The paper presents in-depth studies of the dielectric properties and conduction dynamics of Dy-doped ${\mathrm{CaBaFe}}_4{\mathrm{O}}_7$ which is a recently characterized magnetoelectric material with strong potentials for technological applications as it shows a near-room-temperature ferrimagnetic transition along with strong ferrimagnetic moment, and gigantic electric polarization change. This work demonstrates the direct correlation of the dielectric and electrical transport properties of ${\mathrm{Ca}}_{1-x}{\mathrm{Dy}}_x{\mathrm{BaFe}}_4{\mathrm{O}}_7$ $(x=0, 0.01, 0.03, \text{and} 0.05)$ with structural distortion through various dc, ac conduction, high-energy x-ray diffraction studies, and modeling of the data. ${\mathrm{CaBaFe}}_4{\mathrm{O}}_7$ has a unique structure characterized by alternate stacking of ${\mathrm{FeO}}_4$ tetrahedra in triangular and kagomé layers. Large structural distortion, competing magnetic interactions, exchange striction effects, and possible charge ordering are expected to play a major role in the dielectric and electrical properties of the material. We report observation of short-range polaron hopping conduction mechanism in the low-temperature regime and signature of large polaronic nature of charge carriers. Modeling of the electric modulus using Havriliak-Negami equation points out both distribution and cooperativeness in the polaron dynamics which can be correlated to the interplay of structural distortion, and the background electric field due to the polar nature of the materials. The Havriliak-Negami parameters closely follow orthorhombic distortion of the structures.

Spin-orbit coupling (SOC) emerging at the interfaces of superconducting magnetic tunnel junctions is at the heart of multiple unprecedented physical phenomena, covering triplet proximity effects induced by unconventional (spin-flip) Andreev reflections, giant transport magnetoanisotropies, sizable tunneling anomalous Hall effects, and electrically controlled current-reversing 0–$\pi$(-like) transitions in Josephson contacts. Recent first-principles calculations proposed that the Rashba spin-orbit fields in twisted graphene/transition-metal dichalcogenide and van der Waals multilayers can—owing to broken mirror symmetries—exhibit an unconventional radial component (with spin parallel to the electron's momentum), which can be quantified by the Rashba angle ${\theta }_{\mathrm{R}}$. We theoretically explore the ramifications of radial Rashba SOC at the interfaces of vertical ferromagnet/superconductor tunnel junctions with a focus on the magnetoanisotropies of the tunneling and tunneling-anomalous-Hall-effect conductances. Our results demonstrate that ${\theta }_{\mathrm{R}}$ can be experimentally extracted from respective magnetization-angle shifts, providing a robust way to probe the radial Rashba SOC induced by twisted multilayers that are placed as tunneling barriers between ferromagnetic and superconducting electrodes.

Using a microscopic approach, we revisit the problem of superconducting critical temperature change in the presence of twin boundaries. We show that both critical temperature enhancement and suppression can come purely from single-electron geometric effects. These include aspects of scattering of electrons on these crystalline defects even when the coupling constant is unchanged. We consider two-dimensional rectangular and three-dimensional body-centered-cubic lattices with on-site $s$-wave superconducting pairing, nearest- and next-nearest-neighbor hoppings. In the considered two-dimensional lattice with twin boundaries, the superconducting critical temperature associated with twinning planes is suppressed for moderate band filling and enhanced for an almost empty or filled band. The superconducting phase diagram is more diverse for the three-dimensional lattice, which is caused by the interplay of van Hove singularity, changing coordination number, and modification of distances to nearest and next-nearest neighbors.

Due to the diverging density of states (DOS), Van Hove singularities (VHS) near the Fermi level are known to boost the susceptibility to a wide variety of electronic instabilities, including superconductivity. We propose that the number and type of VHS on the Fermi surface can be detected by the optical conductivity in the superconducting state under an applied current. We theoretically show that having multiple VHS on the Fermi surface is a novel mechanism for activating a divergent optical absorption peak at frequency $\omega =2\mathrm{\Delta }$, resulting from the transition across the gap $\mathrm{\Delta }$ which is forbidden in single-band clean superconductors with inversion symmetry and quadratic bands. In contrast, we find a weak peak with nondivergent intensity when there is only a single VHS. Whether its DOS has logarithmic or power-law divergence can be detected by the anisotropy between the peaks in ${\sigma }_{xx}\left(\omega \right)$ and ${\sigma }_{yy}\left(\omega \right)$. Our prediction can be tested by measurements of optical absorption spectra in monolayer, few-layer, or thin-film superconductors with VHS on the Fermi surface.

Band structures of metamaterials described by a nonlinear eigenvalue problem are beyond the existing topological band theory. In this paper, we analyze non-Hermitian topology under the nonlinearity of eigenvalues. Specifically, we elucidate that such nonlinear systems may exhibit exceptional points and non-Hermitian skin effects which are unique non-Hermitian topological phenomena. The robustness of these non-Hermitian phenomena is clarified by introducing the topological invariants under nonlinearity which reproduce the existing ones in linear systems. Furthermore, our analysis elucidates that exceptional points may emerge even for systems without an internal degree of freedom, where the equation is a single component. These nonlinearity-induced exceptional points are observed in mechanical systems, e.g., the Kapitza pendulum.

Experimental efforts on topological superconductivity (TSC) have primarily focused on the detection of Majorana boundary modes, while the bulk properties of TSC, particularly in two dimensions, remain relatively underexplored. In this work, we theoretically propose a distinctive signature in the spectral function away from the boundaries, capable of detecting two-dimensional (2D) chiral $p$-wave TSC induced in a Rashba spin-orbit-coupled heterostructure. This signature can be probed experimentally through angle-resolved photoemission spectroscopy or momentum- and energy-resolved tunneling spectroscopy under a weak magnetic field $B$. We show that within the topological phase, the spectral intensity of the lowest superconducting band at small momenta $k\sim 0$ brightens (darkens) linearly with increasing $B$, whereas it darkens (brightens) in the trivial phase when the Rashba system is electron (hole) doped. This sharp contrast arises from the phase-space Berry curvature (BC) of Bogoliubov quasiparticles, a novel quantum geometric property that generalizes the conventional momentum-space BC. The effect of this phase-space BC can also be detected by the differential conductance away from the boundaries. Our falsifiable prediction provides an experimental avenue for detecting Rashba-induced chiral $p$-wave TSC without relying on Majorana mode detection, addressing a key challenge in the realization of 2D TSC.

We study quasi-one-dimensional wires of two-band superconductors driven by an electrical current. We find that the onset of dissipation can occur with the nucleation of time-connected phase slips (t-PS). The topological structure of the t-PS consists of two phase slips (one in each order parameter) separated in time and connected via an interband vortex string along the time direction. This shows as a two-peak structure in voltage vs time. We discuss the conditions for observing t-PS, depending on the interband coupling strength and the relaxation time scales for each order parameter.

Magnetic oscillations in strongly correlated insulating systems have garnered interest due to oscillations seemingly originating from the bulk, despite an anticipated gapped spectrum. We use the large-$N$ mean-field theory to study the behavior of normal and topological Kondo insulators under a magnetic field. In both cases spinons acquire a charge and hybridize with electrons, producing magnetic oscillations that resemble two-band noninteracting systems. We show that in such band insulators magnetic oscillations are exponentially suppressed at weak magnetic fields. A self-consistent mean-field calculation for the Kondo insulators reveals that the temperature dependence of the oscillations departs from the noninteracting case due to the temperature and magnetic-field dependence of the hybridization, even though the mean-field parameters remain homogeneous. Higher temperature results in the Kondo breakdown, where the magnetic oscillation is solely due to the decoupled conduction electrons. These findings offer different insights into the magnetic properties of Kondo insulators, with implications for interpreting experimental results in heavy-fermion materials like ${\mathrm{SmB}}_6$.

We report the exact closed-form solutions for higher-order topological states as well as explicit energy-spectrum relationships in two-dimensional (2D) non-Hermitian multiorbital lattices with generalized boundary conditions. These analytical solutions unequivocally confirm that topological edge states in a 2D non-Hermitian system may feature the point-gap topology as well and hence must undergo the non-Hermitian skin effect along the edges. Under double open boundary conditions, the occurrence of the non-Hermitian skin effect for either topological edge states or bulk states can be accurately predicted by our proposed winding numbers. We unveil that the zero-energy topological corner state only manifests itself on a corner where two nearby gapped edge states intersect, and thus can either disappear completely or strengthen drastically due to the non-Hermitian skin effect of gapped topological edge states. Our analytical results offer direct insight into the non-Bloch band topology in two or higher dimensions and trigger experimental investigations into many related phenomena such as quadrupole topological insulators and topological lasing.

The quantum anomalous Hall effect (QAHE) has gained significant attention in recent years due to its potential applications in low-power devices. However, the QAHE still faces the limitations of the relatively small global band gap and low Chern number. In this work, based on the tight-binding (TB) model with magnetic group $P\overline{3}{m}^{\prime }1$, we propose a mechanism whereby quadratic band crossing induces a stable global band gap which is larger than that formed by the linear band crossing. Additionally, the quadratic band crossing induces topological states with high Chern number when spin-orbit coupling is considered. We also propose monolayer $\mathrm{MoT}{\mathrm{e}}_2{\mathrm{F}}_2$ to confirm the TB results by performing calculations of first-principles and low-energy $k·p$ model. The quadratic band crossing is formed by the hybridization of the orbitals from the Mo and the F atoms. The contributions of the $d_{xy}$ and $d_{x^2-y^2}$ orbitals at the quadratic band crossing are bigger than their contributions at the linear band crossing, so the global band gap induced by the quadratic band crossing is large. Furthermore, after biaxial strains are applied, the quadratic band crossing is destroyed and it transfers into a linear band crossing, and the global band gap becomes small. The quadratic band crossing can also be manipulated by a vertical electric field, and a phase transition from the QAHE to the anomalous valley Hall effect can be achieved. Our work not only provides a method to discover two-dimensional materials with a large global band gap and high Chern number but also integrates topological electronics and valleytronics, promoting the development of low-power devices.

Predicting the phase diagram of interacting quantum many-body systems is a challenging problem in condensed matter physics. Strong interactions and correlation effects may lead to exotic states of matter, such as quantum spin liquids and unconventional superconductors, that often compete with other symmetry-broken states including ordered magnets and charge density waves. Here, we put forward a formalism for determining the phase diagram of fermionic systems that combines recent progress in the field of Lee-Yang theory of phase transitions with many-body tensor-network methods. Using this strategy, we map out the phase diagram of a fermionic chain, where charge density waves form owing to strong repulsion. Specifically, from the high cumulants of the order parameter, we extract the dominant zeros of the moment-generating function in chains of finite size. By extrapolating their positions to the thermodynamic limit, we determine the boundaries between competing phases. Our formalism provides a strategy for determining critical points in fermionic systems, and it is based on fluctuations of the order parameter, which are measurable quantities.

Gauge invariance is a fundamental principle that must be preserved in quantum transport. However, when a complex potential is incorporated into the Hamiltonian, we find that the current described by the well-established Landauer-Büttiker formula no longer satisfies gauge invariance. Using the nonequilibrium Green's function method, we derive a current expression for a multiprobe system that includes a complex potential in the scattering region. We observe that an additional current term arises compared to the Landauer-Büttiker formula, which leads to a violation of gauge invariance. To address this, we propose two phenomenological methods for redistributing the conductance to restore gauge invariance in non-Hermitian systems. These methods are applied to various trivial and nontrivial non-Hermitian quantum states, confirming the necessity of gauge-invariant treatments in non-Hermitian systems.

The spin-orbit coupling (SOC) effect is a relativistic effect that is strongly expressed in valence electrons and therefore significantly affects the band structure of solids. Studies on the SOC effect are usually not concerned with its dependence on temperature. Here, using first-principles calculations assisted with molecular-dynamics simulations, we show that the band gap correction due to the SOC $\left(\mathrm{\Delta }{E}_{\mathrm{g}}\right)$ is strongly temperature dependent. Taking PbTe as the example, we found that $\mathrm{\Delta }{E}_{\mathrm{g}}$ can decrease by about 0.25 eV when temperature increases from 300 to 1100 K. Considering that the commonly adopted experimental band gap is about 0.3 eV for PbTe, this temperature dependence of $\mathrm{\Delta }{E}_{\mathrm{g}}$ is significant. The origin of this dependence can be clearly traced to the evolution of the conduction-band minimum state. As the temperature increases, the state becomes less delocalized, which weakens the SOC. This finding is expected to be generally applicable to other semiconductor materials containing elements of high atomic numbers. Future computational studies on such materials, especially for high-temperature applications, would be suggested to carefully include the temperature dependence of SOC.

Residual entropy, which reflects the degrees of freedom in a system at absolute zero temperature, is crucial for understanding quantum and classical ground states. Despite its key role in explaining low-temperature phenomena and ground-state degeneracy, accurately measuring residual entropy remains a difficult task owing to computational limitations. In this Letter, we introduce the temperature incremental Monte Carlo (TIMC) method, our approach to overcoming these challenges. The TIMC method incrementally calculates the partition function ratio of neighboring temperatures within Monte Carlo simulations, enabling precise entropy calculations and revealing many other temperature-dependent properties in a single computational sweep of temperatures. We have rogorously tested TIMC on several complex systems, including the frustrated antiferromagnetic Ising model on both C60 and 2D triangular lattices, the Newman-Moore glassy model, and a 2D quantum transverse field Ising model. Notably, our method overcomes the difficulties encountered in partition function measurements when mapping $d$-dimensional quantum models to ($d+1$)-dimensional classical counterparts. These challenges arise from singular interactions that emerge in the small ${\mathrm{\Delta }}_{\tau }$ limit during the quantum-to-classical mapping procedure. The TIMC method enables precise entropy calculations across the entire temperature range, as demonstrated in our studies of frustrated spin models, glassy phases, and phases exhibiting spontaneous symmetry breaking. This method's capability to calculate residual entropy could provide insights when applied to systems lacking analytical solutions.

The groundbreaking discovery of a negative friction coefficient (NCOF) challenges the long-held classic Amonton's law, ushering in fresh perspectives for comprehending and manipulating friction. Nevertheless, contradictory results about the NCOF have been recently reported by static first-principles calculations, which could foster misconceptions regarding the fundamental physics underlying this intriguing phenomenon. Here, we identify that disparities in computational models used in static friction calculations serve as the pivotal factor causing these inconsistencies through meticulous reproduction and comparison of the contradictory results. Specifically, the NCOF predicted by static first-principles in two-dimensional lamellar materials result from the overlooking of the pivotal role of the work done by the load during sliding. We further verify the indispensability of the work done by the load through theoretically scrutinizing the sliding process under constant load and under constant distance. Our findings propose a correct way for computing friction forces with static simulations, thereby advancing the scientific understanding and practical applications of frictional behavior in various materials systems.

Our understanding of collective spin fluctuation in materials relies largely on Heisenberg-type spin Hamiltonians. Implicit in these spin models is the atomic moment picture wherein, transverse spin dynamics, the magnetization around an atom undergoes precessional motion as a rigid moment, which has been challenged by recent theoretical and experimental advances. To assess the validity of the atomic moment picture in spin dynamics, however, necessitates magnon wavefunctions from ab initio methods without a priori spin models. To this end, we develop an efficient model-free ab initio method for computing magnon spectrum and wavefunctions. Niu-Kleinman's adiabatic spin-wave dynamics is reformulated using linear perturbation theory into a generalized eigenvalue problem, which can be solved to produce magnon spectrum and wavefunctions without assuming atomic moments. We have implemented this method in the framework of density functional perturbation theory (DFPT). A dynamical extension of the Niu-Kleinman equation of motion is proposed to improve inaccurately predicted magnon energies owing to imperfect adiabaticity at higher energies. Based on the obtained ab initio magnon wavefunctions, we find that while the atomic moment picture is observed in typical $3d$ transition metal magnets, magnets with less localized $4d$ and $5d$ orbitals show deviations in varying degrees from this paradigm. In particular, in the so-called molecular orbital crystals, such as ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and ${\mathrm{SrRu}}_2{\mathrm{O}}_6$, the atomic moment picture becomes invalid because of orbital locking via interatomic hopping. Our results suggest that the usual spin Hamiltonian approach should be employed with extra caution. Possible experimental ramifications of the breakdown of the atomic moment picture in magnon excitation are also discussed.

The numerical study of high-dimensional frustrated quantum magnets remains a challenging problem. Here we present an extension of the pseudo-Majorana functional renormalization group to spin-1/2 XXZ-type Hamiltonians with field or magnetization along spin-$Z$ direction at finite temperature. We consider a U(1) symmetry-adapted fermionic spin representation and derive the diagrammatic framework and its renormalization group flow equations. We discuss benchmark results and application to two antiferromagnetic triangular lattice materials recently studied in experiments with applied magnetic fields: First, we numerically reproduce the magnetization data measured for ${\mathrm{CeMgAl}}_{11}{\mathrm{O}}_{19}$ confirming model parameters previously estimated from inelastic neutron spectrum in high fields. Second, we showcase the accuracy of our method by studying the thermal phase transition into the spin solid up-up-down phase of ${\mathrm{Na}}_2\mathrm{BaCo}{\left({\mathrm{PO}}_4\right)}_2$ in good agreement with experiment.

The interplay among heat, spin, and charge is the central focus in spin caloritronic research. While the longitudinal heat-to-spin conversion via the spin Seebeck effect has been intensively studied, the transverse heat-to-spin conversion via the spin Nernst effect (SNE) has not been equally explored. One major challenge is the minuscule signals generated by the SNE, which are often mixed with the background noises. In this work, we overcome this difficulty by studying the thin films of $\mathrm{N}{\mathrm{i}}_{70}\mathrm{C}{\mathrm{u}}_{30}$ alloy with not only a sizable spin Hall angle but also a large Seebeck coefficient. We observe in the $\mathrm{N}{\mathrm{i}}_{70}\mathrm{C}{\mathrm{u}}_{30}$ alloy a large spin Nernst effect with an estimated spin Nernst angle (${\theta }_{\mathrm{SN}}$) ranging from −28% to −72%. In comparison, the ${\theta }_{\mathrm{SN}}$ for Pt is −8.2%. Our ab initio calculation reveals that the large spin Nernst conductivity (${\alpha }_{\mathrm{SN}}$) in $\mathrm{N}{\mathrm{i}}_{70}\mathrm{C}{\mathrm{u}}_{30}$ is caused by the Fermi energy shift to the steepest slope of the spin Hall conductivity curve due to electron doping from 30% Cu. Our study provides critical directions in searching for materials with a large spin Nernst effect.