The Einstein relation linking charge carrier mobility and diffusion coefficient is a fundamental principle of charge transport. However, in disordered organic semiconductors, energetic disorder and carrier filling in localized states lead to a concentration-dependent diffusivity–mobility ratio described by the generalized Einstein relation (GER). Carrier-carrier interactions may further modify carrier occupation and transport behavior in these systems. However, their role in determining GER remains largely unexplored, especially in multicomponent systems. Here, using three-dimensional kinetic Monte Carlo simulations, we investigate the impact of Coulomb correlation on the GER in pure materials, binary systems, and ternary systems. We show that Coulomb correlation systematically modifies the GER, with the magnitude of the modification regulated by the relative permittivity, host-guest energy offset, guest concentration, temperature, and energetic disorder. The underlying mechanism is an interplay between energy-selective filling and Coulomb-induced carrier redistribution. In hostguest systems, the pronounced peak structures arising from multistep filling are progressively modified by Coulomb correlation. These results provide a comprehensive understanding of how Coulomb correlation governs the GER in disordered organic semiconductors and offer valuable insights for parametrizing diffusivity and mobility in drift-diffusion simulations of organic electronic devices.

Computational studies of the thermodynamic properties of materials at the mesoscopic and macroscopic scales—involving lengths and times of at least $\mu \mathrm{m}$ and $\mu \mathrm{s}$, respectively—rely on a coarse-graining approximation such that only a few relevant collective variables are treated explicitly. Those variables typically take the form of fields defined everywhere in space (e.g., a polarization field in dielectric or ferroelectric media) or macroscopic quantities when spatial inhomogeneities can be treated implicitly (e.g., the volume average of the electric polarization). The free energy is usually expressed as a Landau-type potential whose temperature-dependent minima track stable states, characteristic equilibrium fluctuations being implicitly accounted for. Further, the response of the system to external perturbations, and its relaxation toward thermal equilibrium, are described in terms of simple equations of motion governed by effective inertial and viscous-damping constants. There is considerable literature on the problem of deriving Landau-type free energy potentials, from either experiment or predictive atomistic simulations, including recent efforts to develop systematic machine-learning approaches that we denote “third principles.” Much less attention has received the calculation of the effective constants defining the time-dependent Landau equations and the corresponding nonequilibrium macroscopic or mesoscopic dynamics. Here we tackle that problem, describing a protocol that allows us to compute the temperature-dependent inertial and damping coefficients associated to the electric polarization in representative soft-mode ferroelectric ${\mathrm{PbTiO}}_3$. Our scheme follows usual approaches to analyze experimental vibrational spectra. It relies on standard equilibrium molecular-dynamics simulations and is therefore readily applicable with modern machine-learned interatomic potentials. Our results also allow us to comment on common assumptions in the literature of effective dynamic treatments and phase-field simulations of ferroelectrics and related materials.

In this work, magnetic and transport properties of ${\mathrm{LaSrMnRuO}}_6$ are studied in detail. The absence of a superlattice peak at $\sim {19}^{\circ }$ in the x-ray diffraction pattern indicates the Mn/Ru disorder at B-site, known as B-site disorder. The ZFC curve exhibits a weak ferromagnetic transition around $T_{C1}\sim 223\mathrm{K}$, followed by a cluster glass transition at $T_{C2}\sim 32\mathrm{K}$, as validated by frequency-dependent ac susceptibility studies. The high-temperature Curie-Weiss fit reveals predominant ferromagnetic interactions, while the S-shape of the M–H hysteresis loop at 300 K indicates the presence of short-range ferromagnetic correlations above $T_C$. Resistivity follows the small polaron hopping (SPH) model in the 118–380 K temperature range, yielding a room-temperature conductivity of 3.02 S/cm, which suggests semiconducting-like behavior at room temperature. Temperature-dependent magnetoresistance (MR) displays anomalies at ∼230 K and ∼30 K corresponding to the high-temperature ferromagnetic transition $\left(T_{C1}\right)$ and low-temperature cluster glass transition $\left(T_{C2}\right)$, respectively. Field-dependent MR shows a sharp increase at low fields below the cluster glass temperature, suggesting spin-polarized intercluster tunnelling of charge carriers. The gradual linear increase in MR with the applied magnetic field at high temperature is attributed to the intrinsic suppression of spin-disorder scattering induced by the B-site disorder. The absence of signature corresponding to $T_{C2}\sim 32\mathrm{K}$ in the $C_p$ vs T curve further supports cluster glass behavior.

We present a comprehensive first-principles investigation of defects in $4H_b\text{−}{\mathrm{TaS}}_2$. In this layered transition metal dichalcogenide, charge transfer between alternating Mott-insulating 1T and metallic 1H layers gives rise to exotic quantum phases such as the Kondo effect and topological superconductivity. Motivated by recent defect manipulation in $4H_b\text{−}{\mathrm{TaS}}_2$ via STM, we address their microscopic nature and impact on interlayer charge transfer. To this end, we systematically analyze over 90 defects using large-scale density functional theory (DFT) calculations. Our analysis identifies 1H sulfur vacancies, Ta-on-S antisites, and Ta interstitials as the most likely origins of the commonly observed defects, with Ta-on-S antisites producing the strongest charge-transfer modulation. Our extensive dataset, compiled from STM simulations, defect formation energies, work functions, and charge transfer, establishes a foundational resource for future theoretical and experimental studies on defect engineering in $4H_b\text{−}{\mathrm{TaS}}_2$.

We study the nonreciprocal properties of the iron oxide $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ (hematite) in the canted easy-plane antiferromagnetic phase, specifically in the GHz to THz frequency range. First, using the the microscopic spin Hamiltonian, we obtain the correct classical ground state where the canting is induced by the Dzyaloshinskii-Moriya interactions (DMI). The magnon spectrum is simulated using linear spin wave theory. We then compute the polarizability and the subgap optical conductivities using linear response. We find that the conductivity tensor contains frequency peaks at the zero momentum magnon gaps of order $0.1\mathrm{meV}$ which can be tuned by the DMI and on-site anisotropic spin interactions. Furthermore, we show that the canting-induced net magnetic moment $\mathbf{m}$ represents a measure for the effective time-reversal-symmetry breaking and nonreciprocity of the system: A finite $\mathbf{m}$ results in a nonzero Hall conductivity. Finally, we discuss the prospective application of hematite in nonreciprocal circulator design, by computing the nonreciprocal circulator transmission amplitude using the conductivities as input.

Lithium and sodium are the only solids that are known to lose crystalline order upon cooling. The seemingly disordered low-temperature phase shows signatures of various close-packed structures. The lack of order has been attributed to a hidden gauge symmetry that arises when electrons from one layer can hop to a neighboring layer but not further. It makes all close-packed structures nearly degenerate and leads to “structural frustration.” In this article, we examine whether this symmetry is reflected in transport signatures. Taking advantage of in-plane translational periodicity, we map the bulk Bloch Hamiltonian to an effective one-dimensional chain, with stacking disorder mapping to random phases of the hopping amplitudes. We derive an explicit analytic form for the Green's function of electrons and use it to calculate conductance of a bulk crystal. When hopping in the effective one-dimensional chain is restricted to nearest neighbors, conductance is completely insensitive to phase disorder, which indicates that all close-packed structures exhibit the same conductance. We show that the leading correction that can differentiate between close-packed structures arises from hopping to the next-nearest-neighbor layer, equivalent to second-neighbor hopping in the chain model. This process appears when a pair of next-neighbor layers are aligned in a certain way, e.g., at a hexagonal-close-packed-like stacking fault within a face-centered-cubic background. With this hopping included, conductance becomes sensitive to the precise arrangement of layers. When multiple stacking faults are present, the conductance decreases with increasing system size, as expected from Anderson localization. Our results are applicable to pressurized lithium and sodium, where conductance measurements can identify and characterize stacking faults.

We analyze the pairing instability of an altermagnetic metal on a square lattice driven by an attractive nearest-neighbor interaction. This interaction enables multiple pairing channels, including even-parity extended $s$-wave and $d$-wave states, as well as two odd-parity $p$-wave channels. We verify that altermagnetic spinsplitting in the single-particle dispersion gives rise to finite-momentum pairing between electrons with unlike spins, in agreement with earlier predictions. Quite unexpectedly, this pairing typically emerges across multiple channels with mixed parity. Consequently, the resulting finite-momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting phase is expected to exhibit a multicomponent order parameter featuring singlet-triplet mixing. We examine several forms of altermagnetism, specifically $d_{xy}$-wave and $d_{x^2-y^2}$-wave altermagnetic couplings, and present the corresponding phase diagrams. Additionally, we study triplet pairing between electrons with identical spins and find that it always occurs at zero center-of-mass momentum. Although it is unfavorable in the regime of weak altermagnetic coupling and low electron filling, it can dominate the phase diagram when the altermagnetic coupling is sufficiently strong. The influence of on-site attractive interactions on mixed-parity pairing is also explored.

The physics of twisted bilayer graphene away from the exactly solvable chiral limit and the quantum Monte Carlo sign-problem-free charge neutrality point is elusive due to the exponential increase in the computational complexity, which has rendered explanations of experimentally observed insulating and superconducting phases restricted largely to the perturbative level. Here, we focus on the filling factor $\nu =\pm 2$ and address the question of the strain dependence of the interacting ground state by approximate quantum Monte Carlo (AQMC), state-of-the-art exact diagonalization (ED), and Hartree-Fock (HF) mean field, in order to investigate the strain-tuned transition from the Kramers intervalley coherent (KIVC) state to the incommensurate Kekulé spiral (IKS) state. While all three methods capture the KIVC order, only ED and HF detect the weaker IKS order that AQMC does not capture adequately. As the AQMC is still capable of capturing stronger orders like the KIVC, our combined protocol may open the door for further understanding of the rich phases of twisted bilayer graphene and other strongly correlated systems.

    We report a comparative study of the anomalous Hall effect (AHE) in single crystals of the two-dimensional van der Waals (vdWs) ferromagnets ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ and ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$, grown by chemical vapor transport, over wide temperature and magnetic-field ranges. From magnetization, longitudinal resistivity ${\rho }_{xx}$, and Hall measurements, we extract the ordinary and anomalous Hall coefficients and scale the anomalous Hall conductivity ${\sigma }_{xy}$ against the longitudinal conductivity ${\sigma }_{xx}$. In ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2, {\sigma }_{xy}$ is nearly independent of ${\sigma }_{xx}$ and scales linearly with magnetization across the entire ordered phase, with the resistivity scaling ${\rho }_{xy}=a{\rho }_{xx}^2+b{\rho }_{xx}$ yielding a negligible linear term; this identifies a predominantly intrinsic, Berry-curvature-driven AHE consistent with its nodal-line electronic structure. ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$ exhibits a mixed intrinsic and extrinsic anomalous Hall response. Below $T^{*}\approx 100\mathrm{K}$, the scaling analysis reveals a finite skew-scattering contribution, accompanied by a breakdown of the linear ${\sigma }_{xy}\text{−}M$ relationship. In the vicinity of $T^{*}$, we observe a broad maximum in the resistivity, a nonmonotonic evolution of the anomalous Hall resistivity, and a pronounced change in the Hall coefficients, consistent with a temperature-dependent multiband electronic response involving both electron- and holelike contributions. The emergence of a finite topological Hall contribution in the same temperature-field regime is consistent with the development of noncoplanar magnetic textures. These results establish a direct link between sublattice-dependent electronic structure and the intrinsic-to-extrinsic crossover of the AHE in the ${\mathrm{Fe}}_x{\mathrm{GeTe}}_2$ family, with ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ representing the intrinsic limit and ${\mathrm{Fe}}_5{\mathrm{GeTe}}_2$ a tunable mixed regime.

Topological interface states in one-dimensional superlattices provide spatially localized phonon modes protected by the topology of the underlying band structure. In GaAs/AlAs distributed Bragg reflectors (DBRs), such states can be engineered through band inversion between superlattices with opposite Zak phases within the Su-Schrieffer-Heeger framework. Here, we demonstrate topological phonon molecules and extended chains formed by coupled nanophononic interface states. By concatenating three superlattices with alternating topology, we realize two coupled interface states that hybridize into symmetric and antisymmetric modes, whose splitting can be tuned over tens of gigahertz by varying the reflectivity of the central DBR. Extending this concept, we engineer chains of up to $N=6$ coupled interface states that form narrow topological minibands while remaining strongly localized at the interfaces. We experimentally observe these coupled states in molecular-beam-epitaxy-grown GaAs/AlAs heterostructures using time-domain pump-probe transient reflectivity measurements, and reproduce their behavior using transfer-matrix calculations and a simple analytical model for the mode splitting. These results establish topological interface states as a robust platform for engineering coupled phononic systems and tunable nanophononic architectures in the GHz regime.

Two parallel helical edge channels hosting interacting electrons, when proximitized by local and nonlocal pairings, can host time-reversal-invariant pairs of topological zero modes at the system corners. Here, we show that realistic imperfections substantially enrich the physics of such proximitized double helical liquids. Specifically, we analyze this platform and its fractional counterparts in the presence of pairing and interaction asymmetries between the two channels, as well as random spin-flip terms arising from either magnetic disorder or coexisting charge disorder and external magnetic fields. Using renormalization-group analysis, we determine how Coulomb interactions, pairings, and magnetic disorder collectively influence the transport behavior and topological properties of the double helical liquid. As the system now belongs to class BDI, an additional topological phase supporting a single Majorana zero mode per corner emerges. We further show how additional pairing or Coulomb asymmetry influences the stability of various topological phases and uncovers a revival of Majorana zero modes and cascades of successive topological transitions through topological phases characterized by a $\mathbb{Z}$ invariant, which are accessible by controlling the electrical screening effect. We also analyze the spatial structure of the zero modes and the bulk gap closing through channel-resolved density profiles, revealing observable features using scanning tunneling microscopy. In contrast to conventional understanding, disorder is not merely detrimental, as it generally provides a tuning knob that qualitatively reshapes the topological superconductivity in imperfect helical liquids.

Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates symmetries in $k$ dimensions to “bulk” topological orders in $(k+1)$ dimensions. While conceptually profound, most existing bulk construction methods rely on sophisticated mathematical formalisms and can be difficult to apply to certain symmetry types. In this work, we propose a physically intuitive and versatile method, termed the layered gauging construction, to systematically generate $(k+1)$-dimensional (liquid or fracton) topological orders from $k$-dimensional generalized symmetries. Roughly speaking, the prescription is to stack many layers of $k$-dimensional quantum systems with certain symmetries into a $(k+1)$-dimensional pile, and then sequentially gauge a diagonal symmetry acting on each nearest-neighbor pair of layers. The detailed procedure depends on the specific symmetry types. We have successfully implemented the method in a number of examples in different spatial dimensions, with symmetries that are conventional, higher-form, subsystem, anomalous, non-Abelian, or noninvertible. We hence conjecture the method to be very general. For example, from the subsystem symmetry of the $2d$ plaquette Ising model, we derive the X-cube model and also an anisotropic fracton topological order. Additionally, starting from an anomalous ${\mathbb{Z}}_2$ symmetry in $1d$, we construct a new square lattice model realizing the double semion topological order. From a quantum-error-correction perspective, our layered gauging construction may be viewed as a generalization of the hypergraph-product construction beyond the standard Calderbank–Shor–Steane setting.

Motivated by the growing interest in spin liquids and topological phases, as well as the rise of deformation engineering, we study the combined effects of deformation and magnetic fields on the honeycomb Kitaev model. The Kitaev model, as one of the prototypical and exactly solvable spin-liquid-hosting models, serves as a simple platform that demonstrates the rich physics one can expect at the intersection of deformation physics and quantum spin liquids. Our work builds on a simplified solution to the undeformed base model that we present. This simplified solution allows for a straightforward extension of our analysis to the deformed case. After incorporating periodic deformations into the Kitaev model (chosen for its similarity to moiré physics), we investigate the effects of a hexagonally symmetric deformation on the band structure. We find that deformation leads to a smaller Brillouin zone with new band gaps at the edges, indicating the potential for topological transitions. Finally, we introduce a magnetic field to break time-reversal symmetry and thereby allow for nontrivial topology. We find that, under specific parameter conditions, the magnetic field leads to multiple band-gap closings and openings. An investigation into topological properties reveals nontrivial Chern numbers and a plethora of topological transitions. The resulting nontrivial band topology may motivate future investigations of thermal Hall or related transverse responses, which are not calculated here. We also propose a bulk-measurement approach to the Chern numbers and a possible path to their physical realization. Most importantly, our results demonstrate the rich phenomenology that can arise from the interplay between deformation and spin-liquid physics.

The motivation behind the present work is to adopt methodology from field theory and high-energy physics to crystallography. In particular, we establish a relationship between the electromagnetic sector of the standard-model extension (SME) for Lorentz invariance violation and optical media. At an effective level, a broad class of anisotropic and polarization-dependent electromagnetic properties associated with crystal structures is demonstrated to be parametrized in the SME. Crystallographic and magnetic point groups provide the mathematical tools to show this correspondence. Birefringent and magnetoelectric media merit separate studies. Intriguing effects, which have not been described systematically in the modern literature, are rediscovered for the latter and expressed in the SME language. With the setting developed at our disposal, materials with specific symmetries such as birefringent or multiferroic crystals serve as condensed-matter analogs of SME effects. It enables us to propose materials with unusual optical properties, which have not been thoroughly investigated in recent times.

We employ the flux-flow instability (FFI) technique—a widely used method for determining the quasiparticle relaxation time (${\tau }_E$)—to investigate single-crystal superconducting titanium nitride (TiN) films characterized by weak vortex pinning and slow electron-phonon relaxation. By systematically varying the TiN strip width, we show that reliable extraction of the vortex velocity and ${\tau }_E$ is achievable only when the strip width exceeds the electron-phonon relaxation length. A comparative analysis of ${\tau }_E$ values obtained using various FFI models and other experimental methods reveals that quasiparticle relaxation within the vortex core is primarily governed by an increase in quasiparticle temperature. Our analysis provides a reliable way to determine ${\tau }_E$ from FFI measurements and may also be relevant to other superconducting systems in which fast electron-electron scattering is expected to lead to a thermal-like quasiparticle distribution function.

The noncollinear antiferromagnet (AFM), ${\mathrm{Mn}}_3\mathrm{Sn}$, exhibits ultrafast spin dynamics and negligible stray fields, making it a promising candidate for fast and energy-efficient spintronic devices. However, its practical applications remain limited by the relatively small Hall response compared with ferromagnets. Here, we demonstrate through both first-principles calculations and experiments that Cr doping is a promising strategy to enhance the anomalous Hall transport in ${\mathrm{Mn}}_3\mathrm{Sn}$ without breaking the antiferromagnetic order. Our first-principles calculations reveal an effective Cr-doping window that enhances the anomalous Hall conductivity while largely preserving the host coplanar inverse triangular AFM order. Berry curvature and Wannier Hamiltonian analyses further reveal that Cr substitution amplifies the preexisting Berry curvature hot spots through coordinated changes in the energy alignment, local interband gap, and Mn-derived orbital weight of the relevant bands. Experimentally, we have found that Cr doping not only supports our computational predictions (enhancement of the anomalous Hall conductivity), but also suppresses the transition to helical or spin-glass phases at low temperatures. These findings demonstrate that Cr doping is an effective strategy for stabilizing the AFM order while simultaneously improving the anomalous Hall transport properties over a wide temperature range in ${\mathrm{Mn}}_3\mathrm{Sn}$.

The structural evolution and transformation pathways of carbon dioxide phase IV (${\mathrm{CO}}_2$-IV) are investigated over 13.0–76.7 GPa and 296–700 K using synchrotron x-ray diffraction, Raman spectroscopy, and first-principles calculations. ${\mathrm{CO}}_2$-IV was obtained from ${\mathrm{CO}}_2$-I by isothermal compression to 13.0 GPa at 600 K. Subsequent single-crystal diffraction performed at 14.5 GPa and 296 K confirms that ${\mathrm{CO}}_2$-IV adopts a rhombohedral $\text{R}\overline{3}\text{c}$ structure, consistent with Datchi et al. [Phys. Rev. Lett. 103, 185701 (2009)], establishing its purely molecular character without evidence for an “intermediate bonding state”. At room temperature, deviatoric stress promotes a symmetry-lowering distortion of $R\overline{3}c$ ${\mathrm{CO}}_2$-IV at 14.6 GPa, yielding a distorted molecular configuration described by a triclinic $P1$ model, denoted here as an ${\mathrm{IV}}^{\prime }$-type distortion. From 296 to 600 K, the onset pressure of this distortion increases modestly, giving rise to a positively sloped kinetic onset line in the $P$–$T$ diagram. At 650 and 700 K, enhanced thermal relaxation substantially reduces the influence of deviatoric stress, and no symmetry breaking is detected before the molecular-to-nonmolecular transformation, stabilizing the $R\overline{3}c$ structure in the molecular regime. Upon further compression, the molecular solid transforms into metastable nonmolecular states containing mixed three- and fourfold-coordinated carbon atoms. The transformation pathway is temperature dependent: at 296–600 K, amorphization proceeds from the $P1$-distorted form of ${\mathrm{CO}}_2$-IV to a-${\mathrm{CO}}_2$, whereas at 650–700 K the transformation proceeds directly from $R\overline{3}c {\mathrm{CO}}_2$-IV to the more ordered metastable covalent phase VI. The onset pressure of the molecular-to-nonmolecular transformation decreases with increasing temperature. These results reveal that the high-pressure behavior of ${\mathrm{CO}}_2$ is governed by the interplay between deviatoric stress and thermal activation, which controls symmetry lowering within the molecular regime and the subsequent pathways toward amorphous and metastable covalent structures.