The combination of antiferromagnetic (AFM) spintronics and anomalous valley Hall effect (AVHE) is of great significance for potential applications in valleytronics. Here, we propose a way for achieving AVHE in $A$-type hexagonal AFM monolayer. The proposed way involves the introduction of layer-dependent electrostatic potential caused by an out-of-plane external electric field, which can break the combined symmetry ($PT$ symmetry) of spatial inversion ($P$) and time reversal ($T$), producing spin splitting. The spin order of spin splitting can be reversed by regulating the direction of electric field. Based on first-principles calculations, the way can be verified in AFM ${\mathrm{Cr}}_2{\mathrm{CH}}_2$. The layer-locked hidden Berry curvature can give rise to layer-Hall effect, including a valley layer–spin Hall effect and layer-locked AVHE. Moreover, we propose Janus monolayer ${\mathrm{Cr}}_2\mathrm{CHF}$ with internal electric polarization, which can also realize the AVHE. Our works provide an experimentally feasible way to realize AVHE in AFM monolayer.

Antiferromagnetic (AFM) order of ${\mathrm{U}}_2{\mathrm{Pt}}_6{\mathrm{Ga}}_{15}$ with the ordering temperature $T_{\mathrm{N}}$ = 26 K was investigated by resonant x-ray scattering and neutron diffraction on single crystals. This compound possesses a unique crystal structure in which uranium ions form honeycomb layers and then stack along the $c$ axis with a slight offset, which gives rise to a stacking disorder. The AFM order can be described with the propagation vector of $\mathit{q}=(1/6,1/6,0)$ in the hexagonal notation. The ordered magnetic moments orient perpendicular to the honeycomb layers, indicating a collinear spin structure consistent with Ising-like anisotropy. The magnetic reflections are found to be broadened along $c^{*}$, indicating that the stacking disorder results in anisotropic correlation lengths. The semiquantitative analysis of neutron diffraction intensity, combined with group theory considerations based on the crystallographic symmetry, suggests a zigzag-type magnetic structure for the AFM ground state, in which the AFM coupling runs perpendicular to the stacking offset, characterized as $\mathit{q}={(1,0,0)}_{\mathrm{orth}}$. The realization of the zigzag magnetic structure implies the presence of frustrating intralayer exchange interactions involving both ferromagnetic first-neighbor and AFM second- and third-neighbor interactions in this compound.

We report on the effect of magnetic impurities on the microscopic superconducting (SC) properties of the kagome-lattice superconductor $\mathrm{La}{\left({\mathrm{Ru}}_{1-x}{\mathrm{Fe}}_x\right)}_3{\mathrm{Si}}_2$ using muon spin relaxation/rotation. A strong suppression of the superconducting critical temperature $T_{\mathrm{c}}$, the SC volume fraction, and the superfluid density was observed. We further find a correlation between the superfluid density and $T_{\mathrm{c}}$ which is considered a hallmark feature of unconventional superconductivity. Most remarkably, measurements of the temperature-dependent magnetic penetration depth $\lambda$ reveal a change in the low-temperature behavior from exponential saturation to a linear increase, which indicates that Fe doping introduces nodes in the superconducting gap structure at concentrations as low as $x=0.015$. Our results point to a rare example of unconventional superconductivity in the correlated kagome lattice and accessible tunability of the superconducting gap structure, offering new insights into the microscopic mechanisms involved in superconducting order.

Charge-density wave (CDW) and superconductivity, as well as their interplay, are fascinating topics in condensed-matter physics. In this work, we propose a single-layer (SL) CDW material, $1T\text{−}{\mathrm{TaSi}}_2{\mathrm{N}}_4$, among synthesized two-dimensional (2D) ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ family. Through first-principles simulations, its stability, vibrational properties, electronic structures, CDW, and superconductivity have been systematically scrutinized. The Ta-${\mathit{d}}_{z^2}$ orbitals occupy mainly at the Fermi level and SL $1T\text{−}{\mathrm{TaSi}}_2{\mathrm{N}}_4$ exhibits intrinsic metallic property. Besides, the CDW transition temperature ($T_{\mathrm{CDW}}$) is estimated to be $\sim 500$ K by using the temperature dependent effective potential technique. We found that it is the electron-phonon couping (EPC) that drives the CDW to form. Furthermore, its CDW orders can be manipulated by carrier doping and applying strain. At doping of 0.14 h/cell, the CDW instability is effectively suppressed and it changes to a 2D superconductor below $\sim 21.84$ K. Moreover, its superconducting transition temperature ${\mathit{T}}_c$ under the strain of 10% is $\sim 10.47$ K. Physically, the superconductivity in stabilized $1T\text{−}{\mathrm{TaSi}}_2{\mathrm{N}}_4$ monolayer is mainly contributed by the EPC between electrons from the Ta-${\mathit{d}}_{z^2}$ orbitals and phonon vibrations from the $\mathrm{Ta}\text{−}xy$ and $\mathrm{N}\text{−}z$ modes with evident soft phonon mode.

The Kitaev superconducting chain is a model of spinless fermions with tripletlike superconductivity. It has raised interest since for some values of its parameters it presents a nontrivial topological phase that hosts Majorana fermions. The physical realization of a Kitaev chain is complicated by the scarcity of triplet superconductivity in real physical systems. Many proposals have been put forward to overcome this difficulty and fabricate artificial triplet superconducting chains. In this work we study a superconducting chain of spinful fermions forming Cooper pairs, in a triplet $S=1$ state, but with $S^z=0$. The motivation is that such pairing can be induced in chains that couple through an antisymmetric hybridization to an $s$-wave superconducting substrate. We study the nature of edge states and the topological properties of these chains. In the presence of a magnetic field the chain can sustain gapless superconductivity with pairs of Fermi points. The momentum space topology of these Fermi points is nontrivial, in the sense that they can only disappear by annihilating each other. For small magnetic fields, we find well-defined degenerate edge modes with finite Zeemann energy. These modes are not symmetry protected and decay abruptly in the bulk as their energy merges with the continuum of excitations.

Frustrated magnets typically possess a large space of classical ground states. If this degeneracy is not protected by symmetry, thermal fluctuations may “select” certain states via order-by-disorder. In this article, we examine a precursor effect where all ground states are sampled, but with different weights. Geometry plays a key role in determining the weight distribution and its behavior. We demonstrate this with two examples—both clusters with four spins coupled by XY interactions. In the first, the classical ground states form a smooth space. In the second, they form a self-intersecting non-manifold space. Ground-state sampling is very different in these two cases. We first consider the microcanonical ensemble picture, where fluctuations conserve energy. Phase space arguments suggest that the first model exhibits energy-independent probabilities. The second shows a dramatic energy dependence with relative probability increasing as ${\epsilon }^{-1/2}$, where $\epsilon$ is the energy of the system. We simulate low-energy dynamics in both models, confirming the expected behavior. We next consider the canonical ensemble, where the first model produces temperature-independent probabilities. In the second, relative probability rises sharply as $T^{-1/2}$, where $T$ is the temperature. Our results bring out a classical analog of order-by-singularity, a mechanism that has been recently proposed in the context of quantum spin clusters. The sampling of classical orders is qualitatively different in systems with self-intersecting ground-state spaces. It grows at low energies and becomes singular as $\epsilon \to 0$ (microcanonical ensemble) or $T\to 0$ (canonical ensemble). We discuss relevance for disordered phases in macroscopic magnets, particularly for spiral liquids.

${\mathrm{HoNiSi}}_3$ is an intermetallic compound characterized by two successive antiferromagnetic transitions at $T_{N1}=6.3\mathrm{K}$ and $T_{N2}=10.4\mathrm{K}$. Here, its zero-field microscopic magnetic structure is inferred from resonant x-ray magnetic diffraction experiments on a single crystalline sample that complement previous bulk magnetic susceptibility data. For $T<T_{N2}$, the primitive magnetic unit cell matches the chemical cell. The magnetic structure features ferromagnetic ac planes stacked in an antiferromagnetic $\uparrow \downarrow \uparrow \downarrow$ pattern. For $T_{N1}<T<T_{N2}$, the ordered magnetic moment points along $\vec{a}$, and for $T<T_{N1}$ a component along $\vec{c}$ also orders. A symmetry analysis indicates that the magnetic structure for $T<T_{N1}$ is not compatible with the presumed orthorhombic $Cmmm$ space group of the chemical structure, and therefore a slight lattice distortion is implied. Mean-field calculations using a simplified magnetic Hamiltonian, including a reduced set of three independent exchange coupling parameters determined by density functional theory calculations and two crystal electric field terms taken as free-fitting parameters, are able to reproduce the main experimental observations. An alternative approach using a more complete model including seven exchange coupling and nine crystal electric field terms is also explored, where the search of the ground state magnetic structure compatible with the available anisotropic magnetic susceptibility and magnetization data is carried out with the help of an unsupervised machine learning algorithm. The possible magnetic configurations are grouped into five clusters, and the cluster that yields the best comparison with the experimental macroscopic data contains the parameters previously found with the simplified model and also predicts the correct ground-state magnetic structure.

The study of topological superconductivity is largely based on the analysis of simple mean-field models that do not conserve particle number. A major open question in the field is whether the remarkable properties of these mean-field models persist in more realistic models with a conserved total particle number and long-range interactions. For applications to quantum computation, two key properties that one would like to verify in more realistic models are (i) the existence of a set of low-energy states (the qubit states) that are separated from the rest of the spectrum by a finite energy gap, and (ii) an exponentially small (in system size) bound on the splitting of the energies of the qubit states. It is well known that these properties hold for mean-field models, but so far only property (i) has been verified in a number-conserving model. In this work we fill this gap by rigorously establishing both properties (i) and (ii) for a number-conserving toy model of two topological superconducting wires coupled to a single bulk superconductor. Our result holds in a broad region of the parameter space of this model, suggesting that properties (i) and (ii) are robust properties of number-conserving models and not just artifacts of the mean-field approximation.

The superconducting diode effect may exist in bulk systems as well as in junctions when time-reversal and inversion symmetries are simultaneously broken. Magnetization gradients and textures satisfy both requirements and therefore also allow for superconducting diodes. We concretely demonstrate such possibilities in two-dimensional superconductors. We first consider superconducting Rashba metals in the presence of an inhomogeneous out-of-plane exchange field. Using analytical arguments, we reveal that such magnetization gradients stabilize a helical superconducting ground state, similar to homogeneous in-plane magnetic fields. Our predictions are confirmed by employing self-consistent real-space numerical lattice simulations exemplified through the cases of a uniform magnetization gradient or a ferromagnetic domain wall. Furthermore, by considering a phase difference, we determine the nonreciprocal current-phase relations and explore their parameter dependence. Our calculations show that planar devices with out-of-plane magnetization gradients may be as efficient supercurrent rectifiers as their analogs induced by uniform in-plane fields. In addition, they feature the advantage that by means of tailoring the spatial profile of the out-of-plane magnetization, one may optimize and spatially control the diode effect. Finally, we show that superconducting diodes may become also accessible even in the absence of spin-orbit coupling by means of suitable spatially varying magnetization fields.

Using a functional renormalization group approach we derive the renormalization group (RG) flow of a dissipative variant of the Yukawa-Sachdev-Ye-Kitaev model describing $N$ fermions on a quantum dot, which interact via a disorder-induced Yukawa coupling with $M$ bosons. The inverse Euclidean propagator of the bosons is assumed to exhibit a nonanalytic term proportional to the modulus of the Matsubara frequency. We show that, to leading order in $1/N$ and $1/M$, the hierarchy of formally exact flow equations for the irreducible vertices of the disorder-averaged model can be closed at the level of the two-point vertices. We find that the RG flow exhibits a non-Fermi liquid fixed point characterized by a finite fermionic anomalous dimension $\eta$, which is related to the bosonic anomalous dimension $\gamma$ via the scaling law $2=2\eta +\gamma$ with $0<\eta <1/2$. We explicitly calculate $\eta$ and the critical exponents characterizing the linearized RG flow in the vicinity of the fixed point as functions of $N/M$.

The geometric response, which goes beyond the electromagnetic response, of quantum Hall (QH) liquids is crucial for understanding their topological characteristics. According to the Wen-Zee theory, the topological spin is intricately linked to the curvature of the space in which the electrons exist. The presence of conical geometry offers a local, isolated geometric singularity, making it an ideal setting for exploring geometric responses. In the context of two-dimensional electrons in a perpendicular magnetic field, each Landau orbit occupies the same area. The cone geometry naturally provides a structure where the distances between adjacent orbits vary gradually and can be easily adjusted by modifying the tip angle. The cone tip introduces a geometric singularity that impacts electron density and interacts with electron motion, which has been extensively studied. Additionally, this geometry automatically creates a smooth interface or crossover between the crystalline charge-density-wave state and the liquidlike fractional QH state. In this paper, we investigate the properties of this interface from multiple perspectives, shedding light on the behavior of QH liquids in such geometric configurations.

The electrical resistivity of the unconventional superconductor ${\mathrm{UTe}}_2$ shows very anisotropic behavior in the normal state depending on the current direction. In this paper we show that the maximum in the resistivity ${\rho }_c$ for current applied along the $c$ axis at $T_{{\rho }_c}^{\max }\approx 14.75$ K follows the minimum in the thermal expansion $T_{\alpha }^{★}$ along the $b$ axis. Under a magnetic field applied along the $b$ axis, $T_{{\rho }_c}^{\max }$ can be tracked up to the critical point of the first-order metamagnetic transition, which is located near 6 K and 34.5 T. Surprisingly, at the metamagnetic field $H_m$ the resistivity ${\rho }_c$ shows a steplike decrease while the resistivities ${\rho }_a$ and ${\rho }_b$, for current along the $a$ and $b$ axes, respectively, show a steplike increase. Under hydrostatic pressure $T_{{\rho }_c}^{\max }$ and $H_m$ decrease significantly up to the critical pressure $p_c$ at which superconductivity is suppressed and a long-range antiferromagnetic order appears. We show that the phase diagram at different pressures can be scaled by $T_{{\rho }_c}^{\max }$ in field and temperature, suggesting that this temperature scale is governing the main interactions in the normal state.

The low-temperature states of ambient ${\mathrm{URu}}_2{\mathrm{Si}}_2$ and superfluid ${}^4\mathrm{He}$ are both characterized by momentum-dependent energy gaps between the ground and excited states. This behavior weakly persists even above the transition temperatures but becomes overdamped (ungapped) because of the number of excitations present at elevated temperature. We show that, akin to the normal-fluid-to-superfluid transition in ${}^4\mathrm{He}$, the hidden order (HO) transition in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ can be understood by a change of the ungapped excitations to the gapped, elementary excitations (EE) of the unknown ordered state. These underdamped EEs reflect the basic character and order parameters of the different phase transitions. This view accounts for the full amount of entropy released in these transitions, the jumps in the resistivity and thermal conductivity directly below the transition, as well as the reduction of the Fermi surface. We argue that the behavior in the HO phase is that of a gas of weakly interacting excitations from charge density wave or crystal-field states in a similar manner to that of the phonon-roton excitations of the superfluid ${}^4\mathrm{He}$ phase. We discuss the influence of applying pressure and magnetic fields within this scenario and the role of the small moment antiferromagnetic clustering in the hidden order phase.

We reveal the topologically protected persistent oscillatory dynamics of a polariton superfluid which is driven nonresonantly by a super-Gaussian laser beam in a planar semiconductor microcavity subjected to an external C-shaped potential. We find persistent oscillations characterized by an attractor of vortices that are based on the dynamical behavior of small Josephson vortices rotating around the outer boundary of the ring-shaped dense region of the central vortex. The attractor is formed due to the inverse energy cascade accompanied by the growth of incompressible kinetic energy. The attractor displays a remarkable stability towards perturbations, and it may be tuned by the pump laser intensity to two distinct frequency ranges: $20.16\pm 0.14$ and $48.4\pm 1.2\mathrm{GHz}$. This attractor is bistable with respect to the chirality of the vortex. The switching between two stable states is achieved by altering the pump power or by adding an extra incoherent Gaussian pump beam.

We theoretically studied the Floquet state of gated bilayer graphene, which is irradiated by normally incident focused Gaussian beam with orbital angular momentum (OAM). According to the Floquet theory, in-plane and out-of-plane electric field of the OAM beam periodically perturbs the intralayer and interlayer hopping, which are equivalent to the presence of effective staggered sublattice potential and next-nearest-neighboring interlayer hopping within the light spot region, respectively. The combination of the effective terms and the gated voltage form an effective trapping potential, which hosts localized quantum states with energy level being within the energy gap of the nonirradiated gated bilayer graphene. The energy spectrum can be tuned by the amplitude of the optical beam and additional static magnetic field. By engineering the parameters, valley-polarized twofold degenerated zero-energy Floquet states can be induced.

Coherent charge and heat transport through periodically driven nanodevices provide a platform for studying thermoelectric effects on the nanoscale. Here we study a junction composed of a quantum dot connected to two fermionic terminals by two weak links. An AC electric field induces time-dependent spin-orbit interaction in the weak links. We show that this setup supports DC charge and heat currents and that thermoelectric performance can be improved, as reflected by the effect of the spin-orbit coupling on the Seebeck coefficient and the electronic thermal conductance. Our analysis is based on the nonequilibrium Keldysh Green's function formalism in the time domain and reveals an interesting distribution of the power supply from the AC source among the various components of the device.

We present first-principles calculations of the electronic structure and spin texture of a ${\mathrm{MoS}}_2$ monolayer in $\mathrm{Fe}\text{/}\mathrm{MgO}\text{/}{\mathrm{MoS}}_2$ multilayers. These metal/insulator/semiconductor stackings are subject to an electron transfer from the Fe layer to the ${\mathrm{MoS}}_2$ sheet, giving rise to a two-dimensional (2D) electron gas, the density of which depends on the MgO layer thickness. We describe the consequences of this electron transfer and of the magnetic proximity effect on the occupation of the conduction bands of the ${\mathrm{MoS}}_2$ layer, on the nature of its band gap, and on the splitting and dispersion of its valence bands near the $\mathrm{\Gamma }$ point of the 2D Brillouin zone. The spin splitting and spin texture are reproduced and understood by an effective Hamiltonian, which includes Rashba, Dresselhaus, and Zeeman effects. We finally show that the splitting of the ${\mathrm{MoS}}_2$ valence bands induced near $\mathrm{\Gamma }$ by the spin-orbit coupling is rather different when Fe is replaced by a nonmagnetic transition metal such as vanadium.

The identification of the topological invariant of a topological system is crucial in experiments. However, due to the inherent non-Hermitian features, such determination is notably challenging in non-Hermitian systems. Here, we propose that the magnetic effect can be utilized to measure the Chern number of the non-Hermitian Chern insulator. We find that the splitting of non-Hermitian bands under the magnetic field is Chern number dependent. Consequently, one can easily identify the Chern number by analyzing these splitting sub-bands. From the experimental perspective, the measurement of non-Hermitian bands is demonstrated in LC electric circuits. Furthermore, we find that the non-Hermiticity can drive open (closed) orbits of sub-bands in the Hermitian limit closed (open), which can also be identified by our proposal. These phenomena highlight the distinctive capabilities of non-Hermitian systems. Our results facilitate the detection of Chern numbers for non-Hermitian systems and may motivate further studies of their topological properties.

Moiré engineering in two-dimensional van der Waals bilayer crystals has emerged as a flexible platform for controlling strongly correlated electron systems. The competition between valleys for the band extremum energy position in the parent layers is crucial in deciding the qualitative nature of the moiré Hamiltonian since it controls the physics of the moiré minibands. Here we use density functional theory to examine the competition between K and $\mathrm{\Gamma }$ for the valence-band maximum in homo- and hetero-bilayers formed from the transition metal dichalcogenides (TMD), ${MX}_2$ where $M=\text{Mo}$, W and $X=\text{S}$, Se, Te. We shed light on how the competition is influenced by interlayer separation, which can be modified by applying pressure, by external gate-defined electric fields, and by transition metal atom $d$-orbital correlations. Our findings are related to several recent experiments, and contribute to the development of design rules for moiré materials.