Two-dimensional (2D) second-order topological insulators (SOTIs) with corner states have recently attracted significant interest. It is fascinating to explore the coupling of corner states with additional degrees of freedom. Here, we propose that layer-polarized corner states can be induced by a perpendicular electric field in the AA-stacking bilayer 2D SOTIs. Our result reveals that the transition between non-layer-polarized and layer-polarized corner states depends on the interlayer exchange symmetry, which can be controlled by the perpendicular electric field. This finding is further verified in two types of SOTIs: bilayer modified Kane-Mele model and $C_n$-symmetric SOTIs. In contrast to the bilayer modified Kane-Mele model, magnetic $C_n$-symmetric SOTIs are predicted to exhibit corner states that are not only layer polarized but also additionally spin-polarized, as exemplified by 1T-${\mathrm{NiCl}}_2$. Based on the first-principles calculations and tight-binding (TB) model, we predict that ferromagnetic (FM) single-layer 1T-${\mathrm{NiCl}}_2$ exhibits $C_3$-symmetric corner states with nontrivial fractional charge in both spin channels. Notably, in the bilayer ${\mathrm{NiCl}}_2$ with antiferromagnetic (AFM) ground state, applying a perpendicular electric field drives the transition of the corner states from a spin- and layer-degenerate state to a spin- and layer-polarized state. Reversing the electric field direction simultaneously switches both the spin and layer polarizations. Finally, layer-polarized corner states are also confirmed in the nonmagnetic bilayer hexagonal SOTI. These results indicate that electrically tunable layer-polarized corner states could be realized in a variety of bilayer SOTIs and interlayer magnetic configurations. Our work offers a strategy for designing layer-polarized corner states in 2D SOTIs, which could enhance their potential applications in topological electronic devices.

We use the pullback trivialization technique to systematically construct gapped interfaces and anomalous boundaries for fermionic symmetry-protected topological (FSPT) states by extending their symmetry group $G_f={\mathbb{Z}}_2^f{\times }_{{\omega }_2}G$ to larger groups. These FSPT states may involve decoration layers of both Majorana chains and complex fermions. We derive general consistency formulas explicitly for ($2+1$)-dimensional (D) and ($3+1$)D systems, where nontrivial twists arise from fermionic symmetric local unitaries or “gauge transformations” that ensure coboundaries vanish at the cochain level. Additionally, we present explicit example for a ($3+1$)D FSPT of symmetry group $G_f={\mathbb{Z}}_2^f\times {\mathbb{Z}}_4\times {\mathbb{Z}}_4$ with Majorana chain decorations.

Magnetic kagome metals have garnered considerable attention as an ideal platform for investigating intrinsic topological structures, frustrated magnetism, and electron correlation effects. In this paper, we present the synthesis and detailed characterization of ${\mathrm{GdNb}}_6{\mathrm{Sn}}_6$, a metal that features a niobium-based kagome lattice and a frustrated triangular gadolinium network. The compound adopts the ${\mathrm{HfFe}}_6{\mathrm{Ge}}_6$-type crystal structure, with lattice parameters of $a=b=5.765\left(4\right)$ Å and $c=9.536\left(8\right)$ Å. Magnetic susceptibility and specific heat measurements reveal a magnetic transition $\sim 2.3$ K. Electrical transport data confirm metallic behavior, unsaturated positive magnetoresistance, and a hole-dominated multiband Hall effect. Furthermore, first-principles calculations indicate that Nb-$4d$ orbitals predominantly contribute to the electronic states near the Fermi energy, with the band structure showing multiple topologically nontrivial crossings around the Fermi surface. We also compare ${\mathrm{GdNb}}_6{\mathrm{Sn}}_6$ with ${\mathrm{GdV}}_6{\mathrm{Sn}}_6$, highlighting their similarities and differences. Our findings pave the way for exploring $R{\mathrm{Nb}}_6{\mathrm{Sn}}_6$ ($R$ = rare earth) with customized substitutions of $R$ sites to fine-tune their properties.

Low symmetry of armchair lateral heterojunctions between transition metal dichalcogenide monolayers allows for the mixing of electron states in ${\mathit{K}}_{+}$ and ${\mathit{K}}_{-}$ valleys. We show that this valley mixing substantially modifies the fine structure and dynamics of electrons and excitons localized at type-II lateral heterojunctions. In particular, it gives rise to the in-plane electron $g$-factor leading to the valley pseudospin precession in the in-plane magnetic field. Also, the interplay of the valley mixing and long-range exchange interaction leads to the magnetically induced linear polarization of exciton photoluminescence along the heterojunction under unpolarized excitation. The degree of polarization can reach $1/3$. From the tight binding model we obtain an analytical expression for the valley coupling constant and estimate it to be as strong as 0.2 eV Å for typical heteropairs.

Motivated by recent experiments on the quantum magnet ${\mathrm{K}}_2\mathrm{Co}{\left({\mathrm{SeO}}_3\right)}_2$, we study theoretically the excitation spectrum of the nearest-neighbor triangular XXZ model in the limit of strong easy-axis anisotropy, within the up-up-down (1/3-plateau) phase. We make an expansion in $\alpha =J_{xy}/J_{zz}$ instead of $1/S$ and calculate the magnon dispersion for any value of the spin $S$ at second order in $\alpha$, with two important conclusions: (i) the $1/S$ expansion converges very slowly for $S=1/2$, making spin-wave theory quantitatively inaccurate up to very large orders, and (ii) compared to the linear spin-wave predictions, our magnon dispersion presents a much better agreement with experimental results on ${\mathrm{K}}_2\mathrm{Co}{\left({\mathrm{SeO}}_3\right)}_2$, for which $\alpha \simeq 0.08$.

${\mathrm{CeRh}}_2{\mathrm{As}}_2$ is a newly discovered candidate of multiphase heavy-fermion superconductor $(T_{\mathrm{c}}\approx 0.3 \mathrm{K})$ with intriguing physical properties. Here, we employ soft point-contact spectroscopy to investigate its energy gap behaviors in both the normal and superconducting states. The differential conductance below $T_{\mathrm{c}}$ reveals an estimated superconducting energy gap of $2{\mathrm{\Delta }}_{\mathrm{SC}}\approx 0.24$ meV and thus an extremely strong superconducting pairing strength $2{\mathrm{\Delta }}_{\mathrm{SC}}/k_{\mathrm{B}}{T}_{\mathrm{c}}\approx 8.8$, which is comparable to those of cuprates and iron-based high-$T_{\mathrm{c}}$ superconductors as well as infinite-layer nickelates. Above $T_{\mathrm{c}}$, a well-defined pseudogap feature is manifested as a V-shaped dip in the differential conductance spanning an energy scale of $2{\mathrm{\Delta }}_{\mathrm{g}}\approx 0.95-3.0$ meV. The pseudogap feature persists to the highest characteristic temperature of $T_{\mathrm{g}}\approx 8-9$ K and is gradually suppressed by magnetic field of $B_{\mathrm{g}}\approx 9.0\pm 0.5$ T regardless of its direction relative to the crystallographic axes. The observation of pseudogap features prior to the superconducting phase transition enriches the phase diagram of ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ and provides a platform to study the interplay of unconventional superconductivity and pseudogap phenomena.

Since the discovery of the relation between the Chern number and quantum Hall effect, searching for observables of topological invariants has been an intriguing topic. Topological Hopf-link semimetals have attracted tremendous interest, in which the conduction and valence energy bands touch at linked nodal lines. However, it is challenging to identify this sophisticated topology. We propose to use the quantum oscillation in strong magnetic fields to probe the Hopf links. For a generic model of a Hopf-link semimetal that captures the linked-trivial phase transition, we figure out the phase shifts of oscillation for all Fermi pockets in all magnetic-field directions, by presenting self-consistent results from the Fermi-surface tomography, Landau fan diagram, and electrical resistivity. As the magnetic field is rotated, the phase shifts exhibit a unique pattern, which could help to identify Hopf links in real materials, such as those in ${\mathrm{Li}}_2\mathrm{NaN}$.

We analytically study interacting Dirac fermions, described by the Thirring model, under weak local particle number measurements with monitoring rate $\gamma$. This system maps to a bosonic replica field theory, analyzed via the renormalization group. For a nonzero attractive interaction, a phase transition occurs at a critical measurement strength ${\gamma }_c$. When $\gamma >{\gamma }_c$, the system enters a localized phase characterized by exponentially decaying density-density correlations beyond a finite correlation length; for $\gamma <{\gamma }_c$, the correlations decay algebraically. The transition is of Berezinskii-Kosterlitz-Thouless (BKT) type, reflected by a characteristic scaling of the correlation length. In the noninteracting limit, ${\gamma }_c\to 0$ shifts to zero, reducing the algebraic phase to a single point in parameter space. This identifies weak measurements in the free case as an implicit double fine tuning to the critical end point of the BKT phase transition. Along the noninteracting line, we compute the entanglement entropy from density-density correlation functions and find no entanglement transition at nonzero measurement strength in the thermodynamic limit.

We demonstrate that domain walls built from bimeron chains in two-dimensional systems constitute a spontaneously assembled medium that holds magnonic excitations along its direction. We prove that such magnons are topological, leading to protected edge states. We also verify the stability of the domain walls and the resilience of edge modes against disorder. Analytical calculations and micromagnetic simulations support our findings. The robustness of these edge modes holds promise for potential applications in the design of nanoscale magnonic devices for information storage and transport.

This paper discusses the coupling between spin-wave-mediated magnetic interactions and lattice degrees of freedom in bilayer ${\mathrm{La}}_{1.4}{\mathrm{Sr}}_{1.6}{\mathrm{Mn}}_2{\mathrm{O}}_7$ (BL-LSMO-0.3). The thermal evolution of the Raman shift, as obtained from micro-Raman spectroscopic measurements over a wide temperature range, reveals the evolution of phonon dynamics while the system undergoes a balance between double and superexchange spin-spin interactions through spin-wave modulation in different magnetic phases. The evolution of relative magnetoelastic coupling strengths for nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic superexchange interactions in the high-temperature canted antiferromagnetic phases are estimated. We have also demonstrated the existence of orbital ordering and its correlation with spin-phonon dynamics in the canted antiferromagnetic phases of BL-LSMO-0.3 from the detailed analysis of the high-wave-number orbiton-related phonon modes. Our study further reveals the absence of charge ordering in the compound. The complex coupling of lattice distortion, orbital ordering, the nearest- and next-nearest-neighbor spin-spin interactions in determining the canted spin states of the system is discussed.

A magnetic phase diagram for ${\mathrm{EuPdSn}}_2$ is constructed based on magnetization, dc susceptibility and specific heat as a function of applied field $\left(B\right)$, and neutron diffraction results at $B=0$. The contribution of the ferromagnetic (FM) and antiferromagnetic components to the measured magnetic susceptibility can be separated and weighted as a function of $B$ by taking the temperature dependence of the neutron diffraction counts from the FM phase at $B=0$ as reference. In the magnetically ordered phase, the temperature dependence of the specific heat does not follow the mean field prediction for the ${\mathrm{Eu}}^{2+}J=7/2$ quantum number but rather that for $J=5/2$. This deviation and the consequent discrepancy for the entropy evolution is discussed in the context of a non-Zeeman distribution of the eightfold ground state. Comparing the respective variations of the magnetization $M(T,B)$ and the entropy $S(T,B)$, the thermodynamic relationship $\partial M/\partial T=\partial S/\partial B=0$ is observed for the ranges $0<T<10$ K and $0<B<0.4$ T.

Collective modes in superconductors provided the first realization of the Higgs mechanism. The transverse Goldstone mode acquires a gap (i.e., a mass) when it hybridizes with the electromagnetic gauge field. The longitudinal Schmid-Higgs mode, on the other hand, is always massive. In conventional BCS theory, its gap is exactly $2\mathrm{\Delta }$, coinciding with the excitation threshold for quasiparticles. Being situated right at the edge of the continuum spectrum it gives rise to peculiar dynamics for the Schmid-Higgs mode. For instance, when suddenly excited at $t=0$, it exhibits algebraically decaying oscillations of the form $\sim sin\left(2\mathrm{\Delta }t\right)/t^{1/2}$. In this study, we explore the behavior of Schmid-Higgs oscillations in the presence of pair-breaking mechanisms, such as magnetic impurities or in-plane magnetic fields. These processes suppress the quasiparticle excitation threshold down to $2{\varepsilon }_g<2\mathrm{\Delta }$, potentially placing the longitudinal mode within the continuum spectrum. Despite this, we show that the algebraically decaying oscillations persist, taking the form $\sim sin\left(2{\varepsilon }_{g}t\right)/t^2$. The Schmid-Higgs mode becomes truly overdamped and exponentially decaying only in the gapless superconductors with ${\varepsilon }_g=0$.

We study theoretically the thermoelectric effect in a superconducting state having the Bogoliubov-Fermi surfaces which stays in a thin superconducting layer between a conventional superconductor and an insulator. The thermoelectric coefficients calculated based on the linear response theory show the remarkable anisotropy in real space, which are explained well by the anisotropic shape of the Bogoliubov-Fermi surface in momentum space. Our results indicate a way to check the existence of the Bogoliubov-Fermi surfaces in a stable superconducting state because the anisotropy is controlled by the direction of an applied magnetic field.

Random unitary circuits have become a model system to investigate information scrambling in quantum systems. In the literature, mostly random circuits with Haar-distributed gate operations have been considered. In this work, we investigate operator spreading in random unitary circuits in which the elementary gate operations are drawn from general unitary-invariant ensembles, which include the well-studied Haar-distributed random unitary circuits as a special case. Similar to the Haar-distributed case, the long-time behavior of operator spreading with the more general unitary-invariant gate distribution is governed by drift-diffusion equations characterized by the butterfly velocity $v_{\mathrm{B}}$ and a diffusion constant $\mathcal{D}$. Differences with the Haar-random case are (i) that it takes a finite time ${\tau }_{\mathrm{b}}$ until ensemble-averaged Pauli-string weights take a “binary” form, in which they depend only on whether Pauli operators inside the support of the Pauli strong are equal to the identity matrix, and (ii) that the operator spreading is characterized by a finite “domain-wall width” $n_{\mathrm{DW}}$ separating regions with a random-matrix-like Pauli-string distribution. To illustrate these findings, we perform explicit calculations for random unitary circuits distributed according to the Poisson kernel, which interpolates between the trivial and Haar-distributed circuits.

The nickelate superconductors bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ and trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ exhibit remarkable high-temperature superconductivity under applied pressure, sparking considerable research attention. However, the nature of their spin, charge, and orbital order remains elusive. Here, supported by symmetry analysis and density functional theory calculations, we identify a double-stripe ground state of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Such magnetic order is accompanied by a charge density wave in $Pmnm$ phase, intertwined with the $d_{z^2}^1{d}_{x^2-y^2}^1$ ($3d^8$) and $d_{z^2}^1$ ($3d^7$) orbital order. Furthermore, for trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$, we demonstrate the existence of a long-range incommensurate spin density wave. Additionally, we point out that the ${\mathrm{Ni}}^{2+}, {\mathrm{Ni}}^{3+}$, and rare ${\mathrm{Ni}}^{4+}$ orders coexist in the ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ system due to interlayer antiferromagnetic frustration. Our work thus reveals a systematic spin-charge-orbital picture for ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ and ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$, paving the way for further understanding the mechanism of nickelate-based superconductivity.

Quasiequilibrium magnon Bose-Einstein condensates in ferromagnetic insulators have been a field of great interest, while condensation in antiferromagnetic systems has not yet been explored in detail. We analyze the stability of condensed chiral magnons in two antiferromagnetic insulators: a uniaxial easy-axis system and a biaxial system. We show that two-component magnon condensation and intermagnon interactions are essential to create metastable magnon condensation. The uniaxial system with a Rashba-type Dzyaloshinskii-Moriya interaction supports two degenerate condensate populations at finite wave vectors. We find that the condensation state in this model is (meta)stable only when the distribution of condensed magnons between the two populations is symmetric. In addition, we demonstrate the emergence of a zero-sound-like Goldstone mode in antiferromagnetic systems that support two-component magnon condensation. On the other hand, in the biaxial system without Dzyaloshinskii-Moriya interaction, we predict that the magnon condensate cannot stabilize due to the breaking of the magnon degeneracy. Our results suggest that this instability is a general characteristic of single-component quasiequilibrium quasiparticle condensates.

The critical temperature for magnetic order comprises a crucial property of any magnetic material and ranges from a few Kelvin in certain antiferromagnets to 1400 K in ferromagnetic Co. However, the prediction of critical temperatures based on, for example, a spin-wave dispersion is in general nontrivial. For ferromagnets and simple collinear antiferromagnets, estimates may be obtained from the Heisenberg model using either renormalized spin-wave theory or the Green's function random-phase approximation (RPA), but a systematic assessment of the accuracy of such approaches seems to be lacking in the literature. In this work, we propose generalizations of both renormalized spin-wave theory and RPA to calculate the critical temperatures of single-$Q$ helimagnetic ground states, which include ferromagnets and antiferromagnets as special cases. We compare the methods to classical Monte Carlo simulations and mean-field theory, using experimental exchange parameters for a wide range of materials; MnO and NiO (single site Néel ground states), ${\mathrm{MnF}}_2$ (altermagnet), ${\mathrm{Cr}}_2{\mathrm{O}}_3$ and ${\mathrm{Fe}}_2{\mathrm{O}}_3$ (two site Néel states), and ${\mathrm{Ba}}_3{\mathrm{NbFe}}_3{\mathrm{Si}}_2{\mathrm{O}}_{14}$ (incommensurate helimagnet). In all cases, we observe that predictions from RPA are in excellent agreement with experimental values and RPA thus constitutes a rather reliable all-purpose method for calculating critical temperatures.