The emergence of relativistic pseudoparticles described by the Dirac equation in condensed-matter systems, combined with the ability to exert external potentials, highlights the importance of solving the Dirac equation in confined domains with general potentials. In this work, we introduce a finite-difference scheme to solve the Dirac equation in general two-dimensional (2D) domains of arbitrary shapes and potential configurations. These domains may be simply connected or multiply connected (with holes), and the potential can be of electrostatic type, magnetostatic type, or mass type, or their combinations. The method incorporates particle states, hole states, or Klein tunneling cases automatically, and accommodates diverse boundary conditions, such as positive infinite mass, negative infinite mass, or mixed configurations. By transforming the discretized Dirac equation into a sparse generalized eigenvalue problem, our approach efficiently addresses challenges posed by underdetermination or overdetermination, which arise from domain topology, while avoiding nonphysical solutions. This robust numerical framework offers a general and efficient tool for investigating a broad range of relativistic quantum phenomena in 2D Dirac billiards featuring complex potentials and boundaries.

Crossed Andreev reflection (CAR) is a fundamental quantum transport phenomenon that holds significant implications for spintronics and superconducting devices. However, its experimental detection and enhancement remain challenging. Recently, magnetic materials exhibiting $p$-wave magnetic ordering, distinct from conventional spin-orbit coupling, referred to as $p$-wave magnets, have attracted considerable interest. In this work, we propose a junction consisting of $p$-wave magnets and a triplet superconductor as a promising platform to enhance CAR. The setup features a triplet superconductor sandwiched between two collinear $p$-wave magnets rotated by ${180}^{\circ }$ relative to each other, allowing for precise control over transport processes. We demonstrate that CAR can dominate over electron tunneling (ET) within specific parameter regimes, such as the orientation angle of the $p$-wave magnets and their chemical potential. Enhanced CAR occurs when the constant energy contours of the two spins in the $p$-wave magnets are well separated. Furthermore, the conductivities display Fabry-Pérot-type oscillations due to interference effects, with CAR diminishing as the length of the superconductor exceeds the decay length of the wave functions. These findings underscore the potential of collinear $p$-wave magnet-superconductor junctions as a robust platform for the experimental investigation and enhancement of CAR.

This paper theoretically studies the quantum coherence of an electronic state on an artificial chiral Tomonaga-Luttinger (TL) liquid. Coulomb interaction between copropagating integer quantum Hall edge channels causes the TL liquid nature of charge excitations, resulting in the splitting of an electronic state into bosonic eigenmodes. We investigate the single-electron coherence under the splitting process by calculating the Aharonov-Bohm (AB) oscillations in an electronic Mach-Zehnder interferometer employing copropagating spin-up and spin-down edge channels as the interference paths. We investigate the voltage bias dependence of the AB oscillations at zero temperature, taking the interchannel interaction into account using the bosonization technique. The calculation results of the visibility and the phase of the AB oscillations show nonmonotonical bias dependence when the copropagating channels are electrostatically asymmetric. These observations are interpreted as the signatures of the second-order interference between the fractionalized spin excitations with different phase evolutions. We also report finite entanglement entropy between the bosonic eigenmodes split from an electron, which presents an analogy between the electron splitting in a TL liquid and the Cooper-pair splitting at a superconducting junction.

For dynamical quantum matter, many key features and properties address their steady states, such as the fundamental question of thermalization. However, it is a very concrete challenge to determine practically if a system has already relaxed and reached a steady state, as this requires an a priori understanding of steady-state properties, which must, in principle, be verified across a large set of observables individually. In this paper, we introduce a general method to quantify the relaxation of a quantum state by measuring the speed of subsystem evolution. This approach allows us to assess the relaxation of all conceivable observables, providing a general measure of relaxation without requiring any a priori knowledge.

Chiral materials lacking mirror symmetry can exhibit unconventional spin-orbit fields, including fully momentum-aligned radial Rashba fields as seen in twisted van der Waals homobilayers. We theoretically study Cooper-pair transfer in superconductor/ferromagnet/superconductor Josephson junctions with crossed (tangential and radial) interfacial Rashba fields. We find that their interplay leads to what we call the unconventional supercurrent diode effect (SDE), where supercurrent rectification occurs even with collinear (with respect to the current) barrier magnetization, not possible for conventional spin-orbit fields. This SDE, distinct from conventional Rashba-induced effects on Cooper-pair momenta, arises from the spin precession in the magnetic barrier. We propose it as a sensitive probe of chiral spin textures.

Interchannel Coulomb interaction mixes charge excitations in copropagating quantum Hall edge channels, generating coupled excitation eigenmodes propagating at different speeds. This mode transformation causes an electron state to split into fragments, corresponding to the Tomonaga-Luttinger liquid model of a chiral one-dimensional electronic system. This paper reports the coherent evolution of an electron state under the fractionalization process in a Mach-Zehnder interferometer employing copropagating spin-up and spin-down channels as the interference paths. We observe the interference visibility oscillations as a function of the voltage bias applied between the interference paths, which are attributed to the second-order interference between the fractionalized spin excitations with different phase evolutions. This observation contrasts with the single-particle picture that predicts only the first-order interference, reflecting the phase evolution of a spin-up and spin-down superposition state during the one-way transport. The second-order interference manifests the coherent splitting of the superposition state to the mutually independent fast and slow excitations. Our observation offers the fractionalization process as a novel way to encode an electron spin state to spatially separated fragments.

In this study, we investigate the spin and orbital densities induced by magnetization dynamics in a planar bilayer heterostructure. To do this, we employed a theory of adiabatic pumping using the Keldysh formalism and Wigner expansion. We first conduct simulations on a model system to determine the parameters that control the spin and orbital pumping into an adjacent nonmagnetic metal. We conclude that, in principle, the orbital pumping can be as significant as spin pumping when the spin-orbit coupling is present in the ferromagnet. We extend the study to realistic heterostructures involving heavy metals (W, Pt, Au) and light metals (Ti, Cu) by using first-principles calculations. We demonstrate that orbital pumping is favored in metals with $d$ states close to the Fermi level, such as Ti, Pt, and W, but is quenched in materials lacking such states, such as Cu and Au. Orbital injection is also favored in materials with strong spin-orbit coupling, leading to large orbital pumping in Ni/(Pt, W) bilayers.

The Berry curvature has been widely recognized as the intrinsic mechanism of the anomalous Hall effect (AHE) in ferromagnetic metals. However, the Berry curvature induced by the interplay between ferromagnetism and topological structure has been largely unexplored. In this study, we focus on ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ (FGT) nanoflakes, which has been proposed as a candidate of topological nodal-line semimetals. The angular dependence of anomalous Hall resistance shows an anomalous angle-independent Hall resistance up to ∼85 °, violating the conventional Stoner-Wohlfarth rule. This phenomenon indicates that Berry curvature induced by the crystalline symmetries dominates the intrinsic mechanism of AHE. Furthermore, through making the comparison of AHE in ${\mathrm{SrRuO}}_3$ and FGT, we find that the Berry curvature in FGT is topologically protected, which is distinct from the strong dependence of magnetization in ${\mathrm{SrRuO}}_3$. Our findings illustrate a rare example to exhibit the significant implications of topological structure to AHE.

Even in the noninteracting limit, electrons on different Bloch bands of a multiband system do not move as if they are oblivious to the presence of one another. Instead, they move in concert by virtue of a non-Abelian interband Berry connection. While the impact of this quantum geometric attribute manifests most famously through the Hall response of topological bands, the geometric effects in superconductors have attracted significant recent attention. In particular, much has been discussed about the quantum-metric-induced superfluid weight (SW) in flatband superconductors. In this study, we revisit the geometric SW in generic multiband superconductors and trace its origin to a series of microscopic processes. We separately derive the SW of models containing only intraband Cooper pairing and those involving interband pairing. Two classes of processes enabled by the so-called interband velocity (or the closely related interband Berry connection) are identified: One resembles the transfer of Cooper pairs between different bands, and the other corresponds to virtual single-electron back-and-forth tunneling between the bands. The former contribution manifests as effective Josephson coupling between the multiband superconducting order parameters, while the latter constitutes the only source of SW for a superconducting flatband well isolated from other bands. We further numerically evaluate the SW of a simple two-band superconductor with trivial band topology, showcasing how the geometric contribution is sensitive to the details of the multiband pairing configuration. In particular, we highlight an intriguing scenario of negative SW, which may pave the way for the formation of novel pair density wave order. Our study provides deeper and more intuitive insight into the origin and nature of the SW induced by the quantum geometry of paired Bloch states.

Superconductivity arises when electrons form Cooper pairs with phase coherence. In contrast, a lack of phase coherence in Cooper pairs can lead to an uncondensed metallic ground state known as the Bose metal state. In this paper, we investigate an attractively interacting fermionic system with nearest-neighbor hopping (t) and next-nearest-neighbor hopping ($t^{\prime }$) anisotropy between two species of spins in a two-dimensional lattice. Utilizing the constrained path quantum Monte Carlo method, we demonstrate the existence of a $d_{x^2-y^2}$-wave Cooper pair Bose metal (CPBM) phase with $t^{\prime }/t>0.7$. The CPBM phase exhibits a domelike structure in the phase diagram of filling $n\sim 0.65$, with the maximal region around an optimal $t^{\prime }/t\sim 0.2$, suggesting that an appropriate value of $t^{\prime }$ facilitates the formation of the Bose metal. Furthermore, we find that a Bose metal formed by fermions with a closed Fermi surface confirms that the crucial condition for this exotic phenomenon is primarily the anisotropy of the Fermi surface rather than its topology. Our finding of the $d_{x^2-y^2}$-wave CPBM demonstrates the same pairing symmetry as the pseudogap behavior in cuprates, and its experimental realization in ultracold atom systems is also feasible.

The relaxation and mechanical properties of metastable materials are strongly correlated by their thermodynamic stability. However, such correlation has not been fully explored in metallic glasses. Progress in atomistic simulations has been limited by timescale constraints, preventing the reproduction of conditions observed in experimentally studied metallic glass samples. To address this challenge, we employ a hybrid molecular dynamics/Monte Carlo approach, which can generate $\mathrm{C}{\mathrm{u}}_{50}\mathrm{Z}{\mathrm{r}}_{50}$ metallic glasses with low-energy states that closely correspond to experimental conditions. It is found that the large variations in the energy states lead to dramatic differences in both the microscopic shear transformation and the macroscopic shear band behaviors. Thermodynamically, these low-energy state metallic glasses exhibit low vibrational and configurational entropy. Kinetically, these low-energy state metallic glasses are characterized by local atom arrangement with high activation energies, which impede shear transformation and promote strain localization in shear bands. The correlation between mechanical properties and thermodynamic stability is analyzed through entropy, boson peak, activation energy, and structural features in metallic glasses, providing insights into their complex behavior.

We theoretically study Rashba-Edelstein magnetoresistance (REMR) in a two-dimensional electron gas (2DEG) system with Rashba and Dresselhaus spin-orbit interactions. We consider a microscopic model of a junction system composed of a ferromagnetic insulator and a 2DEG, and derive analytic expressions for the spin and current densities in the 2DEG using the Boltzmann equation, while taking into account dynamical contributions from magnons. Our findings reveal that the sign of the REMR varies depending on the type of interface. We also discuss the experimental relevance of our results.

${\mathrm{LaRu}}_3{\mathrm{Si}}_2$ is of current research interest as a kagome metal with a superconducting transition temperature, $T_c\sim 7$ K, and higher-temperature charge density wave orders. Here we report on electrical transport and x-ray diffraction measurements on ${\mathrm{LaRu}}_3{\mathrm{Si}}_2$ under pressure up to 65 GPa and 35 GPa, respectively. The superconducting transition temperature $T_c$ first gets slightly enhanced and reaches a maximum $\sim 8.7$ K at $\sim 8.5$ GPa. With further applied pressure, $T_c$ is initially gradually suppressed, then more rapidly suppressed, followed by gradual suppression, revealing a superconducting dome. Two possible pressure-induced structural phase transitions are also observed at room temperature, from the original hexagonal phase to another hexagonal structure above $\sim 11.5$ GPa, and further to a structure with lower symmetry above $\sim 23.5$ GPa. These transition pressures roughly correlate with features found in our pressure-dependent transport data.

Demonstrating the braiding of Majorana modes remains an unsolved problem in condensed matter physics because of platform-specific challenges. In this paper, we propose a two-dimensional (2D) kagome lattice with $s$-wave and $d$-wave superconductors as an effective platform for manipulating and braiding Majorana modes. Our findings reveal that the topological phase is highly sensitive to the application of uniaxial strain or variations in chemical potential, enabling real-space manipulation of Majorana modes. In proximity to an $s$-wave superconductor, we design the kagome lattice with only $C/B$-type sublattice terminations, and exchange the position of Majorana corner modes (MCMs) along the boundary. We further develop a porous kagome lattice to host and braid multiple MCMs, as experimentally measurable braiding requires at least four Majorana modes. When substituting the $s$-wave superconductor with a $d$-wave superconductor, we observe the emergence of Majorana Kramers pairs (MKPs). Importantly, the positions of the Dirac mass domain walls that bind the MKPs are sensitively dependent on the local boundary topology. By building a kagome lattice featuring solely $C/B$-type sublattice terminations and manipulating the local boundary topology, we can therefore exchange the positions of MKPs through applying inhomogeneous chemical potential and/or nonuniform uniaxial strain.

Time-reversal-odd ($\mathcal{T}$-odd) second-order nonlinear current response has been theoretically proposed and experimentally confirmed recently. However, the role of disorder scattering in the response, especially whether it contributes to the ${\sigma }_{xx}$-independent term, has not been clarified. Here, we derive a general scaling law for this effect, which accounts for multiple scattering sources. We show that the nonlinear conductivity is generally a quartic function in ${\sigma }_{xx}$. The microscopic mechanisms underlying each scaling term are revealed, which include multiple previously unknown extrinsic processes unique to $\mathcal{T}$-odd nonlinear transport. Besides intrinsic contribution, we find that extrinsic contributions also enter the zeroth-order term, and their values can be comparable to or even larger than the intrinsic one. This offers a solution to the conflicting interpretations of recent experiments. In addition, cubic and quartic terms must involve skew scattering, and they signal competition between at least two scattering sources. Our finding reveals the significant role of disorder scattering in $\mathcal{T}$-odd nonlinear transport, and it establishes a foundation for analyzing experimental results.

LX centers are a recently discovered class of impurity centers in diamonds, which are characterized by nearly phononfree, spectral narrowband, and intense fluorescence at room temperature. Such a set of properties pave the way for a variety of applications, including sensing and single-photon emission. The latter requires a detailed study of photophysical processes of single emitters, which is the focus of this paper. The study of the luminescence dynamics of single LX centers in microdiamonds, synthesized by the high pressure-high temperature method, is performed by means of second-order cross-correlation function ($g^{\left(2\right)}$) analysis. Even though the blinking is not observed directly in the measurements, the presence of photon bunching indicates that the fluorescence of a single emitter is intermittent at microsecond scale. The three-level system that is commonly used to describe intermittency of dye molecules is not consistent with the observed power dependences. We suggest a four-level energy system model with two metastable states to describe the results and perform numerical simulations to validate the model. Finally, we discuss the four-level model in the form of fluctuations of photophysical parameters.

We theoretically investigate valley filtering in pristine graphene under irradiation by a bicircular counterrotating laser field. We find that the relative phase between the two counterrotating fields controls quasienergy states and Floquet band occupations in the valleys, enabling highly efficient valley-selective currents and transport responses via an all-optical approach. Varying the relative phase allows us to block contributions from one valley while enabling currents from the opposite valley. For experimental realization, we propose a valley valve configuration involving two graphene nanoribbons irradiated by bicircular counterrotating laser drives with a relative phase shift. Our findings remain robust against moderate disorder and modest changes in laser parameters, enabling the way for practical light-based valleytronics devices.

In this study, we investigate the emergence of a topological non-Fermi liquid (NFL) phase in a modified Su-Schrieffer-Heeger (SSH) chain model subjected to long-range interactions characterized by the Hatsugai-Kohmoto (HK) model. While Fermi liquid theory has been instrumental in understanding low-temperature properties of metals, it fails to account for the complex behaviors exhibited by strongly correlated systems, where interactions lead to emergent phenomena such as non-Fermi liquid behavior. Our analysis reveals that the SSH-HK model supports a rich ground state phase diagram, exhibiting distinct NFL phases marked by many-body Zak phases of $2\pi$ and 0, corresponding to topological and trivial NFL states, respectively. We demonstrate that the topological NFL state manifests unique electronic polarization characteristics akin to those in the noninteracting SSH model. Through exact diagonalization of the interacting SSH-HK Hamiltonian, we explore the spectral functions and density of states, revealing significant departures from traditional quasiparticle behavior in various particle number sectors. Our findings extend the understanding of topological non-Fermi liquids and their potential implications for high-temperature superconductivity and other correlated electron systems, highlighting the intricate interplay between topology and strong electron correlations.

The minimal coupling of strain to Dirac and Weyl semimetals, and its modeling as a pseudogauge field has been extensively studied, resulting in several proposed topological transport signatures. In this work, we study the effects of strain on higher winding number Weyl semimetals and show that strain is not a pseudogauge field for any winding number larger than one. We focus on the double-Weyl semimetal as an illustrative example to show that the application of strain splits the higher winding number Weyl nodes and produces an anisotropic Fermi surface. Specifically, the Fermi surface of the double-Weyl semimetal acquires nematic order. By extending chiral kinetic theory for such nematic fields, we determine the effective gauge fields acting on the system and show how strain induces anisotropy and affects the geometry of the semiclassical phase space of the double-Weyl semimetal. Further, the strain-induced deformation of the Weyl nodes results in transport signatures related to the covariant coupling of the strain tensor to the geometric tensor associated with the Weyl nodes giving rise to strain-dependent dissipative corrections to the longitudinal as well as the Hall conductance. Thus, by extension, we show that in multi-Weyl semimetals, strain produces geometric signatures rather than topological signatures. Further, we highlight that the most general way to view strain is as a symmetry-breaking field rather than a pseudogauge field.