Magnets, with topologically nontrivial Dirac/Weyl points, have recently attracted significant attention owing to their unconventional physical properties, such as a large anomalous Hall effect. However, they typically have a high carrier density and a complicated band structure near the Fermi energy. In this Letter, we report a degenerate magnetic semiconductor ${\mathrm{EuMg}}_2{\mathrm{Bi}}_2$, which exhibits a single valley at the $\mathrm{\Gamma }$ point, where field-tunable Weyl points form via a magnetic exchange interaction with the local Eu spins. By the high-field measurements on high-quality single crystals, we observed quantum oscillations in the resistivity, elastic constant, and surface impedance, which enabled us to determine the position of the Fermi energy $E_F$. In combination with a first-principles calculation, we revealed that the Weyl points are located in the vicinity of $E_F$ when the Eu spins are fully polarized, leading to a peak of energy-dependent anomalous Hall conductivity due to the Berry curvature. Accordingly, in the forced ferromagnetic phase, we observed a large anomalous Hall effect (Hall angle ${\mathrm{\Theta }}_{\mathrm{AH}}\sim 0.07$) qualitatively consistent with the calculation, which demonstrates a marked impact of the Weyl points in the simple band structure.

We reveal a prethermal dynamical regime upon suddenly quenching to the vicinity of a quantum phase transition in the time evolution of one-dimensional spin chains. The prethermal regime is analytically found to be self-similar and its duration is governed by the ground-state energy gap. Based on analytical insights and numerical evidence, we show that this dynamical regime universally exists independently of the location of the probe site, the presence of weak interactions, or the initial state. The resulting prethermal dynamics leads to an out-of-equilibrium scaling function of the order parameter in the vicinity of the transition. Our theory suggests that sudden quench dynamics, besides probing quantum phase transitions, may give rise to a universal critical slowing down near the critical point.

Non-Hermiticity is revolutionizing the common understanding in the Hermitian scope by interfacing with topological physics. A single non-Hermitian band can host nontrivial topology that is defined over the nonzero windings of the system's eigenvalues, but not the eigenvectors, as opposed to the Hermitian topological systems. This unique non-Hermitian band topology is responsible for the intriguing non-Hermitian skin effect. Here, we show that the band topology of non-Hermitian one-band models can experience multiple phase transitions. Each transition is identified by a change of the eigenvalue winding. Such an interesting phenomenon is enabled by strategically manipulating the long-range couplings. Associated with the multiple phase transitions, the non-Hermitian skin effect exhibits anomalous behaviors, i.e., in different phases, the skin modes take on different forms of wave localizations. At the transition points, the skin modes evolve into Bloch-wavelike extended states, as if the Hermiticity is restored. For demonstration, we consider a modified Hatano-Nelson model with nonreciprocal next-nearest neighbor couplings. Therein, two phase transitions are identified, corresponding to a stationary and a dynamic one (with respect to the reciprocal nearest-neighbor coupling). Exact analytical derivations are performed to analyze the phase transitions and the associated anomalous non-Hermitian skin effect, which show consistency with the numerical results based on the generalized Brillouin zone method. Our work reveals rich non-Hermitian topological physics in one-band systems, which are considered to be topologically trivial in Hermitian systems. By further showing the anomalous non-Hermitian skin effect, intriguing wave manipulations may inspire experiments in classical realms such as photonics and phononics where versatile non-Hermitian controls are feasible.

We study Bose-Hubbard models in a family of diamond necklace lattices with $n$ central sites. The single-particle spectrum of these models presents compact localized states (CLSs) that occupy the up and down sites of each diamond. By performing an appropriate basis rotation, the fragmentation of the many-boson Hilbert space becomes apparent in the adjacency graph of the Hamiltonian, showing disconnected subsectors with a wide range of dimensions. The models present a conserved quantity related to the occupation of the single-particle CLSs that uniquely identifies the different subsectors of the many-boson Hilbert space. Due to the fragmentation of the Hilbert space, the distribution of entanglement entropies of the system presents a nested-dome structure. We find weak thermalization through subsector-restricted entanglement evolution and a wide range of entanglement entropy scalings from area-law to logarithmic growth. Additionally, we observe how the distinguishability between the different domes increases with the number of central sites and we explain the mechanism behind this fact by analyzing the graph structure of the Hamiltonian.

The copper fluoride ${\mathrm{Cu}}_2{\mathrm{F}}_5$ is a compound with two-dimensional (2D) magnetic exchange interactions between the Cu ions in the $S=1$ and $S=\frac{1}{2}$ spin states. Using ab initio calculations, we predict that the existence of 5% vacancies in the fluoride sublattice of ${\mathrm{Cu}}_2{\mathrm{F}}_5$ results in a drastic transformation of the spin state of all copper ions and the final spin states are $S=\frac{1}{2}$ and $S=0$. Consequently, the anisotropy of the magnetic interactions increases, and 1D linear chains of Cu $d^9, S=\frac{1}{2}$ ions appear. We also propose a microscopic mechanism of such a transformation of the exchange interaction via ${\mathrm{CuO}}_6$ octahedra elongation.

The direct calculation of magnetoelastic wave dispersion in layered media is presented using an efficient, accurate computational technique. The governing, coupled equations for elasticity and magnetism, the Navier and Landau-Lifshitz equations, respectively, are linearized to form a quadratic eigenvalue problem that determines a complex web of wave-number–frequency dispersion branches and their corresponding mode profiles. Numerical discretization of the eigenvalue problem via a spectral collocation method (SCM) is employed to determine the complete dispersion maps for both a single, finite-thickness magnetic layer and a finite magnetic-nonmagnetic double-layer. The SCM, previously used to study elastic waves in nonmagnetic media, is fast, accurate, and adaptable to a variety of sample configurations and geometries. Emphasis is placed on the extremely high-frequency regimes being accessed in ultrafast magnetism experiments. The dispersion maps and modes provide insight into how energy propagates through the coupled system, including how energy can be transferred between elastic- and magnetic-dominated waves as well as between different layers. The numerical computations for a single layer are further understood by a simplified analytical calculation in the high-frequency, exchange-dominated regime where the resonance condition required for energy exchange (an anticrossing) between quasi-elastic and quasi-magnetic dispersion branches is determined. Nonresonant interactions are shown to be well approximated by the dispersion of uncoupled elastic and magnetic waves. The methods and results provide fundamental theoretical tools to model and understand current and future magnetic devices powering spintronic innovation.

Since Majorana zero mode (MZM) was proposed applicable for topological quantum computing, the past two decades have witnessed a growth of theoretical and experimental advances. Here we propose a Josephson junction setup consisting of intrinsic topological superconductors, and show that with the exchange operation of two MZMs, the single-electron tunneling current will reverse sign as a result of its non-Abelian statistics, which can be further utilized to read out the initial qubit of the system. This work offers a way to demonstrate the non-Abelian statistical properties of MZMs.

Nonlocal quasiparticles in correlated quantum materials can exhibit the proximity effect. For instance, in metal superconductor hybrid systems, the leaking of Cooper pairs to the metallic region induces superconducting correlations in a standard metal. This paper explores the proximity effects of charge density wave (CDW) on metal using the attractive Hubbard model, which harbors CDW state at half filling. Our fully self-consistent calculations demonstrate that periodic charge modulations develop in a metal due to the tunneling of finite momentum particle-hole pairs from the CDW region. Upon doping the normal region, the commensurate CDW changes to an incommensurate one by incorporating regular phase shifts. Furthermore, the induced CDW produces a soft gap in the density of states and thus can be detected in tunneling experiments. We discuss our results in light of recent reports of such proximity-induced charge order in different two-dimensional heterostructures.

Efficient and accurate computational methods for dealing with interacting electron problems on a lattice are of broad interest to the condensed matter community. For interacting Hubbard models, we introduce a cluster slave-particle approach that provides significant computational savings with high accuracy for total energies, site occupancies, and interaction energies. Compared to exact benchmarks using density matrix renormalization group for $d\text{−}p$ Hubbard models, our approach delivers accurate results using two to three orders of magnitude lower computational cost. Our method is based on a slave-particle decomposition with an improved description of particle hoppings, and a density matrix expansion method where the interacting lattice slave-particle problem is turned into a set of overlapping real-space clusters which are solved self-consistently with appropriate physical matching constraints at shared lattice sites between clusters.

The dispersion of quasiparticles in topological nodal-line semimetals is significantly different in different directions. In a certain direction, the quasiparticles behave like relativistic particles with constant velocity. In other directions, they act as two-dimensional electron gas. The competition between relativistic and nonrelativistic dispersions can induce a sign reversal of Casimir-Lifshitz torque. Three different approaches can be applied to generate this sign reversal, i.e., tuning the anisotropic parameter or chemical potential in a nodal-line semimetal, and changing the distance between this material and substrate birefringence. Detailed calculations are illustrated for the system with topological nodal-line semimetal ${\mathrm{Ca}}_3{\mathrm{P}}_2$ and liquid crystal material 4-cyano-4-$n$-pentylcyclohexane-phenyl.

We study electron spin transport at the spin-splitting surface of chiral-crystalline-structured metals and the Edelstein effect at the interface, by using the Boltzmann transport equation beyond the relaxation time approximation. We first define spin relaxation time and spin diffusion length for two-dimensional systems with anisotropic spin-orbit coupling through the spectrum of the integral kernel in the collision integral. We then explicitly take account of the interface between the chiral metal and a nonmagnetic metal with finite thickness. For this composite system, we derive analytical expressions for efficiency of the charge current–spin current interconversion as well as other coefficients found in the Edelstein effect. We also develop the Onsager reciprocity in the Edelstein effect along with experiments so that it relates local input and output, which are respectively defined in the regions separated by the interface. We finally provide a transfer matrix corresponding to the Edelstein effect through the interface, with which we can easily represent the Onsager reciprocity as well as the charge-spin conversion efficiencies we have obtained. We confirm the validity of the Boltzmann transport equation in the present system starting from the Keldysh formalism in supplemental material. Our formulation also applies to the Rashba model and other spin-splitting systems.

Deterministic nonperiodic lattices often exhibit properties intermediate between those of random and periodic crystals. Properties that have attracted interest include complex heirarchical structure factors, the breaking up of the band into a dense set of critical states and minigaps, and the interplay between extended and localized states. In one dimension, considerable attention has focused on nonperiodic lattices showing properties intermediate between periodic and random. We propose a one-dimensional nonperiodic lattice with lattice sites at $0^{2}d, 1^{2}d, 2^{2}d$, ... with length $d$ playing the rôle of the lattice constant. Here we show that the structure factor $S_0\left(k\right)$, which governs how waves are scattered and is reflected in many physical properties, is simply related to the Jacobi theta function ${\vartheta }_3\left(q\right)$. $S_0\left(k\right)$ is periodic in wave vector $k$ and is singular continuous, consisting of a dense set of peaks with $k$ given by rational-fraction multiples of $\frac{\pi }{d}$, though the scaling properties of $S_0\left(k\right)$ are the same as for periodic crystals. The electronic structure considered in a tight-binding model shows a bandlike spectrum, but broken by a dense set of minigaps near peak locations in $S_0\left(k\right)$. These lattices show novel properties such as the coexistence of a singular-continuous spectrum with extended states. Quadratic lattices may enable the physical realization of special functions of mathematical and physical importance as well as for the design of nonperiodic diffraction gratings, antenna arrays, ad coupled optical resonators to produce complex quasirandom behavior and are of interest to study quantum interactions in nonperiodic optical lattices.

Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Previous theoretical work, based on a stringent ultra-short-range assumption on the symmetry-allowed interactions, predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, intervalley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunneling studies universally find Kekulé bond order, and sometimes also charge density wave order. Recently, it was found that if one relaxes the stringent assumption mentioned above a phase with coexisting canted antiferromagnetic and Kekulé order exists in the region of the phase diagram believed to correspond to real samples. In this paper, starting from the continuum limit appropriate for experiments, we present the complete phase diagram of $\nu =0$ graphene in the Hartree-Fock approximation, using generic symmetry-allowed interactions, assuming translation-invariant ground states up to an intervalley coherence. Allowing for a sublattice potential (valley Zeeman coupling), we find numerous phases with different types of coexisting order. We conclude with a discussion of the physical signatures of the various states.

Oligo(indenoindenes) (OInIn) are $\pi$-conjugated ladder carbon polymers with alternating hexagons and pentagons, hosting one unpaired electron for each of the latter in the open-shell limit. Here we study the main magnetic interactions in finite OInIn, classifying the six possible isomers in two different classes of three isomers each. We find that one class can be described by frustrated $S=1/2$ Heisenberg chains, with antiferromagnetic interactions between the second-neighbor sites. The other class is characterized by antiferromagnetic order. Employing several levels of theory, we further show that the ground state of one of the isomers is a valence-bond solid of ferromagnetic dimers ($S=1$). This is topologically similar to that of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, which is known to show fractional $S=1/2$ states at the edges.

An effective model of the hexagonal (NiAs-structure) manganese telluride valence band in the vicinity of the $A$ point of the Brillouin zone is derived. It is shown that whereas for the usual antiferromagnetic order (magnetic moments on the basal plane) band splitting at $A$ is small, their out-of-plane rotation enhances the splitting dramatically (to about 0.5 eV). We propose extensions of recent experiments [Phys. Rev. Mater. 6, 014404 (2022)] where such inversion of magnetocrystalline anisotropy has been observed in Li-doped MnTe to confirm this unusual sensitivity of a semiconductor band structure to magnetic order.

MnTe has recently attracted attention as an altermagnetic candidate. Experimentally it has an altermagnetic order of ferromagnetic $ab$ planes, stacked antiferromagnetically along $c$. We show that this magnetic order (by itself nontrivial, since the in-plane exchange in antiferromagnetic) opens intriguing possibility of manufacturing altermagnetically detwinned samples and generate observable magneto-optical response (which we calculate from first principles) as a signature of altermagnetism.

A superconductor with broken time-reversal and inversion symmetry may exhibit nonreciprocal charge transport, including a nonreciprocal critical current, also known as superconducting diode effect. We report an intrinsic superconducting diode effect in a polar strontium titanate film. Differential resistance measurements reveal a superconducting state whose depairing current is polarity dependent. There is, however, no measurable deviation from Ohmic behavior, implying that this state does not arise from a bulk magnetochiral anisotropy. In the entire measurement range, the only deviation from linearity in the differential resistance is on the edge of the superconducting transition at high magnetic fields, likely due to the motion of flux vortices. Furthermore, the magnitude of the effect is preserved even when the in-plane magnetic field is oriented parallel to the current, indicating that this effect truly does not originate from a bulk magnetochiral anisotropy.

Electronic nematicity, a consequence of rotational symmetry breaking, is an emergent phenomenon in various new materials. In order to fully utilize the functions of these materials, ability of tuning them through a knob, the nematic director, is desired. Here we report a successful manipulation of the nematic director, the vector order parameter (d vector), in the spin-triplet superconducting state of ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ by magnetic fields. At $H=0.5\mathrm{T}$, the ac susceptibility related to the upper critical field shows a twofold symmetry in the basal plane. At $H=1.5\mathrm{T}$, however, the susceptibility shows a sixfold symmetry, which has never been reported before in any superconductor. These results indicate that the $\mathbf{d}$ vector initially pinned to a certain direction is unlocked by a threshold field to respect the trigonal crystal symmetry. We further reveal that the superconducting gap in different crystals converges to $p_x$ symmetry at high fields, although it differs at low fields.

The magnetization of the antiferromagnetic van der Waals material ${\mathrm{FePS}}_3$ is investigated via the spin Nernst magnetoresisance (SNMR) and spin Seebeck effect (SSE). A heater and Pt detector strips are fabricated on top of a ${\mathrm{FePS}}_3$ flake which generates a temperature gradient in ${\mathrm{FePS}}_3$ and in the Pt detector strips. We are able to detect the SNMR in Pt, which is an interface effect, and detect the SSE response, which is a bulk effect. We conclude that there are uncompensated magnetic moments in ${\mathrm{FePS}}_3$ at the interface with Pt. Via the SNMR we are able to extract the real and imaginary parts of the spin mixing conductance assuming a fully uncompensated top layer. For an in-plane thermal conductivity of 10 W/($\mathrm{m}\mathrm{K}$) and therefore a temperature gradient of 6000 K/m in Pt we find that $G_r=1.9\pm 0.06\times {10}^{13}{\mathrm{\Omega }}^{-1}{\text{m}}^{-1}$ and $G_i=4.8\pm 0.02\times {10}^{11}{\mathrm{\Omega }}^{-1}{\text{m}}^{-1}$. In addition, the temperature gradient in ${\mathrm{FePS}}_3$ generates a magnon current in ${\mathrm{FePS}}_3$ via the SSE which can be detected by the Pt detector strips. We are able to extract a magnon diffusion length of $1.3\pm 0.5$ and $0.5\pm 0.1\mu \mathrm{m}$ for thermally generated magnons in ${\mathrm{FePS}}_3$ for 40 and 20 nm thicknesses, respectively.