Non-Hermitian skin-edge states emerge only at one edge in one-dimensional nonreciprocal chains, where all states are localized at the edge irrespective of eigenvalues. The bulk topological number is the winding number associated with the complex energy spectrum, which is well defined for metals. We study non-Hermitian nonreciprocal systems in higher dimensions, and propose to realize them with the use of electric diode circuits. We first investigate one-dimensional interface states between two domains carrying different topological numbers, where all states are localized at the interface. They are a generalization of the skin-edge states. Then we generalize them into higher dimensions. We show that there emerge a rich variety of boundary states and interface states including surface, line, and point states in three-dimensional systems. They emerge at the boundaries of several domains carrying different topological numbers. The resulting systems are the first-order, second-order, and third-order topological metals. Such states may well be observed by measuring the two-point impedance in diode circuits.

In topological insulator edges, the duality between the Zeeman field orientation and the proximitized superconducting phase has been recently exploited to predict a magneto-Josephson effect with a $4\pi$ periodicity. We revisit this latter Josephson effect in the light of this duality and show that the same $4\pi$ quantum anomaly occurs when bridging two spinless Thouless pumps to a $p$-wave superconducting region that could be as small as a single and experimentally relevant superconducting quantum dot, a pointlike defect. This interpretation as a dual Josephson effect never requires the presence of Majorana modes but rather builds on the topological properties of adiabatic quantum pumps with $\mathbb{Z}$ topological invariants. It allows for the systematic construction of dual Josephson effects of arbitrary periodicity, such as $4\pi$ and $8\pi$, by using pointlike defects whose symmetry differs from that of the pump, dubbed symmetry defects. Although adiabatic quantum pumps are typically discussed via mappings to two-dimensional geometries, we show that this phenomenology does not have any counterpart in conventional two-dimensional systems.

ZrSiS is a nodal-line semimetal, whose electronic band structure contains a diamond-shaped line of Dirac nodes. We carried out a comparative study on the optical conductivity of ZrSiS and the related compounds ZrSiSe, ZrSiTe, ZrGeS, and ZrGeTe by reflectivity measurements over a broad frequency range combined with density functional theory calculations. The optical conductivity exhibits a distinct U shape, ending at a sharp peak at around $10000{\mathrm{cm}}^{-1}$ for all studied compounds except for ZrSiTe. The U shape of the optical conductivity is due to transitions between the linearly dispersing bands crossing each other along the nodal line. The sharp high-energy peak is related to transitions between almost parallel bands, and its energy position depends on the interlayer bonding correlated with the $c/a$ ratio, which can be tuned by either chemical or external pressure. For ZrSiTe, another pair of crossing bands appears in the vicinity of the Fermi level, corrugating the nodal-line electronic structure and leading to the observed difference in optical conductivity. The findings suggest that the Dirac physics in $\mathrm{Zr}XY$ compounds with $X=\mathrm{Si},\mathrm{Ge}$ and $Y=\mathrm{S},\mathrm{Se},\mathrm{Te}$ is closely connected to the interlayer bonding.

We experimentally investigate charge transport through a single planar junction between a ${\mathrm{Cd}}_3{\mathrm{As}}_2$ Dirac semimetal and a normal Au lead. For nonsuperconducting bulk ${\mathrm{Cd}}_3{\mathrm{As}}_2$ samples we observe non-Ohmic $dV/dI\left(V\right)$ curves, which strongly resemble standard Andreev reflection with a well-defined superconducting gap. Andreev-like behavior is demonstrated for ${\mathrm{Cd}}_3{\mathrm{As}}_2$ samples with different surface and contact preparation techniques. We connect this behavior with surface superconductivity due to the flat-band formation in ${\mathrm{Cd}}_3{\mathrm{As}}_2$, which has been predicted theoretically. The conclusion on superconductivity is also supported by the gap suppression by magnetic fields or temperature.

In this work, we report on hot carrier diffusion in graphene across large enough length scales that the carriers are not thermalized across the crystal. The carriers are injected into graphene at one site and their thermal transport is studied as a function of applied power and distance from the heating source, up to tens of micrometers away. Superconducting contacts prevent out-diffusion of hot carriers to isolate the electron-phonon coupling as the sole channel for thermal relaxation. As local thermometers, we use the amplitude of the universal conductance fluctuations, which varies monotonically as a function of temperature. By measuring the electron temperature simultaneously along the length we observe a thermal gradient which results from the competition between electron-phonon cooling and lateral heat flow.

High-order harmonic generation (HHG) from atoms is a coherent light source that opens up attosecond physics, but it is the application of HHG to solids that has brought much excitement in the last decade. Here we report a special kind of harmonics in a quasi-one-dimensional and hexagonal barium titanium sulfide: Under circularly polarized laser excitation, harmonics are generated only at first, fifth, seventh, and eleventh orders. These magic harmonics appear only with circularly polarized light, not with linearly polarized light. Neither cubic nor tetragonal cells have magic harmonics even with circularly polarized light. Through a careful group-theory analysis, we find that two subgroups of symmetry operations unique to the hexagonal symmetry cancel out third and ninth harmonics. This feature presents a rare opportunity to develop HHG into a crystal-structure characterization tool for phase transitions between hexagonal and nonhexagonal structures.

Elastic and anelastic anomalies in a ceramic sample of ${\mathrm{La}}_2{\mathrm{FeMnO}}_6$ have been characterized by resonant ultrasound spectroscopy in order to understand the strength and form of magnetoelastic coupling that accompanies the glassy magnetic transitions of a double perovskite with no long-range order of the B-site cations. The first transition, to a cluster glass below $\sim 280\mathrm{K}$, does not appear to involve any significant coupling with strain. The second glassy transition, near 55 K, appears to conform to Vogel-Fulcher dynamics in which magnetic dissipation and acoustic loss peaks arise from freezing driven by interactions between ferromagnetic clusters, with an activation energy of $\sim 0.03\mathrm{eV}$ and time constant ${\tau }_{\mathrm{o}}\sim {10}^{-9}\mathrm{s}$. The magnetoelastic coupling mechanism appears to involve local spin states with strain relaxation enhanced by changes in local electronic structure. Mediation of the coupling via strain also ensures that local heterogeneity in the strain state, such as at ferroelastic twin walls, will contribute to the magnetic heterogeneity of these materials.

We examine the topological superfluid phases for ultracold fermions in the presence of two-dimensional (2D) synthetic spin-orbit (SO) couplings which have been well realized in recent experiments. Specifically, we focus on the 2D Dirac semimetal and the SO coupled quantum anomalous Hall model, together with an attractive Hubbard interaction which can induce a superfluid phase in SO coupled systems. The superfluid phases are studied systematically based on self-consistent theories. In particular, an interesting transition between $(\pi ,\pi )$-momentum superfluid phase and zero center-of-mass momentum superfluid phase is predicted as the strength of SO coupling is increased. The full phase diagrams of the superfluid phases are obtained, with the nontrivial topological superfluids being determined by precisely calculating the topological invariants. We also determine the optimal parameter conditions of the topological superfluid phases, which could be helpful for future real experimental studies.

We combine the pseudofermion functional renormalization group (PFFRG) method with a self-consistent Fock-like mean-field scheme to calculate low-energy effective theories for emergent spinon excitations in spin-1/2 quantum spin liquids. Using effective spin interactions from PFFRG as an input for the Fock equation and allowing for the most general types of free spinon Ansätze as classified by the projective symmetry group (PSG) method, we are able to systematically determine spinon band structures for spin-liquid candidate systems beyond mean-field theory. We apply this approach to the antiferromagnetic $J_1\text{−}{J}_2$ Heisenberg model on the square lattice and to the antiferromagnetic nearest-neighbor Heisenberg model on the kagome lattice. For the $J_1\text{−}{J}_2$ model, we find that in the regime of maximal frustration a SU(2) $\pi$-flux state with Dirac spinons yields the largest mean-field amplitudes. For the kagome model, we identify a gapless ${\mathbb{Z}}_2$ spin liquid with a small circular spinon Fermi surface and approximate Dirac cones at low but finite energies.

$1T-\mathrm{TiS}{\mathrm{e}}_2$ has a semimetallic band structure at room temperature and undergoes phase transition to a triple-$q$ charge-density wave (CDW) state with a commensurate superlattice structure $\left(2a\times 2a\times 2c\right)$ below $T_c\approx 200\mathrm{K}$ at ambient pressure. This phase transition is caused by cooperative phenomena involving electron-phonon and electron-hole (excitonic) interactions, and cannot be described by a standard CDW framework. By Cu intercalation or the application of pressure, this phase-transition temperature is suppressed and superconductivity (SC) appears. However, it is not clear what kind of order parameters are affected by these two procedures. We investigated the crystal structure of $\mathrm{C}{\mathrm{u}}_x\mathrm{TiS}{\mathrm{e}}_2$ and pressurized $1T-\mathrm{TiS}{\mathrm{e}}_2$ around the SC state by synchrotron x-ray diffraction on single crystals. In the high-temperature phase, the variations of structural parameters for the case of Cu intercalation and application of pressure are considerably different. Moreover, the relationship between the critical points of the CDW phase transition and the SC dome are also different for the two cases. The excitonic interaction appears to play an important role in the $P-T$ phase diagram of $1T-\mathrm{TiS}{\mathrm{e}}_2$, but not in the $x-T$ phase diagram.

Plasmonic excitations in metallic nanoparticles are known to depend strongly on nanoparticle size and shape. Here we explore how such excitations can be harnessed to enhance the vibrational signals from molecules adsorbed on nanoparticle surfaces, as detected using electron energy-loss spectroscopy in the scanning transmission electron microscope. We use the Born-Huang formalism in the electrostatic approximation to develop a theoretical model for electron energy-loss from an adsorbed molecule (represented by a point dipole) on the surface of a dielectric nanoparticle. We find that the adsorbate contribution to the energy-loss spectrum is approximately proportional to the square of the electric field at the adsorption site, and hence we find that the enhancement of the molecule's vibrational signal is greatest for molecules adsorbed on small, sharp nanoparticles. When the molecular frequency is near one of the nanoparticle frequencies, we generally find an asymmetric Fano-type spectrum line shape whose asymmetry is attributable to multimodal contributions. Our calculations for a molecule adsorbed on the tip of a prolate spheroidal silver nanoparticle predict that signal enhancements of several hundred times should be readily achievable, and up to several thousand times if the nanoparticle's plasmonic mode is “tuned” to the molecular frequency. Such enhancement effects potentially make vibrational STEM-EELS a powerful tool for the characterization of surface-functionalized nanoparticles and nanomaterials used for chemical sensing.

We present ultrafast optical pump-probe and ultrafast x-ray diffraction measurements of the charge density wave dynamics in ${\mathrm{SmTe}}_3$ at 300 K. We performed ultrafast x-ray diffraction measurements at the Linac Coherent Light Source to directly probe the dynamics of the finite-wave-vector order parameter. The dynamics reveal coherent oscillations at $\sim 1.6$ THz that become overdamped with increasing fluence. We identify this oscillation with the lattice component of the amplitude mode. Furthermore, our data allow for a clear identification of the amplitude mode frequency in the optical pump-probe data. In both measurements, the system reaches the symmetric phase at high fluence, where the order parameter vanishes and the response (reflectivity and x-ray intensity) is quadratic in the order parameter. This is observed in the x-ray diffraction as a small overdamped modulation near zero intensity. Similar overdamped features are observed in the optical reflectivity at high fluence. A time-dependent Ginzburg-Landau model captures qualitatively the essential features of the experimental observations.

We report the magnetotransport properties of ${\mathrm{CaAl}}_4$ single crystals with $C2/m$ structure at low temperature. ${\mathrm{CaAl}}_4$ exhibits large unsaturated magnetoresistance $\sim 3000\%$ at 2.5 K and 14 T. The nonlinear Hall resistivity is observed, which indicates the multi-band feature. The first-principles calculations show the electron-hole compensation and the complex Fermi surface in ${\mathrm{CaAl}}_4$, to which the two-band model with over-simplified carrier mobility can't completely apply. Evident quantum oscillations have been observed with $\mathrm{B}\perp \mathrm{ab}$ and B//ab configurations, from which the nontrivial Berry phase is extracted by the multi-band Lifshitz-Kosevich formula fitting and Landau level index fan diagram. The calculations also elucidate that ${\mathrm{CaAl}}_4$ possesses a Dirac nodal line type band structure around the $\mathrm{\Gamma }$ point in the $Z\text{−}\mathrm{\Gamma }\text{−}L$ plane, which is protected by the mirror symmetry as well as the space inversion and time reversal symmetries. Once the spin-orbit coupling is included, the crossed nodal line opens a negligible gap (less than 3 meV). The ${\mathrm{Z}}_2$ invariant of ${\mathrm{CaAl}}_4$ equals 1, indicating its nontrivial topological properties. The open-orbit topology is also found in the electron-type Fermi surfaces by the first-principles calculations, which is believed to help enhance the magnetoresistance observed.

The suppression of Zeeman energy splitting due to spin-dependent interactions (the spin Meissner effect) was predicted to occur within a Bose-Einstein condensate. We report a clear observation of this effect in semimagnetic microcavities which exhibit a giant Zeeman energy splitting between two spin-polarized polariton states as high as 2 meV and demonstrate that a partial suppression of the energy difference occurs already in the uncondensed phase in a striking similarity to the behavior of up-critical superconductors in the fluctuation-dominated regime. These observations are explained quantitatively by a kinetic model accounting for both the condensed and uncondensed polaritons and taking into account the nonequilibrium character of the system.

The generation of highly confined plasmons through far-field optical illumination appears to be impractical for technological applications due to their large energy-momentum mismatch with external light. Electrical generation of plasmons offers a possible solution to this problem, although its performance depends on a careful choice of material and geometrical parameters. Here we theoretically investigate graphene-based structures and show in particular the very different performances between (i) two layers of graphene separated by a dielectric and (ii) metal/insulator/graphene sandwiches as generators of propagating plasmons assisted by inelastic electron tunneling. For double-layer graphene, we study the dependence on the relative tilt angle between the two sheets and show that the plasmon generation efficiency for $4^{\circ }$ twist angle drops to $\sim 20\%$ from its maximum for perfect stacking. For metal/insulator/graphene sandwiches, the inelastic tunneling efficiency drops by several orders of magnitude relative to double-layer graphene, regardless of doping level, metal/graphene separation, choice of metal, and direction of tunneling (metal to or from graphene), a result that we attribute to the small fraction of the surface-projected metal Brillouin zone covered by the graphene Dirac cone. Our results reveal a reasonable tolerance to graphene lattice misalignment and a poor performance of structures involving metals, thus supporting the use of double-layer graphene as an optimum choice for electrical plasmon generation in tunneling devices.

A four-band exciton Hamiltonian is constructed starting from the single-particle Dirac Hamiltonian for charge carriers in monolayer transition metal dichalcogenides (TMDs). The angular part of the exciton wave function can be separated from the radial part, in the case of zero center of mass momentum excitons, by exploiting the eigenstates of the total exciton angular momentum operator with which the Hamiltonian commutes. We explain why this approach fails for excitons with finite center of mass momentum or in the presence of a perpendicular magnetic field and present an approximation to resolve this issue. We calculate the (binding) energy and average interparticle distance of different excited exciton states in different TMDs and compare these with results available in the literature. Remarkably, we find that the intervalley exciton ground state in the $\mp K$ valley has angular momentum $j=\pm 1$, which is due to the pseudospin of the separate particles. The exciton mass and the exciton Landau levels are calculated and we find that the degeneracy of exciton states with opposite relative angular momentum is altered by a magnetic field.

We study the phase diagram of the interacting spin-$1/2$ Haldane model with chiral phase $\varphi =\pi /2$ at half-filling. Both on-site and long-range Coulomb repulsive interactions (Haldane-Hubbard-Coulomb model) are considered. The problem with on-site interaction $U$ alone was addressed in the past by a variety of approximate and finite-size methods that produced results in disagreement with each other both quantitatively and qualitatively. Here we employ the diagrammatic Monte Carlo technique to accurately locate phase transition points to the topologically nontrivial phases in the $(\mathrm{\Delta },U)$ plane, where $\pm \mathrm{\Delta }$ is the inversion symmetry breaking on-site energy, and establish that momentum dependence of self-energy cannot be neglected in the proper treatment. We also find that even modest long-range interactions, typically discarded in theoretical considerations, result in significant shifts of transition lines.

Many-body localized states are shown to exist in geometrically frustrated lattices if the interacting Hamiltonian generates a network of transition matrix elements between many-body Wannier states with bubblelike structures. We show that such structures occur in the $U/t=\infty$ Hubbard model on the Lieb and kagome lattices and hole-localized eigenstates of these models are standing waves in these bubbles. In the particular case of one hole in a Lieb cluster with arbitrary spin configuration, these bubbles are the fundamental cycles of the network. These bubblelike standing waves constitute an interesting many-body generalization of the concept of most compact localized state. The full set of hole-localized states of the $U/t=\infty$ Hubbard model on the Lieb and kagome lattices is constructed and the general expression of the number of one-hole-localized states with one flipped spin is given for clusters with arbitrary shape. A numerical approach is described for the case of a large number of holes in a large cluster.