We theoretically investigate the consequences of proximity-induced conventional superconductivity in metals that break time-reversal and inversion symmetries through their energy dispersion. We discover behaviors impossible in an isolated superconductor such as an equilibrium supercurrent that apparently violates a no-go theorem and, at suitable topological defects, nonconservation of electric charge reminiscent of the chiral anomaly. The equilibrium supercurrent is expected to be trainable by a helical electromagnetic field in the normal state. Remarkably, if the band asymmetry exceeds the critical current of the parent superconductor in appropriate units, we predict a perfect superconducting diode effect with diode coefficient unity. We propose toroidal metals such as ${\mathrm{UNi}}_4\mathrm{B}$ and metals with directional scalar spin chiral order as potential platforms.

A full picture of dynamic properties through diverse glasses remains a great challenge in glassy physics. The kinetic fragility is introduced to classify glass-forming liquids and its relevance to glassy properties is expected to outline the family characteristics of glasses. In this paper we propose a distinguishable-particle glassy model with simple pair interactions. This model sensitively tunes the kinetic fragility in an ultrawide range covering real glassy materials. Using the model, we study the decoupling of self-diffusion and structural relaxation time close to the glass transition, and present the fragility dependence of the fractional Stokes-Einstein relation. The results support the existence of a decoupling limit, which corresponds to a possible lower bound of the fractional Stokes-Einstein exponent in very fragile glass-forming liquids. The microscopic mechanism of the fractional Stokes-Einstein relation is verified by using the hopping-dynamics approach associated with single particles.

Recently, a concept of generalized multifractality, which characterizes fluctuations and correlations of critical eigenstates, was introduced and explored for all 10 symmetry classes of disordered systems. Here, by using the nonlinear sigma-model ($\mathrm{NL}\sigma \mathrm{M}$) field theory, we extend the theory of generalized multifractality to boundaries of systems at criticality. Our numerical simulations on two-dimensional systems of symmetry classes A, C, and AII fully confirm the analytical predictions of pure-scaling observables and Weyl symmetry relations between critical exponents of surface generalized multifractality. This demonstrates the validity of the $\mathrm{NL}\sigma \mathrm{M}$ for the description of Anderson-localization critical phenomena, not only in the bulk but also on the boundary. The critical exponents strongly violate generalized parabolicity, in analogy with earlier results for the bulk, corroborating the conclusion that the considered Anderson-localization critical points are not described by conformal field theories. We further derive relations between generalized surface multifractal spectra and linear combinations of Lyapunov exponents of a strip in quasi-one-dimensional geometry, which hold under the assumption of invariance with respect to a logarithmic conformal map. Our numerics demonstrate that these relations hold with an excellent accuracy. Taken together, our results indicate an intriguing situation: the conformal invariance is broken but holds partially at critical points of Anderson localization.

Motivated by the observation and prediction of clustering behavior for impurities substituted into the host lattice of a real material and the dramatic impact this can have on electronic properties, we develop a simple approach to describe such an effect via the electron self-energy. We employ a disorder-averaged $T$-matrix expansion taken to second order, which we modify to include a clustering probability parameter. This approach circumvents the need for specific cluster probability distributions, simplifying greatly the analysis of clustered impurities. To gain analytical insights, we study a nearest-neighbor square lattice tight-binding Hamiltonian with clustered impurity substitutions to investigate clustering of off-diagonal hopping impurities. We find that our $T$-matrix approach is in excellent agreement with exact numerical results from a tight-binding computation performed with the kwant package. We observe a variety of interesting impurity clustering-induced effects in the self-energy such as the suppression of quasiparticle lifetimes at certain momenta and an increase in localization, as indicated by the inverse participation ratio. The kwant results are reproduced in our modified $T$-matrix approach. In addition, our method allows for a full analytical treatment of clustering effects which can aid in physical insight.

We study the Wannier-Stark (WS) localization in one-dimensional amplitude-chirped lattices with the $j\mathrm{th}$ on-site potential modulated by a function $Fjcos\left(2\pi \alpha j\right)$, where $F$ is the external field with a period determined by $\alpha =p/q$ ($p$ and $q$ are coprime integers). In the Hermitian (or non-Hermitian) systems with real (or imaginary) fields, we can obtain real (or imaginary) WS ladders in the eigenenergy spectrum. In most cases with $q\ge 2$, there are multiple WS ladders with all the eigenstates localized in the strong field limit. However, in the lattices with $q=4$, the energy-dependent localization phenomenon emerges due to the presence of both spatially periodic and linearly increasing behaviors in the on-site potential. About half the number of eigenstates are gathered at the band center and can extend over a wide region or even the full range of the lattice, even when the field becomes very strong. Moreover, in the non-Hermitian lattices with odd $q$, some of the WS ladders become doubly degenerate, where the eigenstates are evenly distributed at two neighboring sites in a wide regime of field strength. Our work opens an avenue for exploring WS localization in both Hermitian and non-Hermitian amplitude-chirped lattices.

We study the asymptotic bipartite entanglement entropy of the quantum trajectories of a free-fermionic system, when subject to a continuous nonlocal monitoring. The measurements are described by Gaussian-preserving two-point operators, whose strength decays as a power law with exponent $\alpha$. Different behaviors of the entanglement entropy with the system size emerge: for $\alpha$ below a given threshold value a volume-law behavior sets in, while for larger $\alpha$ we observe a transition from subvolume to area law, whose exact location depends on the measurements rate and on the presence of a Hamiltonian dynamics. We also consider the expectation probability distribution of the measurement operators, and find that this distribution features a transition from a unimodal to a bimodal shape. We discuss the possible connections between this qualitative change of the distribution and the entanglement transition points.

A composite pairing structure of the superconducting state is revealed by a density matrix renormalization group study in a two-leg $t\text{−}J$ model. The pairing order parameter is composed of a pairing amplitude and a phase factor, in which the latter explicitly depends on the spin background with an analytic form. Such a stringlike phase factor is responsible for a pair density wave (PDW) induced by spin polarization $m$ with a wave vector $Q_{\mathrm{PDW}}=2\pi m$. By contrast, the pairing amplitude remains smooth, unchanged by the PDW. Moreover, local spin polarization can give rise to a sign change of the order parameter across the local defect. Unlike in an Fulde-Ferrell-Larkin-Ovchinnikov state, the nonlocal phase factor here plays the role as the new order parameter characterizing the PDW, whose origin can be traced back to the essential sign structure of the doped Mott insulator.

Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure of strongly correlated materials. In this paper, Coulomb integrals are analyzed by considering both the point-group symmetry of the site occupied by the atom in the crystal or molecule and the permutation symmetries of the orbitals in the integrals. In particular, the case where one-electron orbitals form the basis of a general (i.e., a real, complex, or pseudoreal) irreducible representation is considered. Explicit formulas are provided to calculate all integrals of the interaction tensor in terms of a minimum set of independent ones. The effect of a symmetry breaking is also investigated by describing Coulomb integrals of a group in terms of those of one of its subgroups. We developed the specific example of $\mathrm{O}\left(3\right)$ as the larger group which can therefore be used to quantify the deviation of a specific system from the spherical symmetry. Possible applications of the presented framework include the calculation of solid-state and molecular spectroscopies via multiplet techniques, dynamical mean-field theory, or the $GW$ approximation.

We propose to realize two-dimensional superstructures of chiral topological superconductors based on marginally twisted bilayers of transition metal dichalcogenides in proximity to a conventional $s$-wave superconductor. Majorana fermions arise at the domain boundaries of the $AB$ and $A^{\prime }{B}^{\prime }$ stacking domains as a result of a sign flip across the domain wall in a Rashba spin-orbit coupling coefficient at the valence band edge. Unlike previous models that only allow for one Majorana per boundary, each domain wall can host two helical Majorana edge states with the same Majorana polarization, preventing hybridization. This offers a promising alternative platform for studying Majorana physics.

We analytically study nonlinear quasimonochromatic plasma waves in a two-dimensional (2D) electron system (ES) set between the two metal electrodes (gates). We derive a nonlinear Schrödinger equation for a slow-varying envelope to describe the waves. We find it to be of either focusing or defocusing type depending on the parameter $qd$, where $q$ is the carrier wave vector and $d$ is the distance between the 2DES and the gates. When $qd<1.61$, we have the defocusing-type equation with the solutions in the form of dark plasma solitons appearing against the background of the stable plane waves. Conversely, for $qd>1.61$, the focusing-type equation has the solutions in the form of bright solitons and the plane waves are unstable. We also address the appearance of the simplest type of breathers in the latter case. A detailed description of the resultant nonlinear waves is given based on the parameters of the two-dimensional electron system.

We model the influence of an in-plane magnetic field on the orbital motion of electrons in rhombohedral graphene multilayers. For zero field, the low-energy band structure includes a pair of flat bands near zero energy, which are localized on the surface layers of a finite thin film. For finite field, we find that the zero-energy bands persist and that level bifurcations occur at energies determined by the component of the in-plane wave vector $q$ that is parallel to the external field. The occurrence of level bifurcations is explained by invoking semiclassical quantization of the zero-field Fermi surface of rhombohedral graphite. We find parameter regions with a single isoenergetic contour of Berry phase zero corresponding to a conventional Landau level spectrum and regions with two isoenergetic contours, each of Berry phase $\pi$, corresponding to a Dirac-like spectrum of levels. We write down an analogous one-dimensional tight-binding model and relate the persistence of the zero-energy bands in large magnetic fields to a soliton texture supporting zero-energy states in the Su-Schrieffer-Heeger model. We show that different states contributing to the zero-energy flat bands in rhombohedral graphene multilayers in a large field, as determined by the wave vector $q$, are localized on different bulk layers of the system, not just the surfaces.

Bound states in the continuum (BICs) and long-lived resonances have become a unique way to produce the extreme localization of light waves. In this paper, we present a theoretical demonstration of BICs and long-lived resonances in photonic comblike structures with two semi-infinite leads, together with their existence conditions. The comb structure is composed of connected guides of length $L$. The BICs correspond to localized resonances of infinite lifetime inside the comb, without any leakage into the surrounding leads. When BICs exist within state continua, they induce long-lived resonances for specific values of some modified lengths of the guides constituting the comb structure. This enables to regulate these resonances by means of these lengths. The obtained results take due account of the state number conservation between the final system and the reference one constituted by the independent comb and semi-infinite leads. This conservation rule enables to find all the states of the final system and among them the bound in continuum ones. In addition, we present a comb structure with highly directional outputs through two different lines. In each output line two different long-lived resonances enable to transmit two different signals. This system enables to demultiplex two different signals through each of two output lines. The analytical results are obtained by means of the Green's function technique. The structures and the long-lived resonances presented in this paper may have potential applications due to their high sensitivities to weak perturbations, in particular in filtering, sensing, and communication technology improvements.

We compute from first principles the electronic, vibrational, and transport properties of four known MXenes: ${\mathrm{Ti}}_3{\mathrm{C}}_2, {\mathrm{Ti}}_3{\mathrm{C}}_2{\mathrm{F}}_2, {\mathrm{Ti}}_3{\mathrm{C}}_2{\left(\mathrm{OH}\right)}_2$, and ${\mathrm{Ti}}_2{\mathrm{CF}}_2$. We study the effect of different surface terminations and monosheet thickness on the electrical conductivity, and show that the changes in conductivity can be explained by the squared velocity density of the electronic state, as well as their phonon scattering lifetime. We also compare the solution of the iterative Boltzmann transport equation (IBTE) to different linearized solutions, namely, the self-energy relaxation time approximation (SERTA) and the momentum relaxation time approximation (MRTA), and we show that the SERTA significantly underestimates the electrical conductivity while the MRTA yields results in better agreement with the IBTE. The computed monolayer conductivity at 300 K is in reasonable agreement with reported experimental measurements.

The Thouless charge pumping protocol provides an effective route for realizing topological particle transport. To date, the first-order and higher-order topological pumps, exhibiting transitions of edge-bulk-edge and corner-bulk-corner states, respectively, are observed in a variety of experimental platforms. Here, we propose the concept of a hybrid-order topological pump that involves a transition of bulk, edge, and corner states simultaneously. More specifically, we consider a Kekulé-textured graphene lattice that features a tunable phase parameter. The finite sample of zigzag boundaries, where the corner configuration is abnormal and inaccessible by repeating unit cells, hosts topological responses at both the edges and corners. The former is protected by a nonzero winding number, while the latter can be explained by a nontrivial vector Chern number. Using our skillful acoustic experiments, we verify these nontrivial boundary landmarks and visualize the consequent hybrid-order topological pump process directly. This work deepens our understanding of higher-order topological phases and broadens the scope of topological pumps.

Van der Waals heterostructures consisting of Bernal bilayer graphene (BLG) and hexagonal boron nitride (hBN) are investigated. By performing first-principles calculations, we capture the essential BLG band structure features for several stacking and encapsulation scenarios. A low-energy model Hamiltonian, comprising orbital and spin-orbit coupling (SOC) terms, is employed to reproduce the hBN-modified BLG dispersion, spin splittings, and spin expectation values. Most important, the hBN layers open an orbital gap in the BLG spectrum, which can range from zero to tens of meV, depending on the precise stacking arrangement of the individual atoms. Therefore, large local band gap variations may arise in experimentally relevant moiré structures. Moreover, the SOC parameters are small (few to tens of $\mu \mathrm{eV}$), just as in bare BLG, but are markedly proximity modified by the hBN layers. Especially when BLG is encapsulated by monolayers of hBN, such that inversion symmetry is restored, the orbital gap and spin splittings of the bands vanish. In addition, we show that a transverse electric field mainly modifies the potential difference between the graphene layers, which perfectly correlates with the orbital gap for fields up to about 1 V/nm. Moreover, the layer-resolved Rashba couplings are tunable by $\sim 5\mu \mathrm{eV}\mathrm{per}\mathrm{V}/\mathrm{nm}$. Finally, by investigating twisted BLG/hBN structures, with twist angles between $6^{\circ }$–${20}^{\circ }$, we find that the global band gap increases linearly with the twist angle. The extrapolated $0^{\circ }$ band gap is about 23 meV and results roughly from the average of the stacking-dependent local band gaps. Our investigations give insights into proximity spin physics of hBN/BLG heterostructures, which should be useful for interpreting experiments on extended as well as confined (quantum dot) systems.

In this study, we propose the concept of harnessing quantum coherence to control electron transport in a many-body system. Combining an open quantum system technique based on Hubbard operators, we show that many-body coherence can eliminate the well-known Coulomb staircase and cause strong negative differential resistance. To explore the mechanism, we analytically derive the current-coherence relationship in the zero electron-phonon coupling limit. Furthermore, by incorporating a gate field, we demonstrate the possibility of constructing a coherence-controlled transistor. This development opens up a new direction for exploring quantum electronic devices based on many-body coherence.

High-pressure electrides have opened a promising path to high-temperature superconductors and attracted considerable attention. However, the origins of superconductivity from discrepant sources remain puzzling. In this study, we propose a different type of $p$-orbital-like electride state to shed light on the causality that induces high $T_c$. Taking our predicted $R-3\mathrm{m}$ phase in ${\mathrm{Li}}_6\mathrm{P}$ as a representative, with a high $T_c$ of 41.36 K, our first-principles studies unveil that the $p$-orbital-like electride states play a dominant role in $T_c$ by softening the acoustic phonon and forming itinerantly hybridized $p$-orbital-like (IHP) electride-states-dependent phonon-coupled bands, which are corroborated by hole doping. Compared to the nonitinerant $s$-orbital-like electride states with low $T_c$, the IHP electride states exhibit greater freedom of orbital multiplicity and hence a higher propensity to form Cooper pairs, promoting electron-phonon coupling (EPC), and demonstrating the derivation of differential $T_c\mathrm{s}$. Of particular note, the IHP electride states originate from the atypical nature of concurrent oxidization states, characterized by electrons donated from electronegative phosphorus and electropositive lithium. Our finding provides crucial insights into the role of electride states in EPC, elucidates the origin of superconductivity, and identifies the characteristics of high-$T_c$ electrides, with profound implications for exploring this class of multifunctional superconductors.

Topological surface states of Bi-doped ${\mathrm{PbSb}}_2{\mathrm{Te}}_4 \left[\mathrm{Pb}{\left({\mathrm{Bi}}_{0.20}{\mathrm{Sb}}_{0.80}\right)}_2{\mathrm{Te}}_4\right]$ are investigated through analyses of quasiparticle interference (QPI) patterns observed by scanning tunneling microscopy. Interpretation of the experimental QPI patterns in the reciprocal space is achieved by numerical QPI simulations using two types of surface density of states produced by density functional theory calculations or the Fu's surface state model [Phys. Rev. Lett. 103, 266801 (2009)]. We found that the Dirac point (DP) of the surface state appears in the bulk band gap of this material and, with the energy being away from the DP, the isoenergy contour of the surface state is substantially deformed or separated into segments due to hybridization with bulk electronic states. These findings provide a more accurate picture of topological surface states, especially at energies away from the DP, providing valuable insight into the electronic properties of topological insulators.

The phenomenon of self-assembly of constituent elements to form molecules at low temperatures appears ubiquitously in transition metal compounds with orbital degrees of freedom. Recent progress in local structure studies using synchrotron radiation x rays is shifting the interest in structural studies in such molecule-forming systems from the low-temperature ordered phase to the short-range order that appears like a precursor at high temperatures. In this study, we discuss both experimentally and theoretically the relationship between the trimer structure that appears in the layered $\mathrm{LiV}{X}_2(X$ = O, S, Se) system with a two-dimensional triangular lattice of vanadium and the zigzag chainlike local structure that appears near the phase transition boundary where molecular formation occurs. The vanadium trimerization that persistently appears in both low-temperature phases of ${\mathrm{LiVO}}_2$ and ${\mathrm{LiVS}}_2$ disappears in ${\mathrm{LiVSe}}_2$, and a regular triangular lattice is thought to be realized in ${\mathrm{LiVSe}}_2$, but this study reveals that the zigzag chain local distortion appears with a finite correlation length. These zigzag chain state local distortions are similar to the motif of local distortions in the high-temperature phase of ${\mathrm{LiVS}}_2$, indicating that the local distortions are persistent away from the trimer phase transition boundary. On the other hand, it is concluded that the zigzag chain order appearing in ${\mathrm{LiVSe}}_2$ is more stable than that in ${\mathrm{LiVS}}_2$ in terms of the temperature variation of atomic displacement and correlation length. The zigzag chain order is considered to be competitive with the trimer order appearing in the $\mathrm{LiV}{X}_2$ system. In this paper, we discuss the similarities and differences between the parameters that stabilize these electronic phases and the local distortions that appear in other molecular formation systems.

Certain point defects in solids can efficiently be used as qubits for applications in quantum technology. They have spin states that are initializable, readable, robust, and can be manipulated optically. New theoretical methods are needed to find the best host materials and defect configurations. Most methods proposed so far rely either on cluster models or restrict the many-body treatment of the defects to a subspace of single-particle orbitals. We explore best practices and theory for the use of quantum Monte Carlo to predict the excitation spectra for spin defects, by using the negatively charged nitrogen vacancy (${\mathrm{NV}}^{-}$) center in diamond as a test system. Quantum Monte Carlo can be used to explicitly simulate electronic correlations with larger systems and sets of orbitals than previous methods due to favorable scaling with respect to system size and computing power. We consider different trial wave functions for variational and diffusion Monte Carlo methods, explore the nodal surface errors of the ground and excited state wave functions, and study whether the variational principle holds for the excited states. We compute the vertical excitation energies in different simulation cell sizes and extrapolate to infinite system size, and include backflow corrections to the extrapolated energies. The final results for vertical excitation energies are found to overestimate the experimental estimates, but the triplet-to-triplet and singlet-to-singlet transitions are accurate against experiment. Finally, we list further developments for QMC needed to address the problem of accurately predicting structural and spin properties of the solid-state defects.