We investigate the entanglement properties in a generalized quantum cluster model under periodic boundary condition. By evaluating the quantum conditional mutual information entropy under four subsystem partitions, we identify clear signatures of long-range entanglement. Specifically, when both the system size $N$ and the interaction range $m$ are odd, the system exhibits nonzero four-part quantum conditional mutual information entropies in infinitesimal but finite field. This nonvanishing four-part quantum conditional mutual information entropy directly signals the presence of long-range entanglement. In contrast, all other combination of $N$ and $m$ yield vanishing four-part quantum conditional mutual information entropy. Remarkably, in the case of $N,m\in \text{odd}$, these long-range entangled features persist even in the presence of a large transverse field, demonstrating their robustness against quantum fluctuations. These results demonstrate how the interplay between system size and interaction range governs the emergence of long-range entanglement in one-dimensional generalized quantum cluster model.

We report the observation of the Purcell effect in a cavity-metallic-magnet hybrid system using electric field mediated coupling. In this configuration, microwave-induced axial currents in the microwire induce circular magnetic fields that drive the ferromagnetic resonance (FMR) of the magnetized microwire. Field-dependent transmission and reflection spectroscopies reveal a clear cavity perturbation consistent with the Purcell regime, in which the magnetic loss rate exceeds the light-matter coupling strength. Despite the small magnetic volume ($\sim {10}^{-13}{\text{m}}^3$), measurements performed at both room temperature and $T=7\mathrm{m}\mathrm{K}$ show coupling rates as high as $g/2\pi =56\mathrm{M}\mathrm{Hz}$, one order of magnitude stronger than the one expected from conventional coupling at the magnetic antinode. Time-domain ringdown measurements directly show the magnetic field-dependent modification of the cavity photon lifetime, in agreement with theoretical predictions. These results establish a versatile approach for coupling microwave fields to metallic magnets via geometric and electric field mediated interactions, opening new opportunities for hybrid cavity-magnet systems.

Binary Bi-Pd/Pt systems have attracted a lot of interest because of their topologically nontrivial nature along with superconductivity. We report the structural and superconducting properties of high-quality single-crystalline BiPt using a comprehensive range of experimental techniques, including X-ray diffraction, electron microscopy, muon spin rotation/relaxation ($\mu \mathrm{SR}$), magnetization, resistivity, and heat capacity. Our findings establish that BiPt is a weak type-II superconductor with a transition temperature ($T_c$) of 1.2 K which exhibits pronounced anisotropic superconducting characteristics attributed to its hexagonal crystal structure. Magnetization and electronic transport studies reveal that BiPt lies within the dirty limit, while $\mu \mathrm{SR}$ and heat capacity data indicate conventional $s$-wave superconductivity that maintains time-reversal symmetry. This work provides valuable insights into the pairing symmetry and superconducting mechanism of topologically trivial BiPt, a sound comparison system for other Bi-based topologically nontrivial superconductors.

We discuss intrinsic relaxation rates in superconductors, and how they may be measured using nonlinear optical (terahertz) response. We consider both $s$- and $d$-wave superconductors, with and without a phenomenological (energy-dependent) damping. Intrinsic relaxation rates of interest include the Higgs mode decay rate, the quasiparticle redistribution rate ($1/T_1$), and the quasiparticle dephasing rate ($1/T_2$), where the latter two rates are zero in the pure BCS model, but nonzero in the presence of damping. Using the Anderson pseudospin formalism, we illustrate how these intrinsic relaxation rates are related to measurable quantities such as the time-dependent gap function and the nonlinear current (also known as third-harmonic generation). Hence, we show how intrinsic relaxation rates may be experimentally extracted and discuss what one may thereby learn about the underlying damping. We also discuss the effects of polarization control (i.e., nonlinear response to light polarized in different directions), which offers a useful experimental knob, especially for $d$-wave superconductors, enabling selective excitation of modes in different irreducible representations (and the readout of their corresponding relaxation rates).

Superconductivity in quasi-one-dimensional ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_6{\mathrm{O}}_{17}$ emerges from an exotic, nonmetallic normal state that exhibits signatures of Tomonaga-Luttinger liquid behavior, emergent symmetry, and excitonic order. The high upper critical field, $H_{c2}$, in ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_6{\mathrm{O}}_{17}$ suggests that that the favored pairing state is spin-triplet in nature. Here, we report measurements of the magnetic penetration depth down to $0.08\mathrm{K}$ ($T/T_c\lesssim 0.04$) and the specific heat down to $0.4\mathrm{K}$ ($T/T_c\lesssim 0.2$), and show that they are consistent with a moderately coupled, fully gapped superconducting state with marked gap anisotropy and a minimum (${\mathrm{\Delta }}_{\min }\simeq 0.4k_{\mathrm{B}}{T}_c$) occurring over a very narrow region in $k$ space. Combined with knowledge of $H_{c2}$, these measurements support the presence of a nodeless and possibly odd-parity spin-triplet superconducting order parameter in ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_6{\mathrm{O}}_{17}$.

We investigate nonequilibrium dynamics and weak ergodicity breaking in a harmonically trapped spin-$3/2$ Fermi gas by using the time-dependent Hartree-Fock equation. The Shannon entropy remains bounded and oscillatory throughout the evolution, indicating restricted and nonuniform exploration of Hilbert space rather than immediate thermalization. The fidelity exhibits pronounced, nearly periodic revivals whose period is largely insensitive to particle number and interaction strength, while the revival amplitude gradually decreases with increasing system size and interaction strength. The Fourier spectrum of the fidelity reveals a set of sharp and approximately equally spaced peaks. By projecting the time-evolved state onto the instantaneous eigenbasis of the self-consistent mean-field Hamiltonian, we identify a sparse and spectrally stable manifold that forms a quasiregular energy ladder, with spacing comparable to the dominant quasienergy interval extracted from the fidelity spectrum. These results indicate that the long-lived coherent oscillations originate from collective phase interference associated with a quasiregular spectral structure embedded in the many-body continuum, rather than from a conventional eigenstate-dominated scar mechanism.

Gallium is a prototypical liquid metal and has gained renewed attention because of its unique properties. Characterizing and elucidating its atomic dynamics remains elusive despite numerous studies, primarily because of the challenges in quantifying atomic-scale dynamics in liquids. Recent developments in inelastic neutron scattering enable us to measure the Van Hove correlation function that describes the real-space motion of liquid atoms. In this work, we use this approach to reveal the dynamics in gallium liquids and find the co-existence of two dynamical medium-range orders (MROs), which have a dynamical behavior distinct from that of the short-range order (SRO). We propose that these MROs are driven by global forces in the form of two density waves, as a direct consequence of the underlying competition between ionic core repulsion and valence electron cohesion. We suggest that the density wave approach is not only applicable to other metallic liquids exhibiting similar structural anomalies, but also offers a promising direction for elucidating the dynamics of complex liquids and glasses by linking electronic-state fluctuations to atomic dynamics.

The star lattice, which can be visualized as a honeycomb network with each vertex replaced by a triangle, provides a rare platform for realizing exotic quantum states such as quantum spin liquids and disorder-driven random-singlet (RS) states. Herein, we investigate the ground-state properties of the three-dimensional (3D) stuffed hyper-star lattice ${\mathrm{Li}}_2{\mathrm{Cu}}_2$(${\mathrm{MoO}}_4{)}_3$, which exhibits a crossover from short-range spin correlations to a disorder-driven RS-like state below $T^{*}\sim 15.8\mathrm{K}$. Thermodynamic and microscopic measurements capture this crossover through a change in the power-law behavior of various observables, from $\sim T^{0.25}$ for $T>T^{*}$ to $\sim T^{-0.50}$ for $T<T^{*}$. Upon further cooling, a quasifrozen state emerges near $T_f=0.32\mathrm{K}$, likely associated with weakly coupled spin chains within the hyper-star spin network. Our results underscore the crucial role of orphan spins and weak residual interactions in stabilizing a disorder-driven quantum-disordered state in three dimensions.

We study interaction-driven quantum phases in a two-dimensional generalized Su-Schrieffer-Heeger (SSH) model defined on a square lattice with inequivalent nearest-neighbor hopping, next-nearest-neighbor hopping, and a staggered on-site potential. In the noninteracting limit, the model hosts either quadratic band touching (QBT) at the Brillouin-zone center or symmetry-protected Dirac nodes, depending on the microscopic parameters. In the parameter regime with QBT, our self-consistent Hartree-Fock analysis shows that weak to intermediate interactions can spontaneously break time-reversal symmetry and stabilize a quantum anomalous Hall (QAH) insulating phase with a finite Chern number. Interestingly, this QAH phase is found to weakly break lattice symmetries, leading to a small but finite nematic bond order. This is in contrast to the standard QAH phase in the checkerboard lattice, which preserves all lattice symmetries. Additionally, we find an enhanced bond-nematic Dirac semimetallic (BNDS) phase due to asymmetric hopping; this phase, previously identified using more advanced numerical approaches, also emerges naturally within an unrestricted Hartree-Fock framework when the bond order sector is analyzed explicitly. In the parameter regimes where QBT splits into two Dirac nodes, the QAH phase survives up to a finite staggered on-site potential. However, as the staggered potential increases, the QAH phase is suppressed while the BNDS phase grows stronger.

(2+1)-dimensional [(2+1)D] topological orders possess emergent ordinary symmetries given by a group ${\text{Aut}}_{br}\left(\mathcal{C}\right)$, which consists of the braided tensor autoequivalences of the modular tensor category $\mathcal{C}$ that describes the anyons. In this paper we discuss cases where ${\text{Aut}}_{br}\left(\mathcal{C}\right)$ has elements that neither permute anyons nor are associated to any symmetry fractionalization but still acts faithfully on the theory, which we refer to as soft symmetries. We point out that one can construct topological defects corresponding to such exotic symmetry actions by decorating with a certain class of gauged symmetry protected topological states that cannot be distinguished by their torus partition function. This gives a physical interpretation to work by Davydov on soft braided tensor autoequivalences. This has a number of important implications for the classification of gapped boundaries, noninvertible spontaneous symmetry breaking, and the general classification of symmetry-enriched topological phases of matter. We also demonstrate analogous phenomena in higher dimensions, such as $(3+1)\mathrm{D}$ gauge theory with gauge group given by the quaternion group $Q_8$.

Quad-helicoid surface states (QHSSs) are unique surface states with two pairs of helicoid surface states in topological semimetals such as Dirac semimetals. So far, topologically protected QHSSs are shown to appear in spinless systems with two $\mathcal{GT}$ symmetries and $\mathcal{T}$ symmetry ($\mathcal{G}$: glide, $\mathcal{T}$: time-reversal). In this paper, we show that topologically protected QHSSs also appear in spinful/spinless systems with only two $\mathcal{GT}$ symmetries by defining new topological charges and establishing the bulk-surface correspondence. We first define a local $Z_2\times Z_2$ monopole charge for gapless nodes at $\mathcal{GT}$-invariant high-symmetry points and a global $Z_2$ charge reflecting the global topological feature of $\mathcal{GT}$-symmetric topological semimetals. Next, we show that the latter $Z_2$ classification corresponds to the presence or absence of QHSSs on the surface with two $\mathcal{GT}$ symmetries. In addition, we provide simplified formulas of the $Z_2$ charge under additional symmetries, and clarify some symmetry conditions where QHSSs are filling enforced.

Motivated by the recent discovery of metallic surface states in the $d$-electron Kondo insulator candidates FeSi and ${\mathrm{FeSb}}_2$, along with some recent reports of magnetic correlations in the surface transport properties of FeSi, we have investigated the low-temperature surface magnetotransport properties of ${\mathrm{FeSb}}_2$. By using a Corbino disk transport geometry, we were able to isolate the electrical transport properties of a single surface of our samples and study the [110] and [101] naturally forming faces separately. Studying the relationship between the applied magnetic field, current direction, and crystal symmetry has allowed us to separate possible contributions to the magnetotransport anisotropy. Unlike previous studies of ${\mathrm{SmB}}_6$ surface states, we find no two-dimensional Drude-like dependence on field orientation relative to current direction, but instead a magnetocrystalline anisotropy that appears to originate from local moment scattering with a well-defined easy axis along the [100] direction. We compare these results with the magnetotransport properties of the conducting surface states on the [111] facet of FeSi. We also find evidence of three-dimensional variable-range-hopping conduction below the bulk-to-surface crossover, extending below 1 K, which implies that the electrical transport at the surface of these materials is carried by a thin but three-dimensional conducting channel, which is inconsistent with the lower dimensional states expected for a strong topological insulator.

${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, a nickelate compound with a reported superconducting transition temperature of $80\mathrm{K}$, has attracted significant attention in recent years. Density-wave phenomena arising from strong electron correlations are widely regarded as key to unraveling the superconductivity mechanism, but the ordering and stability of these density waves remain a subject of contention in existing theoretical studies. In this work, we employ the variational Monte Carlo (VMC) method to thoroughly examine the nature of density waves as functions of Coulomb repulsion and exchange interactions in bilayer two-orbital models proposed for the high pressure phase of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. We analyze the spin and charge correlation functions in a wide range of parameter space, and delineate a schematic phase diagram that separates different density-wave ground states. Our results provide useful insights into the understanding of electron correlations in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, and highlight the potential of VMC to elucidate its superconducting mechanism.

Due to the large number of possible defect sites characterized by different local chemical environments, investigating point defects in semiconductor alloys has been a long-standing challenge for first-principles defect calculations. In practice, it is often assumed that focusing on the energetically most favorable defect site is sufficient to provide a reliable estimation of the defect properties. Here, using a prototypical defect $\left({\mathrm{C}}_{\mathrm{N}}\right)$ in the ${\mathrm{Al}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{N}$ alloy as an example, we show that the site occupation is highly important and critically impacts the defect-assisted nonradiative capture coefficients. We find a positive correlation between the hole capture coefficient $\left(C_p\right)$ and defect formation energy, which brings in a strong temperature dependence: the statistically averaged effective $C_p$ increases substantially with increasing the material growth temperature. Quantitative analysis demonstrates that the effective $C_p$ with equilibrium site occupations at the typical growth temperature is one order of magnitude higher than that with only the lowest-energy site considered. Further, we show that even though the lowest-energy configuration of ${\mathrm{C}}_{\mathrm{N}}$ in the alloy has the same first-nearest-neighbor environment as the one in GaN, $C_p$ in the two cases differs by more than an order of magnitude. The large difference of $C_p$ is primarily attributed to reduced electron-phonon coupling caused by lattice distortions in the alloy, which highlights the importance of lattice distortion in semiconductor alloys in addition to local chemistry. Our study provides essential insights for defect engineering in semiconductor alloys toward enhanced electronic and optoelectronic performance.

Directional scattering enabled by multimode interference in high-index nanostructures provides exceptional control over light manipulation, but achieving flexible spectral tuning remains challenging. To address this, we propose a hybrid nanoantenna that integrates transition metal dichalcogenides (TMDs) with the phase-change material ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Se}}_4{\mathrm{Te}}_1$ (GSST), enabling continuous spectral tuning of unidirectional forward scattering. This tunability arises from the GSST phase transition. With carefully optimized parameters, this transition induces virtually synchronous redshifts of the electric and magnetic dipole Mie resonances while preserving their near-zero phase difference, thereby maintaining the Kerker condition throughout the amorphous-crystalline transformation. This enables on-demand active spectral tuning of the unidirectional forward scattering. We further demonstrate flexible switching between single- and dual-wavelength unidirectional forward scattering enabled by the self-hybridized exciton-Mie interaction in the ${\mathrm{MoTe}}_2$-GSST nanoantenna. Additionally, we explore the influence of the GSST phase transition on the scattering directionality under self-hybridization, showing that the transition alters the overlap between the exciton and Mie resonances and thereby modulates the coupling strength, ultimately suppressing dual-wavelength scattering. Our work introduces a paradigm for actively tunable nanoantennas, combining dynamic phase-change materials with exciton resonances.

On-chip optical superchiral fields are usually generated using nanostructures. Here we demonstrate superchiral field generation using surface waves in a one-dimensional photonic crystal (PhC). The PhC supports nodal rings featuring a bandwidth-enhanced, all-angle degenerate dispersion for transverse magnetic (TM) and transverse electric (TE) surface modes. This unique degeneracy is harnessed to create simultaneous electric field and magnetic field skyrmion bags, resulting in a moiré superchiral field superlattice on the flat crystal surface. We show that the distribution of the superchirality can be modulated by the moiré angle and orbital angular momentum of the excitation scheme and the handedness of chirality is determined by the phase difference between TM and TE waves. This work proposes a simple platform for on-chip chiral sensing using tailored superchiral fields.

Simplicity in chemical composition does not always translate into simplicity in the structures and dynamics of liquids and solids. Some elementary liquid metals, such as gallium, show unusual behaviors in thermodynamic and transport properties as a result of their complex atomic structure and dynamics. In this work, we study the real-space atomic correlation function of liquid gallium by neutron scattering. In the pair-distribution function, there exist two kinds of medium-range order (MRO), characterized by oscillations beyond the first nearest neighbors. On the other hand, the first neighbor shell shows only one kind of bond. The two types of MRO are strongly overlapping in space and fluctuating in time. We propose that they are the basis for anomalous behavior of liquid gallium. This view challenges the current view that liquid gallium consists of fluctuating metallic and insulating domains. These findings shed light on the interpretation of similar microscopic anomalies observed in other semimetallic liquids.

We study the effect of quenched disorder on the non-Hermitian skin effect in systems that conserve a U(1) charge and its associated multipole moments. In particular, we generalize the Hatano-Nelson argument for a localization transition in disordered, nonreciprocal systems to the interacting case. When only U(1) charge is conserved, we show that there is a transition between a skin-effect phase, in which charges cluster at a boundary, and a many-body localized phase, in which charges localize at random positions. In the dynamics of entanglement, this coincides with an area-to-volume-law transition. For systems without boundaries, the skin effect becomes a delocalized phase with a unidirectional current. If dipoles or higher multipoles are conserved, we show that the non-Hermitian skin effect remains stable to arbitrary disorder. Counterintuitively, the system is therefore always delocalized under periodic boundary conditions, regardless of disorder strength.

Ferrimagnetic ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ grown on the (001) surface of paramagnetic ${\mathrm{Gd}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ experiences an exchange bias field, which has been attributed to the magnetism of an interface layer between the two materials. We report here that when grown using sputtering and with lower postannealing temperatures than in previous works, the blocking temperature of the interface magnetic layer of a micron-sized film sample is lowered to about 7 K, while still displaying a strong exchange bias. This exchange bias is then found to be tunable between its two extreme values by varying the field cooling protocol. This is attributed to a slow and complex dynamics of the frustrated spins in the interface layer when the sample is warmed up close to the blocking (or melting) temperature.

It is widely believed that friction between materials could induce local melting. However, the criterion for identifying the occurrence of melting for a friction process is an unresolved issue. In this work, molecular dynamics simulations were conducted to investigate the friction induced melting process. A criterion for identifying liquid phase formation was established based on analysis of friction induced temperature rise and structural order destruction. Specifically, the formation of the liquid phase can only occur when both structural disorder and atomic kinetic energy conditions are satisfied. Under specific friction conditions, the contact region undergoes short-time local melting and exhibits a high local liquid nucleation rate. It is suggested that friction induced melting is a rapid heterogeneous process, which significantly differs from that induced solely by heating. Friction not only generates localized superheating in the contact region, but also causes destruction of structural order, thereby reducing the nucleation barriers for the formation of the liquid phase.