Band convergence is a traditional strategy to optimize the electrical transport properties of SnTe, but conventionally optimized band structures often retain the valence band maximum (VBM) at the low-degeneracy L point $(N\mathrm{v}=4)$. Moreover, the mechanisms of phonon softening remain poorly understood in terms of phonon dispersion, especially regarding the coupling between vacancies and other dopants. Here, the strategic incorporation of ternary ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$ into SnTe via nonstoichiometric alloying introduces a synergistic effect of Sn vacancies and Mn dopants. This synergy weakens the Sn-s/Te-p antibonding state, leading to significant band renormalization. Specifically, the VBM shifts from the L point to the high-degeneracy Σ and Λ points ($N\mathrm{v}=12$ and 8, respectively), where the VBM at these two sites form perfect alignment, substantially enhancing the density-of-states effective mass. In terms of phonon dispersion, both Mn atoms and Sn vacancies soften optical phonon modes at the Γ point, reducing their frequencies from 0.9 THz to 0.3 and 0.6 THz, respectively, forming a pronounced optical-phonon “waterfall” effect. This results in a significant reduction in phonon group velocities and introduces additional optical-acoustic phonon interactions. These combined effects yield a highly optimized thermoelectric quality factor in SnTe-${\mathrm{MnSb}}_2{\mathrm{Te}}_4$ alloys. By further tuning the reduced Fermi level through Ge doping, we achieve a maximum ZT of 1.3 at 723 K and an average ZT of 0.83 (300–823 K), offering a promising pathway for mid-temperature waste heat recovery and shedding light on vacancy engineering in thermoelectrics.

We introduce a light-matter interface that integrates a nanoscale buried heterostructure emitter into a dielectric bowtie cavity, colocalizing the optical hotspot and the electronic wavefunction. This platform enables strong light-matter interaction through deep subwavelength confinement while remaining compatible with scalable fabrication. We show that in this regime an explicit treatment of the emitter's spatial extent is required, and that a confinement-factor approximation more accurately predicts the coupling, revealing design rules inaccessible to dipole-based metrics. For an InP/InGaAsP system, we predict coupling strengths of $0.4–0.7\mathrm{meV}$ for gap sizes of $50–10\mathrm{nm}$, establishing the buried heterostructure-bowtie architecture as a practical route to deterministic strong coupling in solid-state nanophotonics.

We present a comprehensive analysis of magnetotransport across monolayer $1T^{\prime }\text{−}{\mathrm{WTe}}_2$, highlighting the role of nonsymmorphic symmetries in governing edge-state spin behavior. By comparing the electronic transmission in nanoribbons with edges along the crystallographic $\widehat{y}$ and $\widehat{x}$ directions, our analysis reveals a pronounced anisotropy in the magnetic-field response. The $\widehat{y}$-edge ribbon exhibits significant spin splitting of the edge-state bands in both energy and momentum space, together with a strong angular dependence of the conductance. The observed magnetotransport response indicates a spin quantization axis that aligns with the out-of-plane spin quantization axis reported in previous experimental studies. In contrast, the $\widehat{x}$-edge ribbon shows negligible spin splitting with magnetic fields, which is attributed to nonsymmorphic symmetries such as glide mirror and screw rotation, which protects degeneracies along the $\mathrm{\Gamma }\text{−}X$ direction, even when time-reversal symmetry is broken. The energy-resolved current density and angular transmission analysis confirm that this anisotropy originates from edge states, while bulk states remain largely insensitive to the field orientation. Our results establish direct transport spectroscopy based evidence of nonsymmorphic symmetry-protected spin degeneracy in $1T^{\prime }\text{−}{\mathrm{WTe}}_2$, and underscore its promise for spintronic devices that leverage symmetry-protected and directionally selective transport channels.

Motivated by recent experiments on multiterminal Josephson junctions (MJJs) that probe different ranges of the size and bias voltage parameters, we explore the regime of increasing bias voltage in large-scale devices, where the electrochemical potential becomes comparable to the one-dimensional energy level spacing. We find that the relative number of quantum-correlated pairs formed by colliding Floquet-Kulik quartet levels is equal to the inverse of the number of channels. This observation motivates a model for the intermediate regime in which the ballistic central two-dimensional normal metal is treated as a continuum under the adiabatic approximation, while Andreev modes propagate in a background of voltage- and flux-tunable nonequilibrium electronic populations. The model predicts characteristic voltage scales that govern the mesoscopic oscillations of the critical current, and these scales are at the crossroads of interpreting experiments in all sectors of the MJJs: quartets, topology, and Floquet theory. Our model is specifically inspired by the recent Harvard and Penn State group experiments.

We demonstrate how spin-orbit coupling (SOC) controls band topology and induces higher-order topological corner states in a two-dimensional Su-Schrieffer-Heeger (SSH) model. SOC lifts spin degeneracy and, when applied along both lattice directions, generates robust zero-energy corner states. By matching intracell (intercell) hopping strengths to their SOC counterparts, we produce topological flat bands, whose phases are classified by the charge polarization and verified through bulk-edge-corner correspondence. We propose an LC-circuit implementation and show numerically that the corner states remain strongly localized and robust in weak on-site disorder. These results establish SOC as a versatile tool for engineering higher-order topological phases and topological flat bands, offering an experimentally accessible route for realization in circuit systems.

Most topological insulators suffer from intrinsically narrow band gaps, limiting their practical applications. Using tight-binding modeling and first-principles calculations, we show that in the topological state and band gap of the ferroelectric bilayer $\alpha \text{−}\mathrm{I}{\mathrm{n}}_2\mathrm{S}{\mathrm{e}}_3$ ($2\mathrm{L}\text{−}\mathrm{I}{\mathrm{n}}_2\mathrm{S}{\mathrm{e}}_3$) can be effectively tuned by controlling the hybridization strength $\left(V_{\text{hyb}}\right)$ between Se $p_x/p_y$ and $s/p_z$ orbitals through transition metal substitution at In sites. This mechanism is demonstrated in a $\mathrm{ScInS}{\mathrm{e}}_3/\mathrm{I}{\mathrm{n}}_2\mathrm{S}{\mathrm{e}}_3$ van der Waals Heterostructure (vdWH), where enhanced charge transfer from Sc $d$ states to Se atoms strengthens the $\mathit{px}/\mathit{py}\text{−}s/\mathit{pz}$ orbitals' hybridization and enlarges the quantum spin Hall gap to 36 meV. Magnetic Cr substitution further yields a $\mathrm{CrInS}{\mathrm{e}}_3/\mathrm{I}{\mathrm{n}}_2\mathrm{S}{\mathrm{e}}_3$ vdWH with a sizable $\sim 110$ meV quantum anomalous Hall gap and compressive strain-driven topological phase transitions—from a trivial magnetic insulator ($C=0$) to a Chern insulator ($C=1$), and finally, to a magnetic topological metal ($C=2$). These results establish a viable strategy for engineering band gaps and topological phases for low-power spintronic and quantum technologies.

We develop a symmetry-adapted multipolar $\mathbf{k}·\mathbf{p}$ theory close to the bulk $\mathrm{\Gamma }$ point for time-reversal-symmetric, noncentrosymmetric $C_{3v}$ crystals in the strong atomic spin-orbit-coupling ($jj$-coupling) limit. Using a $j\in \{1/2,3/2,5/2\}$ multiplet basis appropriate for heavy-element $p$ and $d$ bands, we systematically construct all symmetry-allowed spin-orbit-coupling terms up to fifth order in momentum and generalize the usual spin texture to a total-angular-momentum texture. For $j>1/2$, multipolar spin-orbit coupling qualitatively reshapes Fermi surfaces and makes the topology of Bloch states band dependent. This leads to anisotropic high-$j$ textures that go beyond a single Rashba helix. We classify these textures by their total-angular-momentum vorticity $W_n$ for every energy band and identify distinct $|W_n|=1,2,5$ phases. We show that their crossovers generate enhanced and nonmonotonic current-induced spin-polarization responses, namely, the Edelstein effect, upon tuning the chemical potential. Our results provide a symmetry-based framework for analyzing and predicting multipolar spin-orbit coupling, total-angular-momentum textures, and spintronic responses in heavy-element materials without an inversion center.

We study quadrupole orders in heavy-fermion compound ${\mathrm{PrIr}}_2{\mathrm{Zn}}_{20}$ under magnetic fields on the basis of the Landau theory. Assuming $E_g$ electric quadrupolar orders in the cubic symmetry with the ordering wave number at the L points in the face-centered-cubic lattice Brillouin zone as observed experimentally, we construct a Landau free energy and analyze the resulting free energy. We find that the unidentified high-temperature ordered phase under the magnetic field $\mathit{H}\parallel \left[001\right]$ reported earlier arises from the rotation of the quadrupole moments of $f$ electrons on the Pr site. We also discuss the phase diagram for other magnetic-field directions and possible double-$\mathit{q}$ quadrupolar orders in this system.

The electronic structure of materials is fundamentally governed by their crystal symmetry. While most research on two-dimensional materials has focused on hexagonal lattices, such as graphene, hexagonal boron nitride, and transition metal dichalcogenides. This work explores a square-lattice system: the experimentally realized phthalocyanine-based metal–organic framework (ZnPc-MOF). Using group representation theory, we classify the electronic bands of ZnPc-MOF monolayer, AA- and AB-stacked bilayers, and twisted bilayers in terms of the irreducible representations (irreps) of their little groups. We find that bands in the AB-stacked bilayer remain two-fold degenerate along the $Y$ and $Y^{\prime }$ high-symmetry lines, as a consequence of the sole presence of two-dimensional irreps along these directions. We further derive optical transition selection rules to interpret the optical conductivity, revealing pronounced polarization-dependent optical responses. Additionally, we investigate the quasicrystalline electronic states in the ${45}^{\circ }$ twisted bilayer (ZnPc-MOF quasicrystal) using the resonant coupling Hamiltonian. Compared to graphene quasicrystals, ZnPc-MOF quasicrystal exhibits weaker resonant coupling strengths, yet its quasicrystalline states lie closer to the Fermi energy, suggesting a greater contribution to low-energy electronic phenomena.

In this work, we propose a scheme to realize the layer Hall effect in the ferromagnetic topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ via proximity to $d$-wave altermagnets. We show that an altermagnet and an in-plane magnetic field applied near one surface gap the corresponding Dirac cone, yielding an altermagnet-induced half-quantized Hall effect. When altermagnets with antiparallel Néel vectors are placed near the top and bottom surfaces, giving rise to the layer Hall effect with vanishing net Hall conductance, i.e., the altermagnet-induced layer Hall effect. In contrast, altermagnets with parallel Néel vectors lead to a quantized Chern insulating state, i.e., the altermagnet-induced anomalous Hall effect. We further analyze the dependence of the Hall conductance on the orientation of the in-plane magnetic field and demonstrate that the layer Hall effect becomes observable under a perpendicular electric field. Our results establish a route to engineer altermagnet-induced topological phases in ferromagnetic topological insulators.

Nonlinear processes can offer pathways to next-generation sensors and frequency mixing devices to overcome modern imaging, detection, and communication challenges. In this article, we report on strong second- and third-order nonlinear optical responses in visible and terahertz light in single crystals of the noble metal dichalcogenide ${\mathrm{PdTe}}_2$. We find that buried conduction and valence topological surface states of ${\mathrm{PdTe}}_2$ lead to resonant optical second-harmonic generation. On the other hand, although the nonlinear responses obtained with terahertz excitation are not close to this resonance, they can be clearly observed in reflection geometry, even in the presence of broadband excitation, where optical filters are not necessary to observe the enhanced odd-order higher harmonic output. By carefully considering the radiative photocurrent framework of stimulated terahertz emission, we are able to extract fingerprints of both second- and third-order processes in the terahertz regime, and show that ${\mathrm{PdTe}}_2$ is a promising material candidate for radio-frequency rectification, frequency mixing, and beam focusing.

Majorana zero modes (MZMs) are bound midgap topological excitations at the ends of a one-dimensional (1D) topological superconductor, which must come in pairs. If the two MZMs in the pair are sufficiently well-separated by a distance much larger than their individual localization lengths, then the MZMs behave as non-Abelian anyons which can be braided to carry out fault-tolerant topological quantum computation. In this ‘‘topological’’ regime of well-separated MZMs, their overlap is exponentially small, leading to exponentially small Majorana splitting, thus enabling the MZMs to be topologically protected by the superconducting gap. In real experimental samples, however, the existence of disorder and the finite length of the 1D wire considerably complicate the situation, leading to ambiguities in defining ‘‘topology’’ since the Majorana splitting between the two end modes may not necessarily be small in disordered wires of short length. We theoretically study this situation by calculating the splitting in experimentally relevant short disordered wires, and explicitly investigating the applicability of the ‘‘exponential protection’’ constraint as a function of disorder, wire length, and other system parameters in realistic models of nanowires currently being used experimentally. We find that the exponential regime is highly constrained and is suppressed for disorder somewhat less than the topological superconducting gap. We provide detailed results and discuss the implications of our theory for the currently active experimental search for MZMs in superconductor-semiconductor hybrid platforms. A general consequence of our work is that topology in finite disordered wires may not be uniquely defined, necessitating a careful analysis which depends on the context.

Topological photonics provides an unprecedented way to control wave propagation that can eliminate backscattering. However, due to the bulk-boundary correspondence inherent in topological physics, the desired topological state usually manifests at the boundary rather than within the bulk, resulting in a sizeable useless bulk area and hindering applications. Here, we present a unique topological photonic crystal fiber (TPCF) by incorporating a one-dimensional bivortex line within a three-dimensional bilayer photonic crystal, where adjacent layers exhibiting π-phase vortex differences generate artificial spins. The spin-core states along the fiber core and their robust spin-momentum locking against disorders are demonstrated in microwave experiments. Besides the single-mode fiber, we also construct a multimode TPCF. Our research may empower photonic crystal fibers with topological band structures, advancing future high-performance communication devices.

Due to spin-orbit coupling (SOC), a quantized spin Hall conductivity has not yet been reported in realistic materials. Here, we tackle this challenge by predicting robust quantized spin Hall conductivity in monolayer ${\mathrm{Fe}}_2{\mathrm{Te}}_2\mathrm{O}$. The underlying physics originates from the unrecognized mirror-spin coupling (MSC), which couples spin-up and spin-down states into two orthogonal mirror eigenstates. We show that the perfect MSC can naturally emerge in the two-dimensional altermagnets with out-of-plane Néel vector and horizontal mirror but without SOC. Remarkably, the MSC can dramatically weaken the spin hybridization of the systems when SOC is included. When SOC is neglected, ${\mathrm{Fe}}_2{\mathrm{Te}}_2\mathrm{O}$ is an altermagnetic Weyl semimetal with MSC. With SOC, it evolves into the first material candidate for two-dimensional magnetic mirror Chern insulator. Remarkably, under the protection of MSC, the spin hybridization of both bulk and topological edge states in ${\mathrm{Fe}}_2{\mathrm{Te}}_2\mathrm{O}$ with SOC at low energy is negligible. As a consequence, a quantized spin Hall conductivity emerges within the bulk band gap of the system. By unveiling this effect, our findings represent a significant advancement in spin Hall transport, and broaden the material candidates hosting intriguing altermagnetic phenomena.

We explore the nonreciprocal intracell hopping mediated non-Hermitian topological phases of an extended Su-Schrieffer-Heeger model hosting second-nearest-neighbor hopping. We microscopically analyze the phase boundaries using the non-Bloch momentum while the off-critical (critical) phases are directly associated with the gapped (gapless) nature of the non-Bloch bands that we derive from the characteristic equation using the gauge freedom. The non-Bloch momentum accurately reflects the bulk boundary correspondence (BBC) explaining the winding number profile under open boundary conditions. We examine the adiabatic dynamics to promote the concept of adiabatic charge transport in a non-Hermitian scenario justifying the BBC in spatiotemporal Bott index and non-Bloch Chern number. Once the non-Bloch bands experience no (a) gap-closing during the evolution of time, quantized flow of is preserved (broken). Our study systematically unifies the concept of non-Bloch bands for both static and driven situations.

We study a generalization of ‘‘Yukawa models’’ in which Majorana fermions, interacting via all-to-all random couplings as in the Sachdev-Ye-Kitaev (SYK) model, are parametrically coupled to disordered bosonic degrees of freedom described by a quantum $p-\text{spin}$ model. The latter has its own nontrivial dynamics leading to quantum paramagnetic (or liquid) and glassy phases. At low temperatures, this setup results in SYK behavior within each metastable state of a rugged bosonic free-energy landscape, the effective fermionic couplings being different for each metastable state. We show that the boson-fermion coupling enhances the stability of the quantum spin-glass phase and strongly modifies the imaginary-time Green’s functions of both sets of degrees of freedom. In particular, in the quantum spin-glass phase, the imaginary-time dynamics is turned from a fast exponential decay characteristic of a gapped phase into a much slower dynamics. In the quantum paramagnetic phase, on the other hand, the fermions' imaginary-time dynamics get strongly modified, and the critical SYK behavior is washed away.

We reveal a fundamental geometric structure of momentum space arising from the nonadiabatic evolution of Bloch electrons. By extending semiclassical wave-packet theory to incorporate nonadiabatic effects, we introduce a momentum-space metric tensor—the nonadiabatic metric. This metric gives rise to two velocity corrections, dubbed geometric and geodesic velocities, providing a unified and intuitive framework for understanding nonlinear and nonadiabatic transport phenomena beyond Berry phase effects. The geometric velocity is related to the nonadiabatic metric itself, whereas the geodesic velocity is a Christoffel symbol of the nonadiabatic metric. As the nonadiabatic metric is related to the energy-gap renormalized quantum metric, it unifies the broad quantum-metric effects in electronic responses. When the nonadiabatic metric is constant, it reduces to an effective mass, modifying flat-band electron dynamics in confining potentials. In a flat Chern band with harmonic attractive interactions, the two-body wave functions mirror the Landau-level wave functions on a torus. Furthermore, we show that the nonadiabatic metric endows momentum space with a curved geometry, recasting wave-packet dynamics as forced geodesic motion.