${\mathbb{Z}}_2$ symmetry is ubiquitous in quantum mechanics, where it drives various phase transitions and emergent physics. The role of ${\mathbb{Z}}_2$ symmetry in the thermalization of a local observable in a disordered system can be understood using random matrix theory. To do so, we consider random symmetric centrosymmetric (SC) matrix as a toy model where a ${\mathbb{Z}}_2$ symmetry, namely, the exchange symmetry, is conserved. Such a conservation law splits the Hilbert space into decoupled subspaces such that the energy spectrum of an SC matrix is a superposition of two pure spectra. After discussing the known results on the correlations of such mixed spectra, we consider different initial states and analytically compute the time evolution of their survival probability and associated timescales. We show that there exist certain low-energy initial states which do not decay over a very long timescales such that a measure zero fraction of random SC matrices exhibit spontaneous symmetry breaking. Later, we look at the equilibrium values of local observables like the density-density correlation, kinetic energy operator, and compare them against the average values from the microcanonical and canonical ensembles. We find that when the observable violates (respects) the global symmetry of the Hamiltonian, the equilibrium value is independent (dependent) of the symmetry of the initial state. However, irrespective of such symmetry constraints, the fluctuations of the diagonal terms of the observables within microcanonical shells decay with system size such that the ansatz of the eigenstate thermalization hypothesis remains valid. We show that the equilibrium value converges to the canonical average for all the observables and initial states, indicating that thermalization occurs despite the presence of a global symmetry.

Antiferromagnetic oxide materials are emerging as key ingredients in spintronic devices and ultrafast terahertz (THz) emitters due to their distinct spin dynamics and vanishing net magnetization. Here, we report an irreversible, time-dependent enhancement of THz emission from exchange-coupled NiO/Fe/Pt trilayers under femtosecond laser excitation, with the THz signal amplitude increasing by up to 150%. Magneto-optical Kerr and x-ray photoelectron spectroscopy measurements reveal that laser exposure drives interfacial ionic reconstruction, specifically the formation of oxygen vacancies in NiO that create Ni-rich regions at the NiO/Fe interface. This magneto-ionic modification boosts spin-current injection into the heavy metal layer and thereby amplifies the emitted THz radiation. Such a phenomenon is strongly dependent on the pump power and demonstrates a threshold behavior. This enhancement is tunable by adjusting the NiO layer thickness and its oxygen richness. Our findings highlight an effective mechanism for ultrafast control of spintronic THz sources and suggest another strategy for engineering antiferromagnet-based THz emitters via laser-driven interfacial ionic processes.

Altermagnets have recently attracted significant attention, yet their coupling to other ferroic orders remains to be explored. In this work, we investigate the interplay of altermagnetism and ferroelectricity in pentagonal $\mathrm{Mn}{X}_2$ ($X=\mathrm{S}$, Se) monolayers using density functional theory (DFT) calculations and symmetry analysis. We show that both materials host robust $g$-wave altermagnetism with a room-temperature Néel transition ($T_N$), stabilized by strong exchange interactions mediated through ligand dimers. At the same time, pronounced Mn-$d$ and S/Se-$p$ hybridization generates type II ferroelectricity, which locks the Néel vector to the out-of-plane polarization, thus enabling electrical stabilization of the magnetic order under finite temperature. Furthermore, we show that compressive strain enhances magnetic couplings, and propose Janus $\mathrm{MnSSe}$ as a system with enhanced altermagnetism and ferroelectricity. These findings unveil how altermagnetism and ferroelectricity coexist in pentagonal $\mathrm{Mn}{X}_2$ ($X=\mathrm{S}$, Se) monolayers at a microscopic level, providing interesting perspectives for designing multifunctional two-dimensional materials in spintronic applications.

The application of most multiferroic ceramic composites is severely hindered by their zero or near-zero magnetoelectric response under zero magnetic field. Currently, there has been no in-depth theoretical exploration into the causes of self-biased magnetoelectric coupling effects in these ceramics or how to regulate them. In this study, we report the observation of self-biased magnetoelectric coupling effect in a $\left(1-x\right)\mathrm{BaTi}{\mathrm{O}}_3-\left(x\right)\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4(x=0.1,0.2,0.3,0.4\mathrm{and}0.5)$ particle composites. P-E and M-H hysteresis loops confirmed the presence of both ferroelectricity and ferromagnetism in the $\left(1-x\right)\mathrm{BaTi}{\mathrm{O}}_3-\left(x\right)\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$ composites. By measuring the magnetoelectric voltages of the composites, we confirmed the existence of self-biased magnetoelectric coupling effects in the $\mathrm{BaTi}{\mathrm{O}}_3$ and $\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$ phases. The highest self-biased magnetoelectric coupling coefficient (1.65 mV/(Oe cm)) was found at $x=0.3$ composite sample. Based on nonlinear magnetoelectric coupling theory, we established a correlation model between magnetic parameters and magnetoelectric coupling coefficients. We demonstrated that the origin of self-biased magnetoelectric coupling lies in the hysteresis dependence of magnetization and proposed that regulating magnetic parameters can effectively control the self-biased magnetoelectric coupling effect. Finite element simulations visually demonstrate displacement variations under different magnetic field conditions, enabling more intuitive observation of changes in internal magnetization and displacement within the material. This lays the foundation for developing high-performance self-biased magnetoelectric coupling devices.

Borides represent a unique category of materials with potential superconductivity and high hardness. Motivated by recent progresses, we conducted thorough searches in a yttrium-boron binary system employing the first-principles density functional theory. Four superconducting yttrium borides have been identified, including ${\mathrm{YB}}_5$ (Pmma) and ${\mathrm{YB}}_8$ ($R\overline{3}m$) of boron clathrate structures with superconducting transition temperatures $T_{\text{c}}$ = 30.5 K at 20 GPa and 19.9 K at the ambient pressure, respectively. The superconductivity in yttrium-boron superconductors originates from the coupling of B-$2p$ electrons to boron vibrational modes and Y-$4d$ electrons to their atomic vibrations. By high-throughput screening of isostructural ${X\mathrm{B}}_8$ ($R\overline{3}m$) borides in which yttrium is replaced by atoms in the periodic table, we have identified four groups of unprecedented superconductors including ${\mathrm{PbB}}_8$ with $T_{\text{c}}$ = 45.5 K at the ambient pressure. We found ${\mathrm{YB}}_3$ (Cmcm) with boron cages has high Vickers hardness value of 35.2 GPa. By screening of ${X\mathrm{B}}_3$ (Cmcm) isostructures, we also identified a series of unprecedented high-hardness borides. Therefore, our discoveries suggest the enormous potentials of borides with clathrate structures in exploring materials of high superconducting transition temperatures and high hardness at the ambient pressure.

We propose a general quantum Hamiltonian formalism of a renormalization group (RG) flow with an emphasis on generalized symmetry by interpreting the elementary relationship between homomorphism, quotient ring, and projection. In our formalism, the noninvertible nature of the ideal of a fusion ring realizing the generalized symmetry of an ultraviolet (UV) theory plays a fundamental role in determining condensation rules between anyons, resulting in the infrared (IR) theory. Our algebraic method applies to the domain wall problem in $2+1$-dimensional topologically ordered systems and the corresponding classification of $1+1$-dimensional gapped phases, for example. An ideal decomposition of a fusion ring provides a straightforward but strong constraint on the gapped phase with noninvertible symmetry and its symmetry-breaking (or emergent symmetry) patterns. Moreover, even in several specific homomorphisms connected under massless RG flows, less familiar homomorphisms appear, and we conjecture that they correspond to partially solvable models in the recent literature. Our work demonstrates the fundamental significance of the abstract algebraic structure (beyond the group structure), namely the ideal, for the RG in physics.

We investigate the interplay between charge density wave (CDW) order and topological nodal-line states in square-net materials. Our Ginzburg-Landau theory predicts a CDW instability that generically opens a gap at the Fermi energy while preserving the nodal-line crossing. However, as the Fermi level approaches the nodal line, the density of states at the nodal line decreases, eventually disappearing as the CDW vector $\mathbf{Q}$ goes to zero. Exactly at $\mathbf{Q}=0$, the order parameter explicitly breaks the glide symmetry protecting the nodal line, which allows a gap to open. Yet, for small but finite $\mathbf{Q}$, the nodal line may vanish within experimental resolution even when the glide symmetry is preserved. Our results provide a consistent explanation for recent experimental observations.

The Kondo lattice compound ${\mathrm{YbV}}_6{\mathrm{Sn}}_6$ has recently been discovered to exhibit antiferromagnetic order at $T_{\mathrm{N}}\approx 0.4\mathrm{K}$ and features a layered structure that combines a triangular lattice network of ${\mathrm{Yb}}^{3+}$ ions with a vanadium-based kagome network. We report a ${}^{51}\mathrm{V}$ nuclear magnetic resonance (NMR) study of the paramagnetic state of ${\mathrm{YbV}}_6{\mathrm{Sn}}_6$. Detailed field-angular dependence of single-crystal NMR spectra determined the principal-axis directions of the electric field gradient tensor at the ${}^{51}\mathrm{V}$ sites, as well as their nuclear quadrupole frequency, ${\nu }_{\mathrm{Q}}$, and asymmetry parameter, $\eta$. The Knight shift, $K$, was measured for different field orientations, and the analysis of $K$ against magnetic susceptibility was used to extract anisotropic hyperfine couplings. Accurate spectral assignments further enabled measurements of the nuclear spin-lattice relaxation rate, $1/T_1$, for both in-plane and out-of-plane field directions. Below $\sim 20\mathrm{K}$, comparable to the energy separation between the crystalline electric field ground-state and first excited doublets of ${\mathrm{Yb}}^{3+}, 1/T_1$ reveals enhanced low-energy spin fluctuations with pronounced in-plane anisotropy. Upon further cooling below $\sim 10\mathrm{K}$, a strongly field-tunable enhancement emerges, suggesting proximity to the very-low-temperature antiferromagnetic instability.

The interplay between unconventional density waves and exotic superconductivity has attracted growing interest. Kagome superconductors $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}$) offer a platform for studying quantum phase transitions and the resulting symmetry breaking. Among these quantum phases, the $4a_0$ stripe charge-density wave (CDW) has been widely observed for $A=\mathrm{Rb}$ and $\mathrm{Cs}$ by scanning tunneling microscopy and nuclear magnetic resonance measurements. However, the microscopic origin of the $4a_0$ stripe CDW remains elusive, and no theoretical studies addressing this phenomenon have been reported so far. In this paper, we propose a microscopic mechanism for the emergence of the $4a_0$ stripe CDW. We analyze the CDW instability in the 12-site kagome lattice Hubbard model with the $2\times 2$ bond order driven by the paramagnon-interference mechanism by focusing on the short-range magnetic fluctuations due to the geometrical frustration of the kagome lattice. We reveal that the nesting vector of the reconstructed Fermi surface, formed by the $2\times 2$ bond order, gives rise to a $4a_0$-period CDW. Remarkably, the obtained stripe CDW is composed of both the off-site hopping integral modulations and on-site potentials. The real-space structure of the stripe CDW obtained here is in good qualitative agreement with the experimentally observed stripe pattern.

We study quantum transport in a one-dimensional Hubbard ring with dimerized nearest-neighbor hoppings and a Fibonacci-modulated on-site potential. For a noninteracting case our analysis reveals that at half filling, the charge current along with the Drude weight decreases with increasing on-site potential when intercell hopping dominates over the intracell hopping, while for dominating intracell hopping it shows nonmonotonic behavior with a sharp peak at certain critical modulation strength, indicating enhanced transport. Moving away from half filling gives rise to reentrant features in both quantities at fillings associated with Fibonacci numbers. On the other hand, in spin-imbalanced systems, both spin and charge current show multiple peaks and reentrant behavior, tunable via hopping dimerization and filling. Including the on-site Hubbard interaction preserves the reentrant behavior in the current and, moreover, favors finite transport which is absent in the noninteracting ring. These results reveal rich interplay among Fibonacci-modulated potential, electron fillings, hopping dimerization, and interaction.

We investigate edge reconstruction scenarios in the $\nu =1$ quantum Hall state, focusing on configurations with upstream and downstream charge and neutral modes. Our analysis shows that the coexistence of upstream charge and neutral modes in a multiterminal geometry can cause pronounced deviations from the expected quantized values of electrical ($e^2/h$) and thermal (${\pi }^2{k}_{\text{B}}^{2}T/3h$) Hall conductance dictated by bulk-boundary correspondence. In particular, we find that both electrical and thermal Hall conductances can be significantly enhanced—exceeding twice their unreconstructed values—offering a clear diagnostic of edge reconstruction.

The recently synthesized two-dimensional Janus material ${\mathrm{Bi}}_2{\mathrm{TeSe}}_2$ offers great potential for nonlinear quantum transport owing to its intrinsically noncentrosymmetric crystal structure. However, its inherent ${\mathcal{C}}_{3v}$ symmetry enforces a cancellation of the Berry curvature dipole (BCD), the key quantity underlying the nonlinear Hall effect. In this work, we demonstrate the controlled generation of a finite BCD through symmetry engineering. By applying uniaxial strain, either compressive or tensile, a finite BCD is induced in monolayer ${\mathrm{Bi}}_2{\mathrm{TeSe}}_2$ which can yield substantial values ($1–10\AA$) near the valence band maximum. Furthermore, our calculations reveal that the inherent inversion symmetry breaking generates a shift current with an intrinsic conductivity of $-1000\mu \mathrm{A}\AA /{\mathrm{V}}^2$ in the undoped case. Most strikingly, hole doping shifts the Fermi level into the valence band, producing a fivefold enhancement of the shift conductivity. This is evidenced by distinct peaks of $\pm 5000 \mu \mathrm{A}\AA /{\mathrm{V}}^2$ in the terahertz regime and at a midinfrared photon energy of 0.2 eV, demonstrating the significant impact of the Fermi energy. Thus, strain selectively modulates the nonlinear Hall effect, while doping drastically improves bulk photovoltaic performance. These approaches offer general strategies for designing Janus materials with tailored transport and optoelectronic properties.

We study anisotropic superconductivity in the nearly quarter-filled $\alpha$–${\mathcal{T}}_3$ lattice. We analyze an extended Hubbard model with off-site attractive interactions within the mean-field framework and find two distinct chiral $d+i{d}^{\prime }$-wave superconducting phases characterized by different Chern numbers. We further investigate the superconducting mechanism mediated by spin fluctuations arising from purely repulsive interactions by applying the fluctuation-exchange (FLEX) approximation to the Hubbard model. The gap symmetry obtained by solving the linearized Eliashberg equation is $d$-wave, which corresponds to a $d+i{d}^{\prime }$-wave superconducting state with a Chern number of 8, including the spin degree of freedom. The $\mathit{q}=\mathit{0}$ antiferromagnetic spin fluctuation, which possesses the largest spectral weight at finite energies arising from the incipient flat band, gives rise to an effective spin-singlet pairing glue between rim sites.

Closing the gap between ray tracing simulations and experimentally observed electron jetting in bilayer graphene (BLG), we study all-electronic, gate-defined BLG cavities using tight-binding simulations and semiclassical equations of motion. Such cavities offer a rich playground to investigate anisotropic electron transport due to the trigonaly warped Fermi surfaces. In this work, we achieve two things: First, we verify the existence of triangular modes (as predicted by classical ray tracing calculations) in the quantum solutions of closed circular BLG cavities. Then, we explore signatures of said triangular modes in transport through open BLG cavities connected to leads. We show that the triangular symmetry translates into anisotropic transport and present an optimal setup for experimental detection of the triangular modes as well as for controlled modulation of transport in preferred directions.

In this work, we describe a localization phenomena, the “topological defect coalescence,” occurring in a non-Hermitian chain with an arbitrary number of defect sites. Specifically, it refers to the localization and coalescence of multiple defect eigenstates at a single defect site closest to the localization edge of the bulk non-Hermitian skin modes. This phenomenon is distinct from the conventional topological defect states in Hermitian systems, where the defect states are separately localized at their respective defect sites. The requirement for the onset of topological defect coalescence is the presence of nonreciprocal coupling which renders the chain non-Hermitian, as well as imaginary on-site potentials at the defect nodes. This allows the defect state coalescence and distribution to be modulated by both the defect site distribution and their corresponding on-site potentials, paving the way for possible applications. Furthermore, this phenomenon is realizable in various synthetic and experimentally realizable platforms, such as topolectrical and photonic systems.

The Magneto-optical effect is a fundamental and well-studied phenomenon in the linear regime, but it is rarely studied in extreme conditions where both the magnetic and the laser fields are strong. Here, we study this effect theoretically in graphene in the nonlinear regime, where high-order harmonics are generated. It is found that the harmonic conversion efficiency can be enhanced by orders of magnitude, and the cutoff energy could be extended from visible to extreme ultraviolet ranges. When the laser intensity reaches a critical value, the cutoff energy is linearly dependent on the laser wavelength, outperforming many semiconductors with a wavelength-independent cutoff. These effects closely link to the dense Landau levels. Our Letter sheds light on a promising prospect for the application of the magneto-optical effect in harmonic generation processes in solids.

Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on cyclic graphs, termed cyclic quantum walks, to simulate exotic topological phenomena using discrete Fourier transforms and an effective Hamiltonian. Our approach enables the generation of both gapped and gapless topological phases, including Dirac conelike energy dispersions, topologically nontrivial flat bands, and protected edge states, all without resorting to resource-intensive split-step or split-coin quantum walk protocols. Odd- and even-site cyclic graphs exhibit markedly different spectral characteristics, with rotationally symmetric flat bands emerging exclusively in $4n$-site graphs ($n\in \mathbf{N}$). We analytically establish the conditions for the emergence of topological, gapped flat bands and show that gap closings in rotation space imply the formation of Dirac cones in momentum space. Further, we engineer protected edge states at the interface between distinct topological phases in both odd and even cycle graphs. We numerically demonstrate that the edge states are robust against moderate static and dynamic gate (coin) disorder as well as remain stable against phase-preserving perturbations and are independent of initial states. This scheme serves as a resource-efficient and versatile platform to engineer topological phases, transitions, edge states, and flat bands in small-scale quantum systems, opening different avenues for robust quantum memory, protected state transfer, and compact implementations of fault-tolerant quantum technologies.