Topological superconductors support Majorana modes, which are quasiparticles that are their own antiparticles and obey non-Abelian statistics in which successive exchanges of particles do not always commute. Here we investigate whether a two-dimensional superconductor with ordinary $s$-wave pairing can be rendered topological by the application of a strong magnetic field. To address this, we obtain the self-consistent solutions to the mean-field Bogoliubov–de Gennes equations, which are a large set of nonlinearly coupled equations, for electrons moving on a lattice. We find that the topological “quantum Hall superconductivity” is facilitated by a combination of spin-orbit coupling, which locks an electron's spin to its momentum as it moves through a material, and a coupling to an external periodic potential which gives a dispersion to the Landau levels and also distorts the Abrikosov lattice. We find that, for a range of parameters, the Landau levels broadened by the external periodic potential support topological superconductivity, which is typically accompanied by a lattice of “giant” $h/e$ vortices as opposed to the familiar lattice of $h/2e$ Abrikosov vortices. In the presence of a periodic potential, we find it necessary to use an ansatz for the pairing potential of the form $\mathrm{\Delta }\left(\mathit{r}\right)e^{i2\mathit{Q}·\mathit{r}}$ where $\mathrm{\Delta }\left(\mathit{r}\right)$ has a periodicity commensurate with the periodic potential. However, despite this form of the pairing potential, the current in the ground state is zero. In the region of ordinary superconductivity, we typically find a lattice of dimers of $h/2e$ vortices. Our work suggests a realistic proposal for achieving topological superconductivity, as well as a helical order parameter and unusual Abrikosov lattices.

We propose a quantum Monte Carlo algorithm capable of simulating the Bose-Hubbard model on arbitrary graphs, obviating the need for devising lattice-specific updates for different input graphs. We show that with our method, which is based on the recently introduced permutation matrix representation quantum Monte Carlo [Gupta, Albash, and Hen, J. Stat. Mech. (2020) 073105], the problem of adapting the simulation to a given geometry amounts to generating a cycle basis for the graph on which the model is defined, a procedure that can be carried out efficiently and in an automated manner. To showcase the versatility of our approach, we provide simulation results for Bose-Hubbard models defined on two-dimensional lattices as well as on a number of random graphs.

Cavity materials are a frontier to investigate the role of light-matter interactions on the properties of electronic phases of matter. In this work, we raise a fundamental question: can nonlocal interactions mediated by cavity photons destabilize a topological electronic phase? We investigate this question by characterizing entanglement, energy spectrum, and correlation functions of the topological Su-Schrieffer-Heeger chain interacting with an optical cavity mode. Employing density-matrix renormalization group and exact diagonalization, we demonstrate the stability of the edge state and establish an area law scaling for the ground state entanglement entropy, despite long-range correlations induced by light-matter interactions. These features are linked to gauge invariance and the scaling of virtual photon excitations entangled with matter, effectively computed in a low-dimensional Krylov subspace of the full Hilbert space. This work provides a framework for characterizing novel equilibrium phenomena in topological cavity materials.

We study a ${\mathbb{Z}}_3$ Kitaev model on the honeycomb lattice with nearest neighbor interactions. Based on matrix product state simulations and symmetry considerations, we find evidence that, with ferromagnetic isotropic couplings, the model realizes a chiral spin liquid, characterized by a possible $\mathrm{U}{\left(1\right)}_{12}$ chiral topological order. This is supported by simulations on both cylinder and strip geometries. On infinitely long cylinders with various widths, scaling analysis of entanglement entropy and maximal correlation length suggests that the model has a gapped two-dimensional bulk. The topological entanglement entropy is extracted and found to be in agreement with the $\mathrm{U}{\left(1\right)}_{12}$ topological order. On infinitely long strips with moderate widths, we find the model is critical with a central charge consistent with the chiral edge theory of the $\mathrm{U}{\left(1\right)}_{12}$ topological phase. We conclude by discussing several open questions.

We study the effect of disorder on $Z_2$ quantum spin liquids with a Majorana Fermi line (respectively a surface in three dimensions), and we show that depending on the symmetries that are preserved on average, qualitatively different scenarios will occur. In particular, we identify the relevant non-Hermitian symmetries for which disorder will effectively split the Fermi line into two exceptional lines, with $\mathrm{Re}\left(E\right)=0$ states filling the area in between. We demonstrate the different scenarios using both toy models as well as large-scale numerical simulations.

A comprehensive understanding of phonon transport is essential to develop effective solutions for heat dissipation. Gallium nitride (GaN), a representative of third-generation power semiconductors, has been extensively studied regarding its thermodynamics and lattice dynamics. However, the temperature-dependent phonon properties, especially the anharmonicity at high temperatures, are poorly understood. Here, by combining inelastic neutron scattering (INS) experiments and calculations including the temperature effect based on machine learning potentials, we report the high-order phonon anharmonicity in GaN over a wide temperature range. Our calculations agree well with the experimental phonon dispersion, density of states and entropy, underlining the significance of anharmonicity of GaN at elevated temperatures. Moreover, considering the four-phonon processes, the calculated thermal conductivity is suppressed by 20%, and the anisotropy is also reduced gradually with increasing temperature. Such behavior arises mainly from the large four-phonon scattering channels between 20 and 30 meV, where the critical scattering rule for the three-phonon process is largely restricted at high temperatures. Our study highlights the importance of high-order phonon anharmonicity for thermal transport in GaN and provides a theoretical reference for thermal management in other related semiconductors.

We investigate the energy spectrum of a single- and two-electron quantum dot (QD) embedded in two-dimensional electron gas at the interface between ${\mathrm{SrTiO}}_3$ and ${\mathrm{LaAlO}}_3$, in the presence of the external magnetic field. For this purpose, the three-band model of $3d$ electrons defined on the square lattice of Ti ions was utilized. We demonstrate that, for the weak parabolic confinement potential, the low-energy spectrum is sufficiently well described by the effective Hamiltonian reduced to the one $d_{xy}$ orbital with the spin-orbit interaction originating from the coupling to the $d_{xz}$ and $d_{yz}$ bands. This is not the case for stronger confinement where contribution of the states related to the $d_{xz/yz}$ orbital is relevant. Based on the time-dependent calculations, we discuss in detail the manipulation of the electron spin in a QD by external AC voltages, in the context of the electric dipole spin resonance. The allowed and forbidden transitions are discussed in detail with respect to the parity selection rule. Our calculations show that, for a single-electron QD, the spin flip in the ground state has the character of a Rabi resonance, while for two electrons, the singlet-triplet transition is forbidden by the parity symmetry. For the two-electron QD, we demonstrate that the spin-flip transition can still be accomplished via a second-order, two-photon process that has a two-state Rabi character for low AC field amplitude. The violation of the parity symmetry on the spin-flip transitions is also analyzed.

Quasiclassical Anderson transition (QAT) represents the crossover from metallic to activated conduction in heavily doped highly compensated semiconductors (HDHCSs) due to large-scale potential fluctuations. The spatial inhomogeneity of the charged dopants in HDHCSs localizes carriers, forming metallic droplets surrounded by potential barriers. Nitride semiconductors are seldom explored for HDHCS studies due to the difficulty in synthesizing stoichiometric high-quality films and self-compensation effects. Here we show conclusive experimental evidence of the QAT in compensated scandium nitride (ScN) single-crystalline films. Mg (hole) doping in $n$-type ScN increases the resistivity by nine orders and leads to semi-insulating films exhibiting a distinct crossover from the hopping conduction at low temperatures to thermally activated percolative transport at high temperature. The sign reversal of the Seebeck coefficient, anomalously low Hall mobility that increases with raising temperature, and persistent photoconductivity support the QAT and carrier transport mechanisms. QAT in single-crystalline nitrides could lead to lattice-matched devices with lasers, modulators, and dynamic holographic applications.

Distinct from the flat band in two dimensions, the three-dimensional (3D) flat band and the corresponding physics have been relatively unexplored. Here, based on tight-binding models, we present a theoretical study of the evolution of the 3D flat band between pyrochlore and perovskite lattices, which are structurally interconvertible through diagonal strain and host double-degenerate flat bands. We discovered the presence of a persistent 3D flat band during the transition, which is stabilized by a robust compact localized state within the preserved kagome plane perpendicular to the diagonal direction. Furthermore, under the influence of spin-orbit coupling and Zeeman field, we can consistently achieve a magnetic Weyl semimetal state during this transition process due to the unique 3D flat band nature. Pairs of Weyl points form near the conserved flat band, leading to a large anomalous Hall conductivity (AHC) peak right at the energy of the flat band. Interestingly, we also observe an enhanced AHC during the transition from pyrochlore to perovskite lattice due to the enlarged momentum separation between Weyl points and the superimposition with another AHC peak from the dispersive Dirac bands.

We investigated the electronic structure of ${\mathrm{BaEu}}_2{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ and ${\mathrm{Eu}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ by means of hard x-ray photoelectron spectroscopy. The Eu $3d$ core level spectra are primarily dominated by ${\mathrm{Eu}}^{2+}$ signals. The well-screened feature in the Nb $3d$ core level spectra of ${\mathrm{BaEu}}_2{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ is suppressed in ${\mathrm{Eu}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$, consistent with the insulating behavior of ${\mathrm{Eu}}_3{\mathrm{Nb}}_5{\mathrm{O}}_{15}$ due to the atomic disorder and/or the rattling effect of the small Eu ions in the spacious $A2$ site. In the valence band spectra, the Nb $4d$ states at the Fermi level are close to the Eu $4f$ states located around 2 eV below it. This suggests that the degree of localization of the Nb $4d$ electrons can be enhanced through the Eu $4f$–Nb $4d$ hybridization with the atomically and magnetically disordered Eu ions at the $A2$ site.

Elementary point charge excitations in three-plus-one-dimensional $(3+1\mathrm{D})$ topological phases can condense along a line and form a descendant excitation called the Cheshire string. Unlike the elementary flux loop excitations in the system, Cheshire strings do not have to appear as the boundary of a 2D disk and can exist on open line segments. On the other hand, Cheshire strings are different from trivial excitations that can be created with local unitaries in zero dimensions and finite depth quantum circuits in one dimension and higher. In this paper, we show that to create a Cheshire string, one needs a linear depth circuit that acts sequentially along the length of the string. Once a Cheshire string is created, its deformation, movement and fusion can be realized by finite depths circuits. This circuit depth requirement applies to all nontrivial descendant excitations including symmetry-protected topological chains and the Majorana chain.

The properties of a two-dimensional (2D) electron system can be drastically altered by a magnetic field applied perpendicular to the 2D plane. In particular, the frequency of its bulk collective excitations becomes gapped at the cyclotron frequency, while the low-frequency localized excitations, the edge magnetoplasmon (EMP), appear near the system's edge. A new type of the delocalized low-frequency excitations, the gradient magnetoplasmon, was recently shown to exist in a 2D electron system with a linear density gradient that breaks the system's cylindrical symmetry [Phys. Rev. B 103, 075420 (2021)]. Like EMP, these new excitations are gapless and chiral, and originate from the classical Hall effect. Here we show that a similar magnetoplasmon mode can exist in a system with strongly inhomogeneous radial distribution of the electron density that preserves the cylindrical symmetry. This is experimentally demonstrated in a pristine system of surface electrons on liquid helium and is confirmed by a numerical simulation. This result extends the variety of known collective excitations in a 2D charge system and presents electrons on helium as a promising model system for their study.

Bismuth-activated materials with broadband luminescence have continued to attract interest for their potential applications in phosphors and broadband optical amplifiers. This study aims to elucidate the near-infrared (NIR) luminescence observed in different oxides via first-principles predictions on the formation energies of intrinsic defects and bismuth dopants, as well as the optical transition processes. The results show that monovalent Bi $\left({\mathrm{Bi}}^{1+}\right)$ ions can replace alkaline metal ions in pollucite ${\mathrm{CsAlSi}}_2{\mathrm{O}}_6$, leucite ${\mathrm{KAlSi}}_2{\mathrm{O}}_6$, and ${\mathrm{CsGaGe}}_2{\mathrm{O}}_6$, forming ${\left(\text{BiO}\right)}^{-}$ complexes with a ligand oxygen ion, producing photoluminescence with photon energy around $1\text{eV}$ with sub-ms decay time. The emission energy is predicted to decrease as the ${\left(\text{BiO}\right)}^{-}$ bond length decreases, manifesting the ligand-field effect. In ${\mathrm{BaZrO}}_3$ and ${\mathrm{SrZrO}}_3$, under a sufficiently strong reducing atmosphere, Bi dopants can replace ${\mathrm{Ba}}^{2+}$ or ${\mathrm{Sr}}^{2+}$ ions as ${\mathrm{Bi}}^{1+}$ ions, producing the observed emission around 1000 nm with a sub-ms decay time. The shorter wavelengths are due to the weaker ligand field in ${\mathrm{BaZrO}}_3$ and ${\mathrm{SrZrO}}_3$ than in pollucite and leucite. This study provides a rational interpretation for the NIR luminescence of sub-ms decay time in the Bi-doped mixed oxides, attributing it to the emission of ${\mathrm{Bi}}^{1+}$ substitution for large alkaline or alkaline earth ions, and offers a guideline for understanding the phenomena in similar systems.

We investigate the topological properties of one-dimensional weakly interacting topological insulators using bosonization. To do that we study the topological edge states that emerge at the edges of a model realized by a strong impurity or at the boundary between topologically distinct phases. In the bosonic model, the edge states are manifested as degenerate bosonic kinks at the boundaries. We first illustrate this idea on the example of the interacting Su-Schrieffer-Heeger (SSH) chain. We compute the localization length of the edge states as the width of an edge soliton that occurs in the SSH model in the presence of a strong impurity. Next, we examine models of two capacitively coupled SSH chains that can be either identical or in distinct topological phases. We find that weak Hubbard interaction reduces the ground-state degeneracy in the topological phase of identical chains. We then prove that, similarly to the noninteracting model, the degeneracy of the edge states in the interacting case is protected by chiral symmetry. We then study topological insulators built from two SSH chains with interchain hopping that represent models of different chiral symmetric universality classes. We demonstrate in bosonic language that the topological index of a weakly coupled model is determined by the type of interchain coupling, invariant under one of two possible chiral symmetry operators. Finally, we show that a general one-dimensional model in a phase with topological index $\nu$ is equivalent at low energies to a theory of at least $\nu$ SSH chains. We illustrate this idea on the example of an SSH model with longer-range hopping.

Line defects (LDs) in borophenes, which occur at the interface between two different boron sheets, have garnered considerable interest. Motivated by recent advancements in the synthesis of diverse borophene polymorphs and heterojunctions, we investigate the contact effects on electron transport through two-terminal disordered borophene nanoribbons (BNRs) with a random distribution of LDs. The source and drain are chosen from the following four semi-infinite electrodes: ${\nu }_{1/5}$ BNR, ${\nu }_{1/6}$ BNR, ${\nu }_{1/3}$ BNR, and square lattice (SL). Despite the substantial reduction in the overall conductance of disordered BNRs, several resonant peaks can appear in the transmission spectra, regardless of inhomogeneous model parameters, nanoribbon length and width, and contact configuration. The amplitude of all the resonant peaks is exactly the conductance quantum $G_0$ when both electrodes are taken as the ${\nu }_{1/5}$ or ${\nu }_{1/6}$ BNR. In contrast, the peak amplitude will be less than $G_0$ when either electrode is taken as the ${\nu }_{1/3}$ BNR or SL. Notably, some resonant peaks completely vanish for the contact configuration of the ${\nu }_{1/3}$ BNR, a phenomenon termed as the resonant peak filtering effect, which can be understood from the structure-property relationships associated with the local current distribution. Additionally, the distribution of conductance at off-resonant energies can be well fitted by the Anderson localization theory. And the evolution of the resonant peaks with the nanoribbon width is also revealed. These findings contribute to the understanding of structure-property relationships, which is valuable for designing borophene-based nanodevices.

We adopt nonequilibrium Green's functions and density functional theory to study the effect of Se atom defects on the transport properties and the photocurrent of a $1T-{\mathrm{TiSe}}_2$ heterojunction. We calculate the photocurrent for two types of defect configurations under the excitation of the linearly polarized light. The results show that Se1 and Se2 vacancy defects can induce large photocurrents, which are explained in terms of the transmission spectrum. The photocurrent shows anisotropic behaviors for different illuminated directions. Meanwhile, the extinction ratio reflecting the polarization sensitivity can reach a maximum value of 445.12. The photoresponsivities of the device with vacancy defects can have relatively large values in certain energy ranges. The $1T-{\mathrm{TiSe}}_2$-based device is a promising candidate for anisotropic light detection.

We theoretically predict the full quantum geometric tensor, comprising the quantum metric and the Berry curvature, for a square lattice of plasmonic nanoparticles. The gold nanoparticles act as dipole or multipole antenna radiatively coupled over long distances. The photonic-plasmonic eigenfunctions and energies of the system depend on momentum and polarization (pseudospin), and their topological properties are encoded in the quantum geometric tensor. By T-matrix numerical simulations, we identify a TE-TM band splitting at the diagonals of the first Brillouin zone, that is not predicted by the empty lattice band structure nor by the highly symmetric nature of the system. Further, we find quantum metric around these regions of the reciprocal space, and even a nonzero Berry curvature despite the trivial lattice geometry and absence of magnetic field. We show that this nonzero Berry curvature arises exclusively from non-Hermitian effects, which break the time-reversal symmetry. The quantum metric, in contrast, originates from a pseudospin-orbit coupling given by the polarization and directional dependence of the radiation.

Charge density waves (CDWs) in two-dimensional materials have received great attention due to their intriguing properties, yet the microscopic evolution process of CDW transition and its impact on charge transport remain to be fully understood. Herein we employed density-functional theory calculations to ascertain the richness of CDW phases in $\mathrm{V}{X}_2$ ($X=\mathrm{S}$, Te) originated from electron-phonon coupling. Reversible transitions between the normal and CDW phases are directly simulated with ab initio molecular dynamics, indicating that the formation of CDW phase is a rapid nucleation process. The corresponding microscopic dynamic processes involve the formation, flipping, translation, and aggregation of characteristic patterns, which are driven by the soft phonon modes. Modifications of electrical conductivity in CDW phase transition are found to stem from the varying orientation and location distributions of relevant wave functions. The revealed dynamic mechanism opens an opportunity for the control of CDW phase transition that is crucial to its applications in logical circuits and neural networks.