Intriguing piezoelectric phenomena have been reported in various two-dimensional quantum materials, where intrinsic geometric characteristics and spin-orbit coupling (SOC) effects play important roles. However, the role of Rashba SOC in piezoelectric properties remains unclear. Here we develop a theoretical model to elucidate the impact of Rashba SOC on the piezoelectricity of two-dimensional Janus materials. The results suggest that conventional piezoelectricity can be significantly enhanced by Rashba SOC due to increased wave-function localization, which reduces the hopping energy and modulates the effective Berry curvature distribution. First-principles calculations were performed on Janus transition metal dichalcogenides and $A_2{\mathrm{P}}_2{X}_6$ ($A$ = Bi, Ga, In; $X$ = S, Se, Te) systems, confirming the dependence of piezoelectricity on Rashba SOC. The conventional piezoelectric coefficient of WSeTe is predicted as 3.62 × ${10}^{-10}$ C/m, which is 40.0% and 98.7% larger than those of $\mathrm{WS}{\mathrm{e}}_2$ and $\mathrm{WT}{\mathrm{e}}_2$, respectively. Empirical formulas were further derived to reveal the general trends of both conventional and unconventional piezoelectricity in Janus systems with $C_{3v}$ symmetry. The extended understanding of the piezoelectric mechanism in quantum materials opens up opportunities for the development of efficient micronano piezotronics and spintronics devices.

Our numerical study of the disordered Hubbard model with nearest-neighbor hopping shows that a two-leg electron ladder has a finite topological entanglement entropy in the regime where the density of states exhibits an exponentially decaying gap. The value of the topological entanglement entropy suggests that two-leg ladders belong to the same universality class as graphene zigzag nanoribbons, despite several structural differences. A Shankar-Witten-type bosonization Lagrangian with disorder captures several features of the numerically obtained results for disordered two-leg ladders. Additionally, we propose a Lagrangian in which the fusion of two semions residing on different chains generates a fermion (instanton). We apply this Lagrangian within the framework of the pinned charge-density-wave model and compute the relevant Green's function using the bosonization method. This approach predicts a linear density of states at a critical disorder strength. Below this threshold, a soft gap emerges, which is in qualitative agreement with our numerical results.

The notion of topological order (TO) can be defined through the characteristic ground state degeneracy of a system placed on a manifold with nonzero genus $g$, such as a torus. This ground state degeneracy has served as a key tool for identifying TOs in theoretical calculations but, to our knowledge, it has never been possible to probe experimentally because fabricating a device in the requisite toroidal geometry is generally not feasible. Here we discuss a practical method that can be used to overcome this difficulty in a class of topologically ordered systems that consist of a TO and its time reversal conjugate $\overline{\mathrm{TO}}$. The key insight is that a system possessing such $\mathrm{TO}\otimes \overline{\mathrm{TO}}$ order fabricated on an annulus behaves effectively as TO on a torus, provided that one supplies a symmetry-breaking perturbation that gaps out the edge modes. We illustrate this general principle using a specific example of a spin-polarized $p_x\pm i{p}_y$ chiral superconductor which is closely related to the Moore-Read Pfaffian fractional quantum Hall state. Specifically, we introduce a simple model with an altermagnetic normal state which, in the presence of an attractive interaction, hosts a helical ${(p_x-i{p}_y)}^{\uparrow }\otimes {(p_x+i{p}_y)}^{\downarrow }$ superconducting ground state. We demonstrate that when placed on an annulus with the appropriate symmetry-breaking edge perturbation, this planar two-dimensional system, remarkably, exhibits the same pattern of ground state degeneracy as a $p_x+i{p}_y$ superconductor on a torus. We discuss broader implications of this behavior and ways it can be tested experimentally.

Non-Hermitian systems exhibit a distinctive type of wave propagation, due to the intricate interplay of non-Hermiticity and disorder. Here, we investigate the spreading dynamics in the archetypal non-Hermitian Aubry-André model with quasiperiodic disorder. We uncover universal transport behaviors: subdiffusion with a spreading exponent $\delta =1/3$ in the localized regime and diffusion with $\delta =1/2$ in the delocalized regime, in stark contrast to their Hermitian counterparts (halted versus ballistic). We then establish a unified framework from a random-variable perspective to determine the universal scaling relations in both regimes for generic disordered non-Hermitian systems. An efficient method is presented to extract the spreading exponents from Lyapunov exponents. The observed subdiffusive or diffusive transport in our model stems from Van Hove singularities at the tail of imaginary density of states, as corroborated by a Lyapunov-exponent analysis.

With the recent discovery of the correspondence between low-dimensional dynamical systems and high-dimensional topological insulators through the pumping process, many efforts have been made to generalize these correspondences to other topological phases. Yet, there is ongoing ambiguity about the correspondence of higher-order topological semimetals. Here, we propose a correspondence between a two-dimensional (2D) dynamic higher-order system and three-dimensional (3D) higher-order Dirac semimetals (HODSMs) through synthetic space consisting of a 2D lattice and a one-dimensional parameter dimension. We explore the evolution of the 2D higher-order topological insulator in a hexagonal acoustic crystal and find all the hallmarks of 3D HODSM in it, including Dirac points, surface states, and higher-order hinge states. By measuring the local density of states and acoustic pressure fields evolved in the 2D acoustic samples, we show that the system undergoes band gap-closing points, mapping to Dirac points in 3D synthetic space. The corner states evolving in nontrivial topological phase constitute hinge states connecting synthetic Dirac points. Our research deepens the understanding of the connections between different topological phases and may inspire further exploration of other topological effects in high-dimensional systems.

The quantum Rabi model exhibits a superradiant phase transition when the coupling becomes strong, even though it involves only two components: a two-level atom and a single bosonic mode. This phase transition is referred to as a finite-component quantum phase transition, in contrast to conventional phase transitions in many-body systems. In this Letter, we investigate heat transport across an atom embedded in bosonic modes, modeled by the quantum Rabi model, between two thermal baths. We found a manifestation of the superradiant phase transition in the thermal conductance, which represents the linear response to a temperature bias. Our Letter can be helpful for the development of quantum heat devices utilizing controllable finite-component quantum phase transitions.

We present a comprehensive investigation of the intricate spin dynamics in the noncentrosymmetric compound ${\mathrm{Sm}}_7{\mathrm{Pd}}_3$, revealing the coexistence of spin-glass, domain-glass, and ferromagnetic (FM) behaviors. Magnetic field-dependent measurements indicate large coercivity, suggesting ferromagnetic domain formation below the Curie temperature ($T_{\mathrm{C}}\approx 173$ K), while temperature-dependent magnetization data point to antiferromagnetic (AFM) coupling, highlighting the competition between FM and AFM interactions. Detailed ac susceptibility, isothermal remanent magnetization, and aging effect measurements demonstrate the presence of two distinct types of glassiness in the sample, and their possible origins are discussed extensively. Magnetization measurements reveal the mixing of the $J=5/2$ ground state of ${\mathrm{Sm}}^{3+}$ with the excited $J=7/2$ multiplet, lying 965 K above. The specific heat data show further crystalline electric field splitting of the $J=5/2$ state into a ground-state doublet and a fourfold-degenerate excited state.

In this paper, we report the structural, electronic, and ferroelectric properties of the layered mixed-valent transition-metal compound ${\mathrm{Sr}}_4{\mathrm{Fe}}_6{\mathrm{O}}_{12}$ (SFO). We demonstrate how SFO undergoes a phase transition from a high-temperature ($T$) centrosymmetric tetragonal phase ($P{4}_2/mnm$) to a low-$T$ polar orthorhombic phase ($Pmn{2}_1$). The transition is primarily driven by charge ordering at tetrahedral Fe-layer creating ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Fe}}^{2+}$ cations between two edge-sharing tetrahedra. This charge ordering induces electronic polarization, which is remarkably larger (3.5 times) in magnitude than ionic polarization and oppositely directed, giving a net polarization of 0.05 C/${\mathrm{m}}^2$ which is comparable to the state-of-the-art rare-earth nickelets and manganite perovskites. The direction of structural distortion, governed by the polar mode irrep ${\mathrm{\Gamma }}_5^{-}$, depends sensitively on the type of magnetic ordering in the Fe-octahedral layer. Consequently, both the ionic and electronic polarization directions are influenced by magnetic ordering, suggesting the potential for multiferroic behavior with strong magnetoelectric coupling in this material.

Magnetic hopfions are three-dimensional topological solitons with nonzero Hopf index $\mathcal{H}$ in the vector field of material's local magnetization. Here elliptical stability of hopfions with $\mathcal{H}=1$ in a classical helimagnet is studied on the basis of a variational model. It is shown that, depending on their internal structure (vortex and antivortex tubes ordering), the hopfions can be either stable in a bulk magnet or unstable with respect to elongation along their central axis. It is found that the energy of stable hopfions is always below the energy of the $2\pi$-skyrmion lattice in the same material, suggesting the possibility to use $2\pi$-skyrmions as a precursor for hopfion nucleation. Stability diagram for hopfions on the magnetic anisotropy-field phase diagram is computed numerically. Explicit analytical expressions for some of its critical lines are derived.

High-pressure elastic and plastic behavior of the amorphous solid, formed after solidification of the mixture of methanol and ethanol in the volume ratio 4:1 (4:1-ME), was investigated using the technique of time-domain Brillouin scattering (TDBS). Isotropic nature of this solid, whose bulk modulus exceeds that of diamond at pressures above 60–70 GPa (provided the earlier-measured dependence of its density on pressure, ρ($P$), holds at $P$>60 GPa), was confirmed thanks to the high 3D resolution of the TDBS technique. This permitted establishing of the relationship between elastic and plastic properties at high pressures because elastic response of the amorphous solid was not affected by anisotropy and texture, as is the case for crystalline solids. Using the TDBS technique, we measured pressure dependence of the Brillouin-oscillation frequencies, $f_{\mathrm{B}}$($P$), of 4:1-ME and, consequently, of its longitudinal sound velocity, $V_{\mathrm{L}}$($P$), and shear modulus, $G$($P$), to $P=78$ GPa. To access pressure dependence of its yield strength, ${\sigma }_{\mathrm{y}}$($P$), we used the here-established secondary pressure scale, based on our experimental $f_{\mathrm{B}}$($P$), and measured the maximal pressure gradients in the compressed samples which are proportional to ${\sigma }_{\mathrm{y}}$. We found that the rapid increase of bulk modulus of 4:1-ME with pressure, deduced from the ρ($P$) measured earlier to 60 GPa and extrapolated here to 78 GPa, is not accompanied by a similarly strong increase of its shear modulus and yield strength. The two parameters remain significantly below those of diamond at atmospheric and high pressures. Comparison of the here-measured ${\sigma }_{\mathrm{y}}$($P$) with the dependences $B$($P$) and $G$($P$) indicated that ${\sigma }_{\mathrm{y}}$ can be similarly well approximated by linear functions where $B$ or $G$ serves as the variable.

The spin-orbit coupled Mott insulator $\alpha \text{−}{\mathrm{RuCl}}_3$ has emerged as a prime candidate for realizing the Kitaev quantum spin liquid (KQSL), characterized by Majorana quasiparticles, the edge states of which exhibit a distinctive half-integer quantized thermal Hall conductivity. However, its van der Waals nature makes its thermal Hall response highly sensitive to structural disorder, leading to sample-dependent variations. Here, we investigate low-energy bulk excitations in the field-induced quantum disordered (FIQD) state of newly available ultraclean single crystals of $\alpha \text{−}{\mathrm{RuCl}}_3$. High-resolution specific heat measurements under in-plane magnetic field rotation reveal an anisotropic excitation gap, the field dependence of which is consistent with the Majorana gap in the KQSL state. Remarkably, when the field aligns with Ru-Ru bond directions, we observe gapless excitations with Dirac-like dispersions that quantitatively match theoretical predictions of Majorana bands based on the reported Kitaev interactions. Our findings in these ultraclean crystals provide strong evidence that the FIQD state of $\alpha \text{−}{\mathrm{RuCl}}_3$ is a robust KQSL, resilient against small disorder perturbations.

The optical conductivity provides a comprehensive view of the electronic response of materials to electromagnetic fields, offering insights into transport phenomena, optoelectronic properties, and other fundamental aspects of condensed matter physics. We present an automatic, high-order accurate, and adaptive Brillouin zone integration algorithm for the calculation of the optical conductivity using the Kubo formula, with a nonzero but small broadening factor $\eta$, focusing on the case in which a Hamiltonian in a downfolded model can be evaluated efficiently using Wannier interpolation. The algorithm uses iterated adaptive integration to exploit the localization of the transport distribution near energy and energy-difference isosurfaces, yielding polylogarithmic computational complexity with respect to $\eta$, rather than the algebraic complexity of uniform integration rules. To demonstrate the method, we compute the AC optical conductivity of a three-band tight-binding model, and are able to resolve the Drude and interband peaks with broadening in the sub-meV regime to several digits of accuracy. Our algorithm automates convergence testing to a user-specified error tolerance, providing an important tool in black-box first-principles calculations of electrical transport phenomena and other response functions.

We derive semiclassical Boltzmann equations describing thermalization of an ensemble of excitons due to exciton-phonon interactions, taking into account the fact that excitons are not ideal bosons but composite particles consisting of electrons and holes. We demonstrate that, with a standard definition of excitonic creation and annihilation operators, one faces a problem of the total particle number nonconservation, and we propose its possible solution based on the introduction of operators with angular momentum algebra. We then derive a set of kinetic equations describing the evolution of the excitonic density in the reciprocal space and analyze how the composite statistics of the excitons affects the thermalization processes in the system.

The quantization of conductance is a fundamental concept in understanding topological phenomena in two-dimensional electronic systems. However, achieving quantization in the realm of nonlinear electric transport remains a significant challenge. In this study, we explore current-induced nonlinear spin generation using a quantum kinetic equation formulated within the framework of the nonequilibrium Green's function method. This approach provides a unified framework for analyzing both linear and nonlinear spin responses. By applying it to a tilted massive Dirac model, we reveal that the $z$ component of nonlinear spin generation exhibits plateaulike features within the band gap. Notably, this phenomenon is isotropic with respect to the applied field, independent of the tilt, and driven by the quantum metric rather than the Berry curvature. These results offer insights into quantization in nonlinear transport and highlight the pivotal role of quantum geometry.

In recent years, there has been a surge of interest in exploring higher-order topology and their semimetallic counterparts, particularly in the context of Dirac, Weyl, and nodal line semimetals, termed higher-order Dirac semimetals (HODSM), higher-order Weyl semimetals, and higher-order nodal line semimetals (HONLSM). The HODSM phase exhibits hinge Fermi arcs (FAs) with a quantized higher-order topological invariant. Conversely, the HONLSM phase is a hybrid-order topological phase manifesting both drumhead-like surface states and hinge FAs as a signature of first- and second-order topology, and also possesses both first- and second-order topological invariants. In this work, we investigate a tight binding model for multi-HODSM (mHODSM) hosting multiple hinge FAs having a quantized quadrupolar winding number (QWN) greater than one. Furthermore, we obtain a multi-HONLSM (mHONLSM) phase from the mHODSM by applying an external magnetic field, which breaks the $\mathcal{PT}$ symmetry. The mHONLSM phase possesses both the dipolar winding number, nonvanishing only inside the nodal loops, being the representative invariant for first-order topology, and the QWN, featuring both drumhead-like surface states and multiple hinge FAs. We study the spectral properties of the mHODSM and mHONLSM in different geometries. We also investigate the hinge FA-mediated transport in HONLSM employing a two-terminal setup.

We present a detailed investigation of ultrafast carrier dynamics in single-crystal graphite using time- and angle-resolved photoemission spectroscopy (Tr-ARPES). By systematically analyzing the electronic temperature $T_e$, chemical potential $\mu$, and nonthermal carrier dynamics across various pump fluence and energy regimes, we provide insights into the multistep relaxation processes that govern the system's evolution from nonequilibrium to quasi-equilibrium states. Our results reveal that at low fluences ($\mathit{F}<0.50\mathrm{mJ}/{\mathrm{cm}}^2$), the electronic system behaves predominantly as a quasithermalized ensemble, aligning well with the Fermi-Dirac distribution. However, at higher fluences ($\mathit{F}⩾0.50\mathrm{mJ}/{\mathrm{cm}}^2$), nonthermal carriers emerge, driving significant deviations from thermal equilibrium. These carriers exhibit ultrafast lifetimes of approximately $284\pm 38$ fs, primarily dictated by electron-electron scattering and strong coupling to optical phonons. Through fluence-dependence analysis, we demonstrate the distinct relaxation dynamics of high-energy carriers ($>0.2$ eV) dominated by ultrafast scattering, compared with low-energy carriers ($<0.2$ eV) where the phonon bottleneck effect prolongs decay times to up to 32 ps at low fluences. In addition, we demonstrate a linkage between dynamic high-temperature quasi-equilibrium states from pump excitation and static ARPES measurements at 1000 K, highlighting the correspondence between dynamic quasi-equilibrium and thermal equilibrium states. Energy region dependent investigations reveal the critical role of free-carrier absorption in the low-energy regime and nonlinear interactions at higher energies, emphasizing the intricate balance between carrier-carrier and carrier-phonon interactions in shaping the relaxation pathways. This study provides a unified framework for understanding carrier dynamics in graphite, bridging static and dynamic perspectives.