At low temperature, the concentration of quasiparticles observed in superconducting circuits far exceeds the predictions of microscopic BCS theory at equilibrium. As a source of dissipation, these excess quasiparticles degrade the performance of various devices. Therefore, understanding their dynamics, especially their recombination into Cooper pairs, is an active topic of current research. In disordered superconductors, spatial fluctuations in the superconducting gap can trap quasiparticles and modify their eigenspectrum. Since this spectrum plays a key role in quasiparticle dynamics, it must be carefully investigated. To this end, we introduce a toy model of a single local gap suppression. Specifically, we consider a shallow disk-shaped gap variation in a clean superconductor. Using a semiclassical approximation, we demonstrate the existence of multiple bound states and give the dependence of their number on the size and depth of the gap suppression. Extending our analysis beyond the semiclassical regime, in dimensions larger than one, we observe an infinite number of bound states very close to the gap edge, even for an arbitrarily small gap variation. These results deepen our understanding of trapped quasiparticles and may have important implications for their recombination in disordered superconductors.

Superconducting coplanar resonators are key building blocks of cryogenic microwave circuits, yet their performance in perpendicular magnetic fields is ultimately limited by Abrikosov vortices. In this work we investigate the dependence of the transmission parameter $S_{21}$ of niobium quarter-wave coplanar resonators on perpendicular magnetic fields up to 40 Oe and at temperatures between 18 mK and 5 K. Beyond the reversible Meissner regime, the entire resonance peak exhibits abrupt, staircaselike jumps as a function of magnetic field. Upon reversal of the field sweep, these jumps form an almost equidistant series with spacing $\mathrm{\Delta }H\simeq 1.7–1.8\mathrm{Oe}$, which, in agreement with theoretical estimates, we interpret as signatures of multiple-vortex entry and exit events. Additionally, we observe the nonproportional responses of the resonant frequency and the internal quality factor that indicate a complex contribution of vortex and antivortex configurations. We expect that our results will stimulate further studies of large vortex-antivortex systems, explicitly accounting for their discrete nature.

We comprehensively study the unconventional pairing and collective modes in the multiband kagome superconductors $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K},\mathrm{Cs},\mathrm{Rb}$). By solving gap equations at zero temperature, we identify a transition from normal $(s++/s\pm )$-wave pairing to time-reversal symmetry- (TRS) breaking pairing with a variation of interpocket interactions or the density of states. This TRS-breaking pairing originates from the superconducting phase frustration of different Fermi pockets and can account for the experimental TRS-breaking signal in kagome superconductors. Moreover, we investigate collective modes, including the Higgs, Leggett, and Anderson-Bogoliubov modes, arising from fluctuations of the amplitude, relative phase, and overall phase of the superconducting order parameters, respectively. Remarkably, due to the presence of multibands, one branch of the Leggett modes becomes nearly massless near the TRS-breaking transition, providing a compelling smoking-gun signature of TRS-breaking superconductivity, in clear contrast to TRS-breaking charge orders. Our results elucidate the rich superconducting physics and its associated collective modes in kagome metals and suggest feasible experimental detection of TRS-breaking pairing.

This study employs Deep-Potential (DP) models with varying exchange-correlation (XC) functional accuracies, combined with large-scale two-phase molecular dynamics simulations, to determine the melting curves of key minerals ${\mathrm{SiO}}_2$ (coesite, stishovite, and $\beta$-stishovite), ${\mathrm{MgSiO}}_3$ (perovskite and postperovskite), and ${\mathrm{CaSiO}}_3$ perovskite under Earth's mantle conditions. This study quantitatively investigated the effect of XC functionals on the melting temperature of silicate phases, and we suggest the strongly constrained and appropriately normed (SCAN)-based DP models as the optimal choice. For ${\mathrm{MgSiO}}_3$, the melting curve predicted by the DP-SCAN model lies at the high-temperature end of the presently studied range, at approximately 6200 K at the core-mantle boundary. For ${\mathrm{CaSiO}}_3$, the DP-SCAN-based results clarify the discrepancy in melting temperatures up to 2000 K at the core-mantle boundary. And the results indicate that ${\mathrm{CaSiO}}_3$ perovskite is the most refractory silicate phase near the core-mantle boundary, with the melting temperature as high as 7000–8000 K. For ${\mathrm{SiO}}_2$, the previously reported steep increase in the Clapeyron slope of the melting curve due to the $\text{stishovite}\to \beta$-stishovite transition is not observed, and a new temperature-induced phase transition at high temperatures is a potential cause. Furthermore, this work provides insights into the crystallization sequence of midocean ridge basalts and underscores the importance of machine learning methods for understanding deep Earth processes.

Raman imaging, based on incoherent spontaneous Raman scattering (SR) or coherent techniques such as broadband coherent anti-Stokes Raman spectroscopy (BCARS), is a powerful tool for visualizing local lattice distortions. It can thus be employed, e.g., to identify and visualize ferroelectric (FE) domain walls (DWs). While SR-based DW imaging relies on small changes in the intensity or position of Raman peaks at the DW, BCARS measurements may detect DW signatures with a drastically increased contrast and orders of magnitude faster imaging speed. However, while SR-based contrasts can be predicted from existing models, the increased DW contrasts in BCARS remain poorly understood. In this work, we develop a first-principles approach for the simulation of CARS spectra to investigate the origin of this BCARS signal contrast at periodically poled stoichiometric lithium niobate (sPPLN) DWs. Combining these atomistic simulations with strain modeling allows us to explore how strain affects the CARS signal generation at FE DWs. We then apply polarization-sensitive BCARS to image sPPLN DWs for different polarization configurations. Our results reveal additional Raman peaks specific to the DWs across all investigated polarization combinations, yielding a strong DW-to-bulk contrast that enables in situ identification and localization of DWs in two-dimensional BCARS maps. This study demonstrates the practical utility of polarization-sensitive BCARS for fast DW imaging and provides fundamental insights into the BCARS contrast mechanism in FE materials, both in strained regions and in the unstrained bulk.

We investigate a ferroelectric instability of a magnon Bose-Einstein condensate, mediated by its interaction with an electric field through a geometric Aharonov-Casher (AC) phase. A distinct feature of the system is the positive feedback loop in which an electric field induces magnon orbital motion via the AC phase, generating electric polarization that in turn enhances the original field. Based on bosonic Bogoliubov–de Gennes (BdG) mean-field theory, we show that this feedback drives a spontaneous ferroelectric transition in the magnon superfluid, accompanied by a persistent magnon supercurrent. In the resulting ferroelectric phase, the quasiparticle excitation spectrum becomes nonreciprocal, reflecting spontaneous breaking of spatial inversion symmetry. At the critical point of the transition, the bosonic BdG Hamiltonian exhibits a global coalescence of both eigenvalues and eigenvectors, forming exceptional points throughout the entire Brillouin zone. The corresponding eigenstate is an equally weighted superposition of bosonic quasiparticle and quasihole states and is invariant under particle-hole transformation, allowing it to be interpreted as a bosonic analog of a Majorana fermion.

We formulate a microscopic theory of the Raman response of superconducting collective modes in multicomponent superconductors. Starting from a general Bogoliubov–de Gennes (BdG) Hamiltonian with a separable pairing interaction, we derive a gauge-invariant expression for the Raman susceptibility, including a long-range Coulomb interaction. The resulting Raman susceptibility is directly computable for an arbitrary BdG Hamiltonian, which contains single- and multiband systems, spin-singlet and triplet order parameters, and time-reversal-symmetric and time-reversal-symmetry-breaking superconducting states. Based on the microscopic coupling between a Raman source field and collective modes, we derive a symmetry selection rule for Raman-active collective modes and show a group-theoretical classification for all crystalline point groups. This classification provides a unified framework based on the “higher-order Lifshitz-invariant” to identify Raman-active collective modes such as Leggett mode, Bardasis-Schrieffer mode, and clapping mode. As an application, we focus on an effective model of the heavy-fermion superconductor ${\mathrm{UTe}}_2$ with a fully gapped multicomponent odd-parity pairing state. We find sharp in-gap Raman resonances below the quasiparticle continuum, which do not correspond to a conventional Leggett mode but arise from the intraband relative modes between different pairing components.

We present an experimental investigation of the Pb-induced changes on the electronic structure of selected topological insulators, namely, ${\mathrm{TlBiSe}}_2$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. Using spatially resolved and surface-sensitive techniques, including micro-angle-resolved photoemission ($\mu$-ARPES) and micro-core-level photoemission ($\mu$-PES), we track the evolution of the electronic states during adsorbate growth. For low Pb coverage on ${\mathrm{TlBiSe}}_2$, we identify the formation of a disordered interface. For thicker films, $\mu$-ARPES measurements clearly resolve well-defined electron confinement (quantum well) states within the metallic Pb layers and no migration of the topological surface state onto the Pb film is observed. Furthermore, $\mu$-PES results on both Pb/${\mathrm{TlBiSe}}_2$ and Pb/${\mathrm{Bi}}_2{\mathrm{Se}}_3$ heterostructures can be rationalized in terms of a significant chemical interaction between Pb and Se, leading to substantial surface degradation and Bi atom segregation. The ab initio modeling performed on the adsorption of lead on topological insulator surfaces, which includes the consideration of the swapping of Pb adsorbates with Bi substrate atoms, validates the scenario derived from experimental observations. It also suggests that the development of a disordered interface is due to the formation of PbSe nuclei, whose size is constrained by the compressive stresses exerted by the TI substrate.

We formulate a continuum quantum mechanics for nonrelativistic, dipole-conserving fractons. Imposing symmetries and locality results in novel phenomena absent in ordinary quantum mechanical systems. A single fracton has a vanishing Hamiltonian, and thus its spectrum is entirely composed of zero modes. For the two-body problem, the Hamiltonian is perfectly described by Sturm-Liouville (SL) theory. The effective two-body Hamiltonian is an SL operator on $(-1,1)$ whose spectral type is set by the edge behavior of the pair inertia function $K\left(x\right)\sim |x-x_{\mathrm{edge}}{|}^{\theta }$. We identify a sharp transition at $\theta =2$: for $\theta <2$ the spectrum is discrete and wave packets reflect from the edges, whereas for $\theta >2$ the spectrum is continuous and wave packets slow down and, dominantly, squeeze into asymptotically narrow regions at the edges. For three particles, the differential operator corresponding to the Hamiltonian is piecewise defined, requiring several “matching conditions” which cannot be analyzed as easily. We proceed with a lattice regularization that preserves dipole conservation and implicitly selects a particular continuum Hamiltonian that we analyze numerically. We find a spectral transition in the three-body spectrum and find evidence for quantum analogs of fracton attractors in both eigenstates and in the time evolution of wave packets. We provide intuition for these results which suggests that the lack of ergodicity of classical continuum fractons will survive their quantization for large systems.

Achieving polarization-independent strong light-matter coupling remains a central challenge for practical integrated photonic platforms. Conventional metasurfaces based on bound states in the continuum (BICs) can sustain ultrahigh quality ($Q$) factors, yet their intrinsic polarization sensitivity limits their applicability in polarization-insensitive systems. Here, we propose a $C_{4v}$ symmetric ${\mathrm{WSe}}_2$ metasurface that supports degenerate toroidal quasi-BIC resonances and enables polarization-independent exciton-polaritons. Electromagnetic field analyses and multipole decomposition reveal that the dual degenerate modes originate from electric and magnetic toroidal dipole excitations, whose resonance wavelengths and $Q$ factors can be precisely tuned through a structural asymmetry parameter. Leveraging these polarization-independent resonances, we demonstrate strong coupling between the quasi-BIC modes and ${\mathrm{WSe}}_2$ excitons, evidenced by persistent anticrossing behavior for all polarization angles and coupling strengths that can be flexibly controlled via geometric perturbation. These results establish a viable route toward polarization-independent exciton-polaritons in van der Waals metasurfaces and provide a promising platform for robust light-matter interaction, sensing, and integrated nanophotonic devices.

Bound states in the continuum (BICs) with ultrahigh quality ($Q$) factors hold great promise for enhancing wave–matter interactions. However, their practical realization is hindered by extreme fragility to structural imperfections. Here, we report an anomalously robust Fabry–Pérot (FP) BIC in a coupled triple-resonator system. Unlike conventional two-state systems, in which the formation of an FP BIC typically requires strict matching between two identical resonators, the proposed three-state system substantially relaxes this requirement and can still support an FP BIC even when the central resonator is distinct from the two side resonators. More importantly, this system intrinsically supports a pinned eigenvector of the form $\{-1,0,+1\}$, which enforces a vanishing field in the central resonator and thereby endows the BIC with strong robustness against local structural perturbations, a feature absent in two-state systems. Using a coupled waveguide–triple-resonator platform, we numerically and experimentally demonstrate the existence of both robust and sensitive BICs. This work deepens our understanding of BICs in finite systems and provides a viable way to realize ultrahigh-$Q$ resonances.

The magnons in altermagnets exhibit chiral splitting even in the absence of spin-orbit coupling and external magnetic fields. Typically, this chiral splitting behavior can be well described by alternating isotropic spin exchanges (ISEs) near the zero temperature. However, its finite-temperature dynamics, particularly when incorporating spin-orbit coupling, remains elusive. In this Letter, we reveal that, when including magnon-magnon interactions, long-range anisotropic spin exchanges (ASE) of altermagnets can effectively induce chiral splitting of magnons at finite temperatures. Crucially, the ASE-induced chiral splitting competes with that arising from ISE, leading to a pronounced temperature-dependent modulation. Moreover, this competition is intimately coupled to quantum spin fluctuations, and can reverse the spin current driven by the band splitting as temperature increases. Our work uncovers the intrinsic competition governing collective spin excitations in altermagnets, providing insights into their finite-temperature dynamical behavior.

In this work, we report that ${\mathrm{Bi}}_2{\mathrm{Ta}}_3{\mathrm{S}}_6$-family superconductors exhibit nontrivial band topology. They possess a natural quantum-well structure consisting of alternating stacks of ${\mathrm{TaS}}_2$ and honeycomb Bi layers, which contribute superconducting and topological properties, respectively. Symmetry-based indicators $({\mathbb{Z}}_4;{\mathbb{Z}}_2{\mathbb{Z}}_2{\mathbb{Z}}_2)=(2;000)$ reveal that the topological nature arises entirely from the Bi layers, which belong to a quantum spin Hall phase characterized by a $p_x\text{−}{p}_y$ model on a honeycomb lattice. The topological zigzag (ZZ) and armchair (AC) edge states are obtained. Using vasp2kp, the in-plane $g$ factors of these topological edge states are computed from the ab initio calculations: $g_{x/y}^{\mathrm{ZZ}}=2.07/1.60$ and $g_{x/y}^{\mathrm{AC}}=0.50/0.06$. The strong anisotropy of the edge-state $g$ factors allows us to explore Majorana zero modes in the Bi monolayer on a superconductor, which can be obtained by exfoliation or molecular beam epitaxy. Furthermore, using the experimental superconducting gap $\mathrm{\Delta }$ and the computed $g$ factors, we obtain the phase diagram, which shows that the in-plane field $B_y>2.62\mathrm{T}$ can generate corner Majorana zero modes in the Bi monolayer of the superconductor ${\mathrm{Bi}}_2{\mathrm{Ta}}_3{\mathrm{S}}_6$. A similar paradigm also applies to the ${\mathrm{Bi}}_2{\mathrm{Ta}}_3{\mathrm{S}}_6$ bulk with the emergence of Majorana hinge states. These natural quantum-well superconductors therefore offer ideal platforms for exploring topological superconductivity and Majorana zero modes.

First-principles studies of superconductivity often neglect anharmonic effects (AHE), despite their crucial role in achieving quantitative accuracy in many materials. To bridge this gap, we introduce a general computational approach, termed anharmonic superconducting density functional theory (ah-SCDFT) which systematically incorporates anharmonic corrections into standard SCDFT. This approach allows for high-fidelity predictions of superconducting properties with only a modest increase in computational cost for a limited number of superconducting calculation convergence steps. We demonstrate the effectiveness and reliability of ah-SCDFT by applying it to the prototypical superconductor ${\mathrm{MgB}}_2$, accurately reproducing its superconducting behavior under both ambient conditions and applied pressure in excellent agreement with experiment. Our results establish ah-SCDFT as a powerful, efficient, and broadly applicable approach for quantitatively reliable studies of superconductivity and a promising tool for the prediction of new superconducting materials.

The strange metal remains a major unsolved problem for modern condensed matter physics. Since the early development of marginal Fermi liquid phenomenology, it has been clear that progress requires detailed knowledge of the momentum- and frequency-dependent charge susceptibility $\chi (\mathbf{q},\omega )$, particularly at large momenta. Electron energy-loss spectroscopy (EELS), performed in either reflection or transmission geometry, provides the most direct probe of $\chi (\mathbf{q},\omega )$. However, measurements over the past four decades have yielded conflicting results, with authors of some studies reporting a dispersing random phase approximation (RPA)-like plasmon and others observing a strongly overdamped, incoherent response. Here, we report a transmission EELS study of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}$ (Bi-2212) that simultaneously achieves high-energy resolution ($\mathrm{\Delta }E\approx 30\mathrm{meV}$) and high-momentum resolution ($\mathrm{\Delta }q\approx 0.01{\AA }^{-1}$). To address issues of reproducibility, measurements were repeated 10 times on five different Bi-2212 flakes, benchmarked against aluminum, a well-characterized Fermi liquid, and quantitatively compared with those of prior studies spanning four decades. At momenta $q<0.15{\AA }^{-1}$, we observe a highly damped plasmon whose linewidth is comparable with its energy. At larger momenta $q>0.15{\AA }^{-1}$, this excitation does not disperse but instead evolves into an incoherent continuum, with no evidence for the RPA-like dispersion reported in some earlier works. Comparison with recent resonant inelastic x-ray scattering measurements on Bi-based cuprates supports the view that Bi-2212 is an incoherent metal with strongly damped charge excitations.

Rhombohedral multilayer graphene (RMG) proximity coupled to a Haldane substrate provides a platform to investigate the interplay between band topology, layer number, and electric-field control of orbital magnetism. Using a tight-binding model and the modern theory of orbital magnetization, we study the layer-dependent magnetic response in bilayer, trilayer, tetralayer, and pentalayer graphene under Haldane proximity. While monolayer graphene develops a global topological gap with quantized magnetization slope, multilayer systems remain metallic due to protected low-energy bands associated with unperturbed sublattices. Despite the absence of a global gap, finite valley-contrasting Berry curvature produces nontrivial layer-dependent Chern numbers. We decompose the total orbital magnetization into self-rotation ($M_{\mathrm{SR}}$) and center-of-mass ($M_C$) contributions, revealing their distinct behaviors across doping and applied interlayer bias. In bilayer graphene, magnetization remains negative and monotonic. Remarkably, trilayer and tetralayer graphene display a bias-induced sign reversal of orbital magnetization beyond critical thresholds ($\mathrm{\Delta }\simeq -55\mathrm{meV}$ for 3LG, $-50\mathrm{meV}$ for 4LG) in the hole-doped regime, a feature completely absent in the bilayer. It is further established in the case of 5LG, that the magnetization reversal is independent of the topological transition, and depends on the direction of bias and hole doping. The effect persists across both hole and electron doping, demonstrating that layer count serves as a key tuning parameter for orbital magnetism. Our findings establish topologically proximitized multilayer graphene as a versatile platform for electric-field-manipulable orbitronic and valleytronic devices.

We study the edge state properties of a two-dimensional kagome lattice using a tight-binding approach, focusing on the role of lattice termination, spin-orbit coupling, and magnetic order. In the pristine limit, we show that the existence of localized edge states is highly sensitive to boundary geometry, with certain terminations completely suppressing edge modes. Kane-Mele spin-orbit coupling opens a bulk gap and stabilizes topologically protected helical edge states, yielding a robust ${\mathbb{Z}}_2$ insulating phase that is insensitive to termination details. In contrast, the combined effect of a Zeeman field and Rashba spin-orbit coupling drives the system into Chern insulating phases, with Chern numbers consistent with the number of chiral edge modes. We further demonstrate that noncoplanar magnetic textures generate multiple Chern phases through finite scalar spin chirality, with Kane-Mele coupling strongly tuning the topological gaps. Our results provide important insights into the tunability of edge states in the kagome lattice, which can be key to designing materials with novel electronic properties and topological phases.

Moiré patterns in magnetic bilayers generate spatially modulated interlayer exchange interactions that can give rise to nonuniform magnetic textures. We study a minimal classical bilayer Ising model with a moiré-modulated interlayer coupling, generated either by relative twist or differential strain between the layers. Using large-scale classical Monte Carlo simulations, we show that the ordering transition remains in the conventional two-dimensional Ising universality class, even when the low-temperature state is domain-textured. At low temperatures, we find a smooth crossover between a uniform ferromagnet and a domain-textured state, in which the spins locally follow the sign of the interlayer exchange. We demonstrate that there is no breaking of layer symmetry for twisted bilayers. The location of the crossover is determined by a simple geometric energy balance between bulk interlayer exchange and intralayer domain-wall costs. Our results provide a minimal framework for understanding how moiré-modulated magnetic textures can emerge from geometric energetics without requiring a thermodynamic phase transition.

We study the orbital magnetic moment of Bogoliubov quasiparticles in superconductors with the semiclassical approach. We derive the orbital magnetic moment of a quasiparticle wave packet by considering the energy correction of the wave packet to the linear order of the magnetic field. The semiclassical result is further verified by a linear response calculation with a full quantum mechanical method. From the analytical expression, we find that nontrivial structure in the superconducting pairing gap alone is unable to produce quasiparticle orbital magnetic moment, which is in sharp contrast with the behavior of quasiparticle Berry curvatures. We apply the formula to study a tight-binding model with a chiral $d$-wave superconducting gap and show the influence of orbital magnetic moment on the energy spectrum and local density of states. We also calculate the orbital Nernst effect driven by the interplay between the orbital magnetic moment and the Berry curvature of Bogoliubov quasiparticles.