55% larger than $\Delta V_\infty$. The saddle barrier $\Delta V(r)$ is also the least action needed to enter the basin of extinction, but the density threshold can be crossed more cheaply: at $r=0.5$ the cheapest crossing costs 7.7% less action, keeps the signal high, and is usually followed by recovery. Simulated arrival times in this neighbourhood, which include failed attempts, grow with slopes within two fitted standard errors of the saddle barrier at every tested rate, and within $0.004$ of it if the logarithmic prefactor term is omitted. Under either regression model they exclude $\Delta V_\infty$ at $r\le2$ by at least $4.4$ fitted standard errors, without using the action solver.

Grain boundaries fundamentally dictate the macroscopic properties of polycrystalline materials by breaking long-range symmetry. In ferroelectrics, these structural discontinuities are conventionally considered as detrimental features that induce depolarization fields and accumulate defects, thereby suppressing or pinning local polarization. Here, we demonstrate that the commensurability of grain boundaries inherently governs the polar-orthorhombic phase stability in polycrystalline Hf0.5Zr0.5O2 (HZO) thin films. Using depth-resolved multislice electron ptychography, we map the three-dimensional (3D) phase distribution across diverse boundaries with atomic resolution, revealing that highly commensurate grain boundaries effectively suppress the nonpolar-tetragonal phase by compensating for lattice mismatch while mitigating geometric frustration. Monte Carlo simulations uncover the atomistic and energetic origins of polar-phase stabilization, showing that commensurate grain boundaries favor the polar-orthorhombic phase more strongly than other grain boundaries. Guided by this principle, we epitaxially engineer HZO thin films to promote the preferential formation of commensurate grain boundaries, resulting in an approximately 60% enhancement in the remanent polarization of ferroelectric devices. These findings provide direct 3D experimental and theoretical evidence that establishes grain boundary commensurability as a critical degree of freedom for designing functional interfaces, guiding the construction of novel ceramics and polycrystalline ferroelectrics.

We introduce a classification of quantum phases of mixed states based on the ability to preserve and fault tolerantly transfer information. We formulate phase equivalence between sets of states that encode logical quantum information and are connected by shallow local channel circuits assisted by local measurements and global classical communication of measurement outcomes, where all quantum operations, including measurements, must be robust to noise. We show that the existence of a recovery threshold for local noise is a property of an entire phase. We prove that any two sets of states with nonzero thresholds that are related by finite-depth local channel circuits belong to the same fault tolerant phase. Our approach leads to a classification of subsystem codes without favoring any state of the gauge subsystem, and we demonstrate phase equivalence between 2D and 3D color codes using dimensional jumps within the 3D gauge color code. Lastly, we study how syndrome structure affects fault tolerance in circuits with measurements. We show that qudit stabilizer codes with extended syndromes permit single-shot state preparation, whereas a broad class of shallow circuits measuring point-like syndromes, including state preparation for 2D topological codes and non-Abelian topological orders with solvable anyon theories, is not fault tolerant.

Two-dimensional materials are promising candidates for electronic applications beyond the operating limits of conventional semiconductor technologies. Within this class, transition-metal dichalcogenides offer attractive properties for field-effect transistor operation, with tungsten disulphide (WS$_2$) emerging as a particularly promising material for operation at cryogenic temperatures. Here, we investigate the electrical performance of a back-gated multilayer WS$_2$ transistor at deep cryogenic temperature, down to 20 mK. The device remains strongly gate-tunable throughout the cryogenic regime, with an effective on/off current ratio exceeding $10^{5}$. Most notably, the low-temperature turn-on characteristics exhibit reproducible shoulder-like features, which we describe using a phenomenological model comprising multiple effective conduction branches operating in parallel.

Large-scale events such as political scandals or misinformation campaigns can abruptly shift the collective opinion of a population and reshape the dynamics in ways that standard local-interaction models of sociophysics do not capture. Here, we investigate the dynamics of opinion formation when a group of interacting agents is subjected to sudden, macroscopic exogenous shocks. Our framework is general and applies to arbitrary opinion dynamics models; to illustrate its scope, we consider the voter model and variations thereof. We verify that the mathematical description is excellent in describing the first-passage properties to consensus of the voter model on the complete graph and on complex networks. Remarkably, we identify the conditions under which shocks can be advantageous or detrimental to reach consensus. For the case of the all-to-all noisy voter model under exogenous events, we unveil a rich phase diagram characterized by novel trimodal and asymmetric bimodal states. Ultimately, this work provides a rigorous yet flexible stochastic-process framework for understanding the out-of-equilibrium behavior of opinion dynamics under recurrent exogenous stressors.

Floquet band engineering has been intensively studied for its potential to control material properties via laser driving. In particular, Floquet topological states have been measured on the surface of Bi$_2$Se$_3$. Nonetheless, the original prediction of Floquet topological bands in graphene remains unobserved, with works only measuring non-topological Floquet-Bloch states or indirect features. Here, we theoretically explore graphene irradiated by circular lasers with non-phenomenological electron-phonon (e-ph) coupling. We show that e-ph interactions substantially broaden Floquet bands due to graphene's large zero-point motion, as expected from phenomenological treatments. However, we further find that larger displacement $\Gamma$ optical phonons reduce Floquet gaps by about half, even in absence of instrumentation broadening, and can also induce additional features like flat bands. These phonons "enter the gap" and blur photoemission signatures. Including non-$\Gamma$ phonons closes the gap and greatly reduces visibility. When these modes couple to reasonably expected instrumentation broadening, the effect is significantly exacerbated. Our results shed light on the missing Floquet topological gaps and also lead to possible mitigation strategies: (i) Pre-pumping coherent phonons to counteract blurring, or (ii), transition to a Dirac system with more favorable phonon statistics. Moreover, our real-space analysis proposes that Floquet topological physics is alive in localized regions, such that properties of interest like transport should be accessible. We expect this work to impact experimental analysis and lead to set-ups where graphene Floquet topology might finally be directly observed.

We investigate the magnetization dynamics crossover from single-particle to collective behavior in a one-dimensional chain of dipolar-coupled nanomagnets with uniaxial anisotropy. Using both an intermediate-to-high damping (IHD) analytical approach based on Langer's theory and time-quantified Monte Carlo (TQMC) simulations, we derive and validate semi-analytical expressions for the relaxation rate and the magnetization relaxation curves. Our main results include: (i) a closed-form expression for the relaxation rate accounting for (weak) dipolar interactions, (ii) a two-exponential semi-analytical formula for the magnetization dynamics $m(t)$ of an interacting chain, and (iii) a systematic comparison with TQMC simulations, showing good agreement for a wide range of parameters. The analysis reveals a field-controlled crossover from uniform (macrospin-like) reversal to edge-nucleation propagation, driven by the spatial inhomogeneity of dipolar stabilization. The derived expressions provide a computationally efficient framework for predicting the relaxation behavior of dipolar-coupled nanomagnetic assemblies.

Fe$_3$GeTe$_2$ is a quasi-two-dimensional itinerant ferromagnet with a van-der-Waals layered structure that exhibits substantial magnetic anisotropy. In bulk samples, this material becomes magnetically ordered below 220~K, while in thin samples, the gate-tunability of the ferromagnetic moment has attracted significant interest. Alongside high-temperature ferromagnetism, a low-temperature magnetic state occurs whose nature has not been conclusively identified, with some studies suggesting a transition between ferromagnetism and antiferromagnetism with temperature. Here we present magnetometry and $\mu$SR data that demonstrate that Fe$_3$GeTe$_2$ exhibits three-dimenional Ising-like ferromagnetism over the entire temperature range between $T_{C}=220$~K and 2~K. The feature at 170~K that has previously been proposed to be a transition to antiferromagnetism is instead likely to represent a domain-freezing transition.

We present a physics-based multiscale full-band Monte Carlo framework for modeling avalanche multiplication and excess noise in complex alloy avalanche photodiodes (APDs), demonstrated on Al$_{0.7}$InAsSb as a representative quaternary system. The framework links atomistic material structure to device-level avalanche statistics: an environment-dependent $sp^3d^5s^\ast$ tight-binding calculation resolves the full conduction- and valence-band structure of the random- or digital-alloy configuration – including $\Gamma$, X, and L valley ordering, non-parabolicity, anisotropy, and spin-orbit-induced valence-band splitting – and supplies the band-structure inputs for stochastic high-field transport. A central element of the framework is a physics-derived treatment of alloy-disorder scattering, in which the quaternary disorder potential is constructed from atomic valence differences, covalent radii, and Thomas–Fermi screening through a composition-weighted decomposition into binary contributions, complemented by composition-interpolated polar-optical, acoustic, intervalley-phonon, impurity, and impact-ionization models. Because every material-dependent input is generated from the atomic composition and configuration by the same well-defined procedure, the framework transfers without structural modification to arbitrary zinc-blende ternary and quaternary alloys. Applied to a \SI{1}{\micro\meter} Al$_{0.7}$InAsSb p-i-n APD, the framework reproduces the measured gain and excess-noise characteristics with only the impact-ionization softness parameters calibrated. The approach provides a documented, reproducible route for analyzing and designing complex alloy APDs in which band structure, disorder, and scattering physics jointly determine gain and ionization statistics.

Topological polaritons provide a route to engineer optical Chern bands, but realizing large gaps or efficient electrical tunability remains challenging because time-reversal-symmetry breaking in semiconductor polariton systems is typically limited by weak Zeeman splittings. Here, we demonstrate a topological Bose-Fermi mixture — Fermi-polaron polaritons —where large gaps and electrically invertible topology emerge from the interplay of Fermi-polaron many-body interactions, photonic symmetry, and strong light–matter coupling. Using a gate-controlled monolayer transition-metal dichalcogenide integrated with a symmetry-engineered photonic crystal, we create Fermi-polaron polaritons with topological band structures. The direct coupling between band topology and gate-tunable many-body interactions provides a mechanism for amplified time-reversal-symmetry breaking beyond bare Zeeman splitting and enables electrical inversion of topological gaps, Berry curvature, and Chern numbers. These results establish an electrically reconfigurable platform for interaction-driven topological states and programmable topological photonics.

Membrane curvature has been shown to bias the location of lipid or protein domains, but the roles of bending rigidity, spontaneous curvature, Gaussian bending modulus, and line tension are difficult to separate in general. We develop a small-domain description for a membrane whose shape is held fixed, e.g. by strong adhesion to a curved substrate. Combining a local Helfrich energy with the small-area isoperimetric expansion gives a position-dependent energy determined by the local mean and Gaussian curvatures. We identify four generic regimes of curvature preference whose boundaries depend on only two dimensionless parameters. On specific membrane shapes with complex curvature, we show that this curvature preference determines the energy landscapes experienced by small domains, which are strongly dependent on the size of the domain through the line tension contribution. For example, on an oblate-shaped membrane, very small domains tend to localize at the poles, whereas larger domains prefer to localize at the equator. Whether this transition is continuous or discontinuous is found to strongly depend on the spontaneous curvature of the domain. This ordering suggests a mechanism by which small domains can collect and coalesce at one location before relocating as they grow.

Real nodal lines (RNLs) featuring real Chern numbers and second-order boundary modes have attracted widespread attention. In all previously reported realizations, an RNL is linked by another nodal line, and whether an RNL can be linked by other types of band degeneracies has remained open. Here, we propose a second-order real nodal-line semimetal in which a pair of RNLs is linked by a nodal surface. We show that this state can be realized in spinless systems with both $PT$ and nonsymmorphic $S_{2z}T$ symmetries, where the $S_{2z}T$-enforced nodal surface prevents the pair of RNLs from annihilation. Each nodal line carries a nontrivial real Chern number $\nu_R=1$, giving rise to topological hinge Fermi arcs located at a pair of $PT$-related hinges. Guided by this construction, we identify the interpenetrated graphene network (IGN) as a promising material realization. First-principles calculations confirm that a pair of nodal lines traversing the Brillouin zone are linked by a nodal surface and each nodal line carries double nontrivial $Z_2$ charges. The bulk-boundary correspondence of IGN manifests as a pair of hinge Fermi arcs together with drumhead surface states. Our work establishes nodal surfaces as a new linking partner for real nodal lines and provides a roadmap for exploring higher-order real topology in carbon-based and other light-element systems.

Melting temperature calculation is one of the important topics in computational materials science. In high-throughput in silico screening and artificial intelligence assisted design of materials, it usually requires a rapid and autonomous assessment of the melting temperature of the target. Unfortunately, molecular dynamics (MD) simulations of the melting point require many cumbersome and manual operations, making large-scale calculation of the melting point challenging. In this work, we introduce MyTm, a toolkit that employs MD to automatically determine the melting point. The method is fully modularized, and by combining these modules, the program enables fully automated melting calculations by using commonly adopted approaches, including the direct-heating method, the void method, the modified void method, the solid-liquid coexistence method, and the Z method. Moreover, a machine learning (ML) method is proposed and employed to recognize and classify the solid like and liquid like atoms, which effectively resolve the low accuracy issue in conventional classification approaches, thus making the automated high throughput pipeline of melting-point calculation possible. The robustness and efficacy of MyTm have been demonstrated by several well studied systems.

Classical phase-field models typically use the Allen–Cahn evolution law to model interface motion as a consequence of energy-gradient descent. This implies a linear kinetic relation between the velocity of an interface (e.g., a domain wall in a ferroelectric) and its driving force. When nonlinear kinetic relations are to be modeled, as commonly found in ferroelectric ceramics, an alternative evolution law and hence an alternative model is needed. Here, we propose an electromechanically (stress-driven) coupled multiphase-field framework with a general kinetic formulation, which integrates a prescribed kinetic relation directly into the evolution law. We show that this model correctly evolves domain walls with the assigned nonlinear kinetics, e.g., of mixed exponential-power law type, following the so-called Merz–Stadler law. The multiphase formulation further enables distinct kinetic relations and interfacial energies to be assigned to different order-parameter pairs, which reflects the distinguishable properties of the different types of ferroelectric domain walls. The proposed framework is broadly applicable for simulating kinetic relations in materials with applications beyond ferroelectrics.

Inferring the entropy production rate $\sigma$ from recorded trajectories is a key challenge in stochastic thermodynamics. In experiments, the forces governing the dynamics are usually unknown and often only some of the system's degrees of freedom can be observed. Building on a recently introduced method [I. Di Terlizzi, Phys. Rev. Lett. 135, 237101 (2025)], we develop and validate CYNAR (computation yields nonequilibrium analysis and reconstruction), a pipeline that estimates $\sigma$ from trajectories. It exploits a kinetic decomposition of $\sigma$ into a traffic term ${\cal T}$, inferred from the short-time curvature of correlation functions, and an inflow rate ${\cal G}$, computed from the steady-state score, i.e., the gradient of the log-density. We show that the same decomposition, evaluated on any subset of observed coordinates, always bounds $\sigma$ from below, for any diffusion tensor and without knowledge of the hidden degrees of freedom. We then compare CYNAR with a more standard approach that estimates $\sigma$ from steady-state probability currents, on four systems of increasing complexity. CYNAR proves to be more reliable, with no detectable bias close to equilibrium, weak dependence on spatial discretization, and marked robustness to measurement noise. It is also readily applicable to high-dimensional systems, where the traffic alone provides a lower bound close to $\sigma$, and remains informative under partial observation, including cases where the flux-based estimate vanishes identically. CYNAR is provided as an open-source Python package.