In this work we investigate the supercurrent in a hybrid topological Josephson junction consisting of two planes of topological insulator (TI) in a specific configuration, which allows both local (LAR) and crossed (CAR) Andreev processes at the interfaces with two conventional $s$-wave superconductors. We describe the effects of gate voltage and magnetic flux controls applied to the edge states of each TI. In particular, we demonstrate that the voltage gating allows the manipulation of the entaglement symmetry of nonlocal Cooper pairs associated to the CAR process. We establish a connection between the Josephson current-phase relationship of the system and the action of the two external fields, finding that they selectively modify the LAR or the CAR contributions. Remarkably, we find that the critical current of the junction takes a very simple form which reflects the change in the symmetry occurred to the entangled state and allows to determine the microscopic parameters of the junction.

We study transport across junctions of a Weyl (WSM) and a multi-Weyl semimetal (MSM) separated by a region of thickness $d$ which has a barrier potential $U_0$. We show that in the thin barrier limit ($U_0\to \infty$ and $d\to 0$ with $\chi =U_{0}d/\left(\hslash v_F\right)$ kept finite, where $v_F$ is velocity of low-energy electrons and $\hslash$ is Planck's constant), the tunneling conductance $G$ across such a junction becomes independent of $\chi$. We demonstrate that such a barrier independence is a consequence of the change in the topological winding number of the Weyl nodes across the junction and point out that it has no analog in tunneling conductance of either junctions of two-dimensional topological materials (such as graphene or topological insulators) or those made out of WSMs or MSMs with the same topological winding numbers. We study this phenomenon both for normal-barrier-normal and normal-barrier-superconductor junctions involving WSMs and MSMs with arbitrary winding numbers and discuss experiments which can test our theory.

We report on the discovery of a quantum tricritical point (QTP) separating a line of first-order topological quantum phase transitions from a continuous transition regime in a strongly correlated one-dimensional lattice system. Specifically, we study a fermionic four-leg ladder supporting a symmetry-protected topological insulator phase in the presence of on-site interaction, which is driven towards a trivial gapped phase by a nearest-neighbor interaction. Based on DMRG simulations, we show that, as a function of the interaction strength, the phase transition between the topological and the trivial phase switches from being continuous to exhibiting a first-order character. Remarkably, the QTP as well as the first-order character of the topological transition in the strongly correlated regime are found to clearly manifest in simple local observables.

The interplay between topology and correlation lies at the forefront of modern condensed matter physics. In this paper, we study the extended fermion-Hubbard model, including the on-site as well as the nearest-neighbor repulsive interactions, on a topological square lattice that supports the Chern insulator. Within the mean-field method, we find that the spontaneous symmetry breaking (SSB) charge-density wave or antiferromagnetic insulator dominates the system when the onsite or nearest-neighbor interactions are strong enough. It is interesting that the antiferromagnetic Chern insulator will appear in the phase diagram when there is an explicitly nonvanishing sublattice potential. In addition, we explore how a finite-size ribbon structure affects the phase diagram and point out that the critical interaction for SSB occurs with weaker strength than the bulk system.

Rigorous coupled-wave analysis (RCWA) is a very effective tool for studying optical properties of multilayered vertically invariant periodic structures. However, it fails to deal with arrays of small particles because of high gradients in a local field. In this paper, we implement the discrete dipole approximation (DDA) for the construction of scattering matrices of arrays of resonant nanoparticles. This strongly speeds up the calculations and therefore provides an opportunity for thorough consideration of various layered structures with small periodic inclusions in terms of the RCWA. We demonstrate the performance of the proposed method by considering plasmonic lattices embedded in a homogeneous ambience and placed inside and onto an optical waveguide. Both localized surface plasmon resonances (LSPRs) and lattice plasmon resonances (LPRs) are observed as well as their hybridization with photonic guided modes. High accuracy and fast convergence of our approach are shown by comparison with the finite element method (FEM) and RCWA calculations correspondingly.

We study the appearance of a sharp collective mode which features transverse current fluctuations within the bosonization approach to interacting two-dimensional Fermi liquids. This mode is analogous to the shear sound modes in elastic media, and, unlike the conventional zero sound mode, it is damped in weakly interacting Fermi liquids and only separates away from the particle-hole continuum when the quasiparticle mass becomes twice the transport mass $m^{*}\gtrsim 2m$. The shear sound should be present in a large class of interacting charged and neutral Fermi liquids especially those proximate to critical points where the quasiparticle mass diverges. In metals this mode remains linearly dispersing in the presence of the long-ranged Coulomb force, unlike the conventional zero sound mode which becomes the plasma mode. We also detail a quick path between bosonization and classical Landau's Fermi liquid theory by constructing a mapping between the solutions of the classical kinetic equation and the quantized bosonic eigenmodes. By further mapping the kinetic equation into a one-dimensional tight-binding model we solve for the entire spectrum of collective and incoherent particle-hole excitations of Fermi liquids with nonzero $F_0$ and $F_1$ Landau parameters.

Non-Hermitian Hamiltonians, which describe a wide range of dissipative systems, and higher-order topological phases, which exhibit novel boundary states on corners and hinges, comprise two areas of intense current research. Here we investigate systems where these frontiers merge and formulate a generalized biorthogonal bulk-boundary correspondence, which dictates the appearance of boundary modes at parameter values that are, in general, radically different from those that mark phase transitions in periodic systems. By analyzing the interplay between corner/hinge, edge/surface, and bulk degrees of freedom we establish that the non-Hermitian extensions of higher-order topological phases exhibit an even richer phenomenology than their Hermitian counterparts and that this can be understood in a unifying way within our biorthogonal framework. Saliently this works in the presence of the non-Hermitian skin effect, and also naturally encompasses genuinely non-Hermitian phenomena in the absence thereof.

The effect of next-nearest-neighbor hopping $t_2$ on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite $t_2$, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that $t_2$ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong $J$, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker $J$, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak $J$, with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.

We present a quantum optics theory, numerical calculations, and experiments on coupled quantum dots in semiconductor nanowire waveguides. We first present an analytical Green function theory to compute the emitted spectra of two coupled quantum dots, treated as point dipoles, fully accounting for retardation effects, and demonstrate the signatures of coherent and incoherent coupling through a pronounced splitting of the uncoupled quantum dot resonances and modified spectral broadening. In the weak excitation regime, the classical Green functions used in models are verified and justified through full three-dimensional solutions of Maxwell equations for nanowire waveguides, specifically using finite-difference time-domain techniques, showing how both waveguide modes and near-field evanescent mode coupling is important. The theory exploits an ensemble-based quantum description, and an intuitive eigenmode-expansion-based Maxwell theory. We then demonstrate how the molecular resonances (in the presence of coupling) take on the form of bright and dark (or quasidark) resonances, and study how these depend on the excitation and detection conditions. To go beyond the weak excitation regime, we also introduce a quantum master-equation approach to model the nonlinear spectra from an increasing incoherent pump field, which shows the role of the pump field on the oscillator strengths and broadening of the molecular resonances, with and without pure dephasing. Next, we present experimental photoluminescence spectra for spatially separated quantum dot molecules (InAsP) in InP nanowires, which show clear signatures of pronounced splittings, although they also highlight additional mechanisms that are not accounted for in the dipole-dipole coupling model. Two different approaches are taken to control the spatial separation of the quantum dot molecules, and we discuss the advantages and disadvantages of each.

The effective interaction between resonant magnetic Anderson impurities in graphene, mediated by conduction electrons, is studied as a function of the strength of the on-site energy level of the impurities and the amplitude of coupling to conduction electrons. The sign and character of the interaction depend on whether the impurities reside on the same or opposite sublattices. For the same (opposite) sublattice, the potential interaction is attractive (repulsive) in the weak coupling limit with $1/R^3$ dependence on the distance; the interaction reverses sign and becomes repulsive (attractive) in the strong coupling limit and displays $1/R$ behavior. The spin-exchange coupling is ferromagnetic (antiferromagnetic) at both large and small distances, but reverses sign and becomes antiferromagnetic (ferromagnetic) for intermediate distances. For opposite sublattices, the effective spin-exchange coupling is resonantly enhanced at distances where the energy levels cross the Dirac points.

We report a giant enhancement of the midinfrared magneto-optical complex Kerr angle (polarization change of reflected light) in a variety of materials grown on SiC. In epitaxially grown multilayer graphene, the Kerr angle is enhanced by a factor of 68, which is in good agreement with Kerr signal modeling. Strong Kerr enhancement is also observed in Fe films grown on SiC and Al-doped bulk SiC. Our experiments and modeling indicate that the enhancement occurs at the high-energy edge of the SiC reststrahlen band where the real component of the complex refractive index ${\tilde{n}}_{}$ passes through unity. Furthermore, since the signal is greatly enhanced when $\tilde{n}=1$, the enhancement is predicted to exist over the entire visible and IR spectrum for a free-standing film. We also predict similar giant enhancement in both Faraday (transmission) and Kerr rotation for thin films on a metamaterial substrate with refractive index ${\tilde{n}}_{}=-1$. This paper demonstrates that the substrate used in magneto-optical Kerr effect (MOKE) measurements must be carefully chosen when investigating magneto-optical materials with weak MOKE signals or when designing MOKE-based optoelectronic devices.

The distribution and manipulation of oxygen defects, including oxygen vacancies $\left(O_v\right)$ and interstitial oxygen $\left(O_i\right)$, directly results in modifications in a variety of emergent functionalities in transition metal oxides. This is applicable in nanoscale control, which is a key issue in data and energy storage devices, such as resistive switching memory. Among all the oxygen-defect-related topics, nanoscale oxygen defect migration paths have a direct impact on the performance of memory devices, and are intrinsically determined by the structural anisotropy. Here, we use layered single-crystalline ferroelectric, hexagonal manganites $\left(h-\mathrm{REMn}{\mathrm{O}}_3\right)$ to demonstrate ${\mathrm{O}}_{\mathrm{i}}$-migration-induced nanoscale manipulation of conductance in the $ab$ plane. Conversely, this unique phenomenon cannot be achieved along the $c$ axis. Furthermore, a density functional theory calculation reveals that the energy barriers are lower for planar migrations of ${\mathrm{O}}_{\mathrm{i}}$, when compared to out-of-plane migration, and are responsible for such anisotropic resistance switching.

Building on the foundational work of Brown, Milton, and Torquato, we present a tractable approach to analyze the effective permittivity of anisotropic two-phase structures. This methodology accounts for successive dipolar interactions, providing a recurrent series expansion of the effective permittivity to arbitrary order. Within this framework, we also demonstrate a progressive method to determine tight bounds that converge toward the exact solution. We illustrate the utility of these methods by using ensemble averaging to determine the microstructural parameters of anisotropic level-cut Gaussian fields. We find that the depolarization factor of these structures is equivalent to that of an isolated ellipse with the same stretching ratio, and we discuss the contribution of the fourth-order term to the exact anisotropy.

We describe an artificial spin ice (ASI) composed of exchange biased heterostructured nanomagnetic elements with unidirectional anisotropy and compare it with a conventional ASI constituted by ferromagnets with uniaxial anisotropy (Ising spins). The introduction of a local exchange bias field, aligned along one of the sublattices of the square ASI, lifts the spin-reversal symmetry of the vertices. By varying the lattice constant of the square array, we control the ratio of exchange bias (EB) to dipolar field ($H_{\mathrm{EB}}/H_{\mathrm{dip}}$) and tune the ground state from an antiferromagnetic to a ferromagnetic configuration with an effective magnetic moment. The geometric frustration of dipolar interactions is moderated by a nonfrustrated local field, leading to a mesoscopic system with specific metastable states observed during the demagnetization process.

Low-temperature (22 K) irradiation with 2.5-MeV electrons, creating point defects affecting elastic scattering, was used to study the competition between stripe ${\mathrm{C}}_2$ and tetragonal ${\mathrm{C}}_4$ antiferromagnetic phases which exist in a narrow doping range around $x=0.25$ in hole-doped ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$. In nearby compositions outside of this range, at $x=0.22$ and $x=0.19$, the temperatures of both the concomitant orthorhombic/stripe antiferromagnetic transition $T_{\mathrm{C}2}$ and the superconducting transition $T_{\mathrm{c}}$ are monotonically suppressed by added disorder at similar rates of about 0.1 K/$\mu \mathrm{\Omega }\mathrm{cm}$, as revealed through using resistivity variation as an intrinsic measure of scattering rate. In a stark contrast, a rapid suppression of the ${\mathrm{C}}_4$ phase at the rate of 0.24 K/$\mu \mathrm{\Omega }\mathrm{cm}$ is found at $x=0.25$. Moreover, this suppression of the ${\mathrm{C}}_4$ phase is accompanied by unusual disorder-induced stabilization of the ${\mathrm{C}}_2$ phase, determined by resistivity and specific heat measurements. The rate of the ${\mathrm{C}}_4$ phase suppression is notably higher than the suppression rate of the spin-vortex phase in the Ni-doped ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ (0.16 K/$\mu \mathrm{\Omega }\mathrm{cm})$.

We elucidate as-yet-unidentified spatially extended oxygen vacancy states in $\mathit{AB}{\mathrm{O}}_3$ perovskite oxides using first-principles calculations. When $B$ sites are occupied with $d^0$ transition-metal ions, charged oxygen vacancies are found to be long ranged in one direction because of charge transfer accompanied with atomic displacement along a chainlike structure. This finding offers two important results. First, it explains the reason why accurate calculations of oxygen vacancy formation energies necessitate very large supercells in $d^0$ perovskite and related oxides. It is remarkable especially for ${\mathrm{KNbO}}_3$ and ${\mathrm{WO}}_3$ on account of their anomalous Born effective charges. Second, such elongated vacancy states tend to show lower formation energies and thereby shallower donor levels. Our discussion is extendable to systems other than perovskites. Since the chainlike structure also appears in anatase ${\mathrm{TiO}}_2$ but not in its rutile counterpart, it could be a reason why the oxygen vacancy is a double shallow donor in the former while constructing a deep state in the latter.

We report a comprehensive study on the intrinsic spin Hall conductivity (SHC) of the semimetals ${\mathrm{MoTe}}_2$ and ${\mathrm{WTe}}_2$ by ab initio calculations. Large SHC at the Fermi energy and desirable spin Hall angles have been discovered, due to the strong spin-orbit coupling effect and the low charge conductivities of the semimetals. The unusual reduced crystalline symmetry of ${\mathrm{MoTe}}_2$ and ${\mathrm{WTe}}_2$ results in diverse anisotropic SHC values, consistent with the symmetry restrictions of the response tensor according to the magnetic Laue group. We report an effective method on SHC optimization by Fermi energy tuning, and demonstrate the mechanism of SHC variation with respect to the Fermi energy shifting by the spin Berry curvature. Our work provides insights into the realization of strong and anisotropic spin Hall effects in low-symmetry semimetals.