A Weyl point in a superconducting nanostructure is a generic minimum model of a topological singularity at low energies. We connect the nanostructure to normal leads thereby immersing the topological singularity in the continuous spectrum of the electron states in the leads. This sets another simple and generic model useful to comprehend the modification of low-energy singularity in the presence of a continuous spectrum. The tunnel coupling to the leads gives rise to new low-energy scale $\mathrm{\Gamma }$ at which all topological features are smoothed. We investigate superconducting and normal currents in the nanostructure at this scale. We show how the tunnel currents can be used for detection of the Weyl point. Importantly, we find that the topological charge is not concentrated in a point but rather is spread over the parameter space in the vicinity of the point. We introduce and compute the resulting topological charge density. We also reveal that the pumping to the normal leads helps to detect and investigate the topological effects in the vicinity of the point.

The integer quantum Hall state occurs when Landau levels are fully occupied by fermions, while the fractional quantum Hall state usually emerges when the Landau level is partially filled by strongly correlated fermions or bosons. Here, we report two fractional Chern insulating states of hard-core bosons in a multiband lattice model hosting topological flat bands with a high Chern number. The previously proposed $\nu =1/3$ fractional Chern insulating state inherited from the high Chern number $C=2$ of the lowest topological flat band is revisited by the infinite density matrix renormalization group algorithm. In particular, we numerically identify a bosonic $1/2$-Laughlin-like fractional Chern insulating state at the integer fillings. We show two lower topological flat bands jointly generate an effective $C=1$ Chern band with half filling. Furthermore, we find a strictly particle-hole-like symmetry between the $\nu$ and $3-\nu$ filling in our model. These findings extend our understanding of quantum Hall states and offer a route to realize fractional states in the system with multibands and high Chern numbers.

We theoretically introduce and study a three-dimensional Hofstadter model with linearly varying non-Abelian gauge potentials along all three dimensions. The model can be interpreted as spin-orbit coupling among a trio of Hofstadter butterfly pairs since each Cartesian surface ($xy, yz$, or $zx$) of the model reduces to a two-dimensional non-Abelian Hofstadter problem. By evaluating the commutativity among arbitrary loop operators around all axes, we derive its genuine (necessary and sufficient) non-Abelian condition, namely, that at least two out of the three hopping phases should be neither 0 nor $\pi$. Under different choices of gauge fields in either the Abelian or the non-Abelian regime, both weak and strong topological insulating phases are identified in the model.

Semiconductor microcavities can exhibit various macroscopic quantum phenomena, including Bose-Einstein condensation of polaritons, Bardeen-Cooper-Schrieffer (BCS) states of polaritons, and photon lasing (lasing with negligible Coulombic exciton effects). An important aspect of possible experimental identification of these states is a gap in the excitation spectrum (the BCS gap in the case of a polaritonic BCS state). Similar to the polaritonic BCS gap, a light-induced gap can exist in photon lasers. Although polaritonic BCS states have been observed on the basis of spectroscopy in the vicinity of the laser frequency, the direct observation of polaritonic BCS gaps using light spectrally centered at or around the emission frequency has not been achieved. It has been conjectured that low-frequency (terahertz) spectroscopy should be able to identify such gaps. In this first of two studies, a theory aimed at identifying features of light-induced gaps in the linear terahertz spectroscopy of photon lasers is developed and numerically evaluated. It is shown that spectral features in the intraband conductivity, and therefore in the system's transmissivity and absorptivity, can be related to the light-induced gap. For sufficiently small Drude damping this includes spectral regions of THz gain. A future study will generalize the present formalism to include Coulomb effects.

We study electron transport through a multichannel fractional quantum Hall edge in the presence of both interchannel interaction and random tunneling between channels, with emphasis on the role of contacts. The prime example in our discussion is the edge at filling factor 2/3 with two counterpropagating channels. Having established a general framework to describe contacts to a multichannel edge as thermal reservoirs, we particularly focus on the line-junction model for the contacts and investigate incoherent charge transport for an arbitrary strength of interchannel interaction beneath the contacts and, possibly different, outside them. We show that the conductance does not explicitly depend on the interaction strength either in or outside the contact regions (implicitly, it only depends through renormalization of the tunneling rates). Rather, a long line-junction contact is characterized by a single parameter which defines the modes that are at thermal equilibrium with the contact and is determined by the interplay of various types of scattering beneath the contact. This parameter—playing the role of an effective interaction strength within an idealized model of thermal reservoirs—is generically nonzero and affects the conductance. We formulate a framework of fractionalization-renormalized tunneling to describe the effect of disorder on transport in the presence of interchannel interaction. Within this framework, we give a detailed discussion of charge equilibration for arbitrarily strong interaction in the bulk of the edge and arbitrary effective interaction characterizing the line-junction contacts.

The moiré pattern of hBN/Ru(0001) provides a template for the adsorption of the alkali metals Cs and K: Scanning tunneling microscopy reveals that the adatoms prefer to adsorb in the valley areas of the moiré unit cell. Distinctive from transition metal adatoms that tend to agglomerate, the alkali metal adatoms avoid each other within the valleys, leading to a sharper distribution than the Poisson statistics expected for noninteracting particles. This sub-Poissonian distribution is further explored via Monte Carlo simulations. The average charge $q$ of the alkali metal adatoms is extracted for different alkali metal concentrations $\lambda$, which reveals a monotonically decreasing $q\left(\lambda \right)$ dependence. We explain this dependence with the energy trade-off between the charge transfer from the alkali metals to the more electron-affine Ru(0001) substrate and the static electric field created by this charge transfer.

Quasi-one-dimensional iron-based ladders and chains, with the $3d$ iron electronic density $n=6$, are attracting considerable attention. Recently, a new iron chain system ${\mathrm{Ba}}_2{\mathrm{FeS}}_3$, also with $n=6$, was prepared under high-pressure and high-temperature conditions. Here the magnetic and electronic phase diagrams are theoretically studied for this quasi-one-dimensional compound. Based on first-principles calculations, a strongly anisotropic one-dimensional electronic band behavior near the Fermi level was observed. In addition, a three-orbital electronic Hubbard model for this chain was constructed. Introducing the Hubbard and Hund couplings and studying the model via the density matrix renormalization group (DMRG) method, we studied the ground-state phase diagram. A robust staggered $\uparrow \text{−}\downarrow \text{−}\uparrow \text{−}\downarrow$ AFM region was unveiled in the chain direction, consistent with our density functional theory (DFT) calculations. Furthermore, at intermediate Hubbard $U$ coupling strengths, this system was found to display an orbital selective Mott phase (OSMP) with one localized orbital and two itinerant metallic orbitals. At very large $U/W$ $(W=\mathrm{bandwidth})$, the system displays Mott insulator characteristics, with two orbitals half-filled and one doubly occupied. Our results for high pressure ${\mathrm{Ba}}_2{\mathrm{FeS}}_3$ provide guidance to experimentalists and theorists working on this one-dimensional iron chalcogenide chain material.

We analyze quantum fluctuation effects at the onset of charge or spin-density wave order in two-dimensional metals with an incommensurate nesting ($2k_F$) wave vector connecting two pairs of hot spots on the Fermi surface. We first compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a perturbation expansion (one loop). Non-Fermi liquid behavior with a linear (in energy) quasiparticle decay rate and a logarithmically vanishing quasiparticle weight is obtained. The momentum dependence of the self-energy entails only finite renormalizations of the Fermi velocity and the Fermi-surface curvature at the hot spots. The perturbative one-loop result is not self-consistent and casts doubt on the stability of the $2k_F$ quantum critical point. We construct a self-consistent solution of the one-loop equations with self-energy feedback, where the quantum critical point is stabilized rather than being destroyed by fluctuations, while the non-Fermi liquid behavior as found in the perturbative one-loop calculation is confirmed.

Spin defects in silicon carbide (SiC) have attracted increasing interest due to their excellent optical and spin properties, which are useful in quantum information processing. In this paper, we systematically investigate the temperature dependence of the spin properties of divacancy defects in implanted $4H$-SiC. The zero-field splitting parameter $D$, the inhomogeneous dephasing time $T_2^{*}$, the coherence time $T_2$, and the depolarization time $T_1$ are extensively explored in a temperature range from 5 to 300 K. Two samples implanted with different nitrogen molecule ion fluences $({\mathrm{N}}_2{}^{+},$ $1\times {10}^{14}/{\mathrm{cm}}^2 \mathrm{and} 1\times {10}^{13}/{\mathrm{cm}}^2)$ are investigated, whose spin properties are shown to have similar temperature-dependent behaviors. Still, the sample implanted with a lower ion fluence has longer $T_2$ and $T_1$. We provide possible theoretical explanations for the observed temperature-dependent dynamics. Our work promotes the understanding of the temperature dependence of spin properties in solid-state systems, which can be helpful for constructing wide temperature-range thermometers based on the mature semiconductor material.

The discovery of the hydrodynamic electron liquid (HEL) in graphene [D. Bandurin et al., Science 351, 1055 (2016) and J. Crossno et al., Science 351, 1058 (2016)] has marked the birth of the solid-state HEL which can be probed near room temperature in a table-top setup. Here we examine the terahertz (THz) magneto-optical (MO) properties of a graphene HEL. Considering the case where the magnetic length $l_B=\sqrt{\hslash /eB}$ is comparable to the mean-free path $l_{ee}$ for electron-electron interaction in graphene, the MO conductivities are obtained by taking a momentum balance equation approach on the basis of the Boltzmann equation. We find that when $l_B\sim l_{ee}$, the viscous effect in a HEL can weaken significantly the THz MO effects such as cyclotron resonance and Faraday rotation. The upper hybrid and cyclotron resonance magnetoplasmon modes ${\omega }_{\pm }$ are also obtained through the RPA dielectric function. The magnetoplasmons of graphene HEL at large wave-vector regime are affected by the viscous effect, and results in red-shifts of the magnetoplasmon frequencies. We predict that the viscosity in graphene HEL can affect strongly the magneto-optical and magnetoplasmonic properties, which can be verified experimentally.

The fractional quantum Hall state at the Landau level filling factor $5/2$ is extremely interesting because it is likely the first non-Abelian state, but its precise nature remains unclear after decades of study. We demonstrate this can be resolved by studying the chirality of its graviton excitations, using circularly polarized Raman scattering. We discuss the advantage of this bulk probe over the existing edge probes.

Vector-chiral (VC) antiferromagnetism is a spiral-like ordering of spins which may allow ferroelectricity to occur due to loss of space inversion symmetry. In this Letter we report direct experimental observation of ferroelectricity in the VC phase of $\beta -\mathrm{Te}\mathrm{V}{\mathrm{O}}_4$, a frustrated spin chain system with pronounced magnetic anisotropy and a rich phase diagram. Saturation polarization is proportional to neutron scattering intensities that correspond to the VC magnetic reflection. This implies that an inverse Dzyaloshinskii-Moriya mechanism is responsible for driving electric polarization. Linear magnetoelectric coupling is absent; however an unprecedented dependence of electric coercive field on applied magnetic field reveals a distinct way of manipulating multiferroic information.

Although the contact theory between rough surfaces is designed for adhesion energies $\gtrsim 100\mathrm{mJ}/{\mathrm{m}}^2$, microsystems are controlled by much weaker adhesion $\lesssim 100\mu \mathrm{J}/{\mathrm{m}}^2$, which is critical for their operation. The weakest adhesion is related to the omnipresent fluctuation-induced dispersion forces. We develop a theory for such a weak adhesion emphasizing that the adhesion energy as a function of the average distance separating the bodies is almost entirely defined by the dispersion interaction. This dependence can be evaluated using the Lifshitz theory, but the effects of contact interaction or plastic deformations give only small contribution to the adhesion. Such a behavior is explained by a specific roughness of the deposited thin films used in microtechnologies. The films deposited on cold substrates have a much larger number of high asperities than is predicted by the Gaussian distribution and the contact occurs over a few asperities with heights much larger than the root-mean-square roughness. Finally, we discuss application of the effect for more precise determination of the distance upon contact, which is crucial for precise measurements of the dispersion forces especially at short separations in the range $5<h<50\mathrm{nm}$.

The spin Hall effect (SHE) is responsible for electrical spin current generation, which is a key concept of modern spintronics. We present a theoretical study of an extrinsic mechanism of SHE arising from a spin-dependent s-d scattering in ferromagnets. In order to investigate the spin conductivity in a ferromagnetic $3d$ alloy model, we employ a microscopic transport theory based on the Kubo formula and the averaged $T$-matrix approximation. From the model, we derived an extrinsic mechanism that contributes to both the SHE and the time-reversal odd SHE known as the magnetic SHE. This mechanism can be understood as the contribution from anisotropic (spatial-dependent) spin-flip scattering due to the combination of the orbital-dependent anisotropic shape of s-d hybridization and spin flipping, with the orbital shift caused by spin-orbit interaction with the $d$ orbitals. We also show that this mechanism is valid under crystal-field splitting among the $d$ orbitals in either the cubic or tetragonal symmetry.

A new mechanism for the topological Hall effect (THE) was recently proposed for the spiral magnet ${\mathrm{YMn}}_6{\mathrm{Sn}}_6,$ which requires transverse conical spiral magnetism, induced by external magnetic field, combined with thermally excited helical spiral magnons. In principle, this mechanism should be applicable to other itinerant spiral magnets as well. In this paper, we show that another magnetic compound, ${\mathrm{Fe}}_3{\mathrm{Ga}}_4$, in which THE was observed experimentally before, in one of its phases satisfies this condition, and the proposed theory of thermal-fluctuation-driven THE is quantitatively consistent with the experiment. This finding suggests that this mechanism is indeed rather universal, and the effect may have been observed in other compounds before but overlooked.

We propose sum rules of x-ray magnetic circularly polarized emission (XMCPE) at $L$ edges for $3d$ transition metals. By making use of combinations of incident and emitted photon helicities, $z$-component expectation values of spin, orbital, magnetic dipole, and quadrupole terms can be obtained separately. The fundamental difference in the sum rules between x-ray magnetic circular dichroism and XMCPE arises from the variety of electron transitions involving core states split by the spin-orbit interaction. The additional electron transition in XMCPE causes complicated angular dependence of the sum rule relation for the spin moment. Our findings promote future $L$-edge XMCPE measurements, which have not been observed at present.

We present a computational approach, based on density functional theory and screened configuration interaction, able to accurately treat highly correlated electron spins localized around semiconductor defects, typically occurring in the context of qubit implementations. The method is computationally not more demanding than a usual density functional theory calculation, which makes it suitable for the calculation of isolated defects, or defect complexes, typically requiring large simulation cells. We illustrate the approach by applying it to the three different charge states of the nitrogen vacancy defect in diamond and obtain very good agreement with experiment.

The relaxation of out-of-time-ordered correlators (OTOCs) has been studied as a means to characterize the scrambling properties of a quantum system. We show that the presence of local conserved quantities typically results in, at the fastest, an algebraic relaxation of the OTOC provided (i) the dynamics is local and (ii) the system follows the eigenstate thermalization hypothesis. Our result relies on the algebraic scaling of the infinite-time value of OTOCs with system size, which is typical in thermalizing systems with local conserved quantities, and on the existence of finite speed of propagation of correlations for finite-range-interaction systems. We show that time independence of the Hamiltonian is not necessary as the above conditions (i) and (ii) can occur in time-dependent systems, both periodic or aperiodic. We also remark that our result can be extended to systems with power-law interactions.