We measure collective excitations of a harmonically trapped two-dimensional (2D) SU($N$) Fermi gas of ${}^{173}\mathrm{Yb}$ confined to a stack of layers formed by a one-dimensional optical lattice. Quadrupole and breathing modes are excited and monitored in the collisionless regime $|ln(k_F{a}_{2D}\left)\right|\gg 1$ with tunable spin. We observe that the quadrupole mode frequency decreases with increasing number of spin components due to the amplification of the interaction effect by $N$ in agreement with a theoretical prediction based on 2D kinetic equations. The breathing mode frequency, however, is measured to be twice the dipole oscillation frequency regardless of $N$. We also follow the evolution of collective excitations in the dimensional crossover from two to three dimensions and characterize the damping rate of quadrupole and breathing modes for tunable SU($N$) fermions, both of which reveal the enhanced interparticle collisions for larger spin. Our result paves the way to investigate the collective property of 2D SU($N$) Fermi liquid with enlarged spin.

We investigate the intrinsic magnon spin current in a noncollinear antiferromagnetic insulator. We introduce a definition of the magnon spin current in a noncollinear antiferromagnet and find that it is in general nonconserved, but for certain symmetries and spin polarizations the averaged effect of nonconserving terms can vanish. We formulate a general linear response theory for magnons in noncollinear antiferromagnets subject to a temperature gradient and analyze the effect of symmetries on the response tensor. We apply this theory to single-layer potassium iron jarosite ${\mathrm{KFe}}_3{\left(\mathrm{OH}\right)}_6{\left({\mathrm{SO}}_4\right)}_2$ and predict a measurable spin current response.

I construct a diagrammatic technique for non-Hermitian fermionic systems which allows addressing correlation effects in the steady state by systematic expansion. Applying this method to exceptional points or rings, I find that nodal objects in non-Hermitian systems are generically displaced in momentum-space due to interactions. This is a consequence of the fact that exceptional points invariably break a class of orthonormal symmetries that are generally present for nodal points in Hermitian systems and which protect the integrity of the node at low energy scales.

Bravais lattices are the most fundamental building blocks of crystallography. They are classified into groups according to their translational, rotational, and inversion symmetries. In computational analysis of Bravais lattices, fulfillment of symmetry conditions is usually determined by analysis of the metric tensor, using either a numerical tolerance to produce a binary (i.e., yes or no) classification or a distance function which quantifies the deviation from an ideal lattice type. The metric tensor, though, is not scale invariant, which complicates the choice of threshold and the interpretation of the distance function. Here, we quantify the distance of a lattice from a target Bravais class using strain. For an arbitrary lattice, we find the minimum-strain transformation needed to fulfill the symmetry conditions of a desired Bravais lattice type; the norm of the strain tensor is used to quantify the degree of symmetry breaking. The resulting distance is invariant to scale and rotation, and is a physically intuitive quantity. By symmetrizing to all Bravais classes, each lattice can be placed in a 14-dimensional space, which we use to create a map of the space of Bravais lattices and the transformation paths between them. A software implementation is available online under a permissive license.

Kitaev materials are promising for realizing exotic quantum spin liquid phases, such as a non-Abelian chiral spin liquid. Motivated by recent experiments in these materials, we theoretically study the novel field-induced quantum phase transitions from the non-Abelian chiral spin liquid to the symmetry-broken zigzag phase and to the trivial polarized state. Utilizing the recently developed dualities of gauge theories, we find these transitions can be described by critical bosons or gapless fermions coupled to emergent non-Abelian gauge fields, and the critical theories are of the type of a ${\mathrm{QCD}}_3$-Chern-Simons theory. We propose that all these exotic quantum phase transitions can potentially be direct and continuous in Kitaev materials, and we present sound evidence for this proposal. Therefore, besides being systems with intriguing quantum magnetism, Kitaev materials may also serve as table-top experimental platforms to study the interesting dynamics of emergent strongly interacting quarks and gluons in $2+1$ dimensions.

We use quantum electrodynamics and the confinement-induced nonlocal dielectric response model based on the Keldysh-Rytova electron interaction potential to study the epsilon-near-zero modes of metallic films in the transdimensional regime. Peculiar effects are revealed such as the plasmon mode degeneracy lifting and the dipole emitter coupling to the split epsilon-near-zero modes, leading to thickness-controlled spontaneous decay with rates increased by up to three orders of magnitude.

Interaction-driven symmetry breaking in a metallic (doped) Dirac system can manifest in the spontaneous gap generation at the nodal point buried below the Fermi level. Across this transition linear conductivity remains finite, making its direct observation difficult in linear transport. We propose the nonlinear Hall effect as a direct probe of this transition when inversion symmetry is broken. Specifically, for a two-dimensional Dirac material with a tilted low-energy dispersion, we predict a transformation of the characteristic interband resonance peak into a non-Lorentzian form in the collisionless regime. Furthermore, we show that inversion-symmetry-breaking quantum phase transition is controlled by an exotic tilt-dependent line of critical points. As this line is approached from the ordered side, the nonlinear Hall conductivity is suppressed owing to the scattering between the strongly coupled incoherent fermionic and bosonic excitations. Our results should motivate further studies of nonlinear responses in strongly interacting Dirac materials.

We report a strain-induced direct-to-indirect band gap transition in mechanically deformed $\mathrm{W}{\mathrm{S}}_2$ monolayers (MLs). The necessary amount of strain is attained by proton irradiation of bulk $\mathrm{W}{\mathrm{S}}_2$ and the ensuing formation of 1-ML-thick, ${\mathrm{H}}_2$-filled domes. The electronic properties of the curved MLs are mapped by spatially and time-resolved microphotoluminescence, revealing the mechanical stress conditions that trigger the variation of the band gap character. This general phenomenon, also observed in $\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{WS}{\mathrm{e}}_2$, further increases our understanding of the electronic structure of transition metal dichalcogenide MLs and holds a great relevance for their optoelectronic applications.

“Magnetic monopole” is an exotic quantum excitation in three-dimensional U(1) spin liquid, and its emergence is purely of quantum origin and has no classical analog. We predict topological thermal Hall effect (TTHE) of “magnetic monopoles” and present this prediction through non-Kramers doublets on a pyrochlore lattice. We observe that when the external magnetic field polarizes the Ising component of the local moment, internally this corresponds to the induction of emergent dual U(1) gauge flux for the “magnetic monopoles.” The motion of “magnetic monopoles” is then twisted by the induced dual U(1) gauge flux. This emergent Lorentz force on “magnetic monopoles” is the fundamental origin of TTHE. Therefore, TTHE would be a direct evidence of the “monopole” gauge coupling and the emergent U(1) gauge structure in pyrochlore U(1) spin liquid. Our result does not depend strongly on our choice of non-Kramers doublets for our presentation and can be well extended to Kramers doublets. Our prediction can be readily tested among the pyrochlore spin liquid candidate materials. We give a detailed discussion about the expectation for different pyrochlore magnets.

We present a unified description of the response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$ to applied magnetic fields along the orthorhombic directions $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$. This description is based on the minimal nearest-neighbor $J-K-\mathrm{\Gamma }$ model and builds on the idea that the incommensurate counter-rotating order observed experimentally at zero field can be treated as a long-distance twisting of a nearby commensurate order with six spin sublattices. The results reveal that the behavior of the system for $\mathbf{H}\parallel \mathbf{a}$, $\mathbf{H}\parallel \mathbf{b}$, and $\mathbf{H}\parallel \mathbf{c}$ share a number of qualitative features, including (i) a strong intertwining of the modulated, counter-rotating order with a set of uniform orders; (ii) the disappearance of the modulated order at a critical field $H^{*}$, whose value is strongly anisotropic with $H_{\mathbf{b}}^{*}<H_{\mathbf{c}}^{*}\ll H_{\mathbf{a}}^{*}$; (iii) the presence of a robust zigzag phase above $H^{*}$; and (iv) the fulfillment of the Bragg peak intensity sum rule. It is noteworthy that the disappearance of the modulated order for $\mathbf{H}\parallel \mathbf{c}$ proceeds via a “metamagnetic” first-order transition which does not restore all broken symmetries. This implies the existence of a second finite-$T$ phase transition at higher magnetic fields. We also demonstrate that quantum fluctuations give rise to a significant reduction of the local moments for all directions of the field. The results for the total magnetization for $\mathbf{H}\parallel \mathbf{b}$ are consistent with available data and confirm a previous assertion that the system is very close to the highly frustrated $K-\mathrm{\Gamma }$ line in parameter space. Our predictions for the magnetic response for fields along $\mathbf{a}$ and $\mathbf{c}$ await experimental verification.

Weyl semimetals (WSMs) are characterized by topologically stable pairs of nodal points in the band structure that typically originate from splitting a degenerate Dirac point by breaking symmetries such as time-reversal or inversion symmetry. Within the independent-electron approximation, the transition between an insulating state and a WSM requires the local creation or annihilation of one or several pairs of Weyl nodes in reciprocal space. Here, we show that strong electron-electron interactions may qualitatively change this scenario. In particular, we reveal that the transition to a Weyl semimetallic phase can become discontinuous, and, quite remarkably, pairs of Weyl nodes with a finite distance in momentum space suddenly appear or disappear in the spectral function. We associate this behavior with the buildup of strong many-body correlations in the topologically nontrivial regions, manifesting in dynamical fluctuations in the orbital channel. We also highlight the impact of electronic correlations on the Fermi arcs.

Symmetry indicators have proven to be extremely helpful in identifying topological crystalline insulators using symmetry-group representations of their Bloch states. An extension of this approach to superconducting systems requires defining an appropriate atomic limit for Bogoliubov-de-Gennes Hamiltonians. Here, we introduce such a notion of atomic limit and derive a ${\mathbb{Z}}_{2^d}$-valued symmetry indicator for inversion-symmetric superconductors in $d$ dimensions. This indicator allows for a refined topological classification including higher-order phases for systems in the superconducting symmetry classes D and DIII. We further elucidate their bulk-boundary correspondence using Dirac surface theories. Requiring only the normal-state band structure and the superconducting order-parameter symmetry as input, this indicator is well suited for a search of topological superconductors using first-principles calculations.

The multiferroic ferrimagnet ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ with a chiral crystal structure has attracted a lot of recent attention due to the emergence of a magnetic skyrmion order in this material. Here, the topological properties of its magnon excitations are systematically investigated by linear spin-wave theory and inelastic neutron scattering. When considering Heisenberg exchange interactions only, two degenerate Weyl magnon nodes with topological charges $\pm 2$ are observed at high-symmetry points. Each Weyl point splits into two as the symmetry of the system is further reduced by including into consideration the nearest-neighbor Dzyaloshinskii-Moriya interaction, crucial for obtaining an accurate fit to the experimental spin-wave spectrum. Also, one additional pair of Weyl points appears near the $\mathbf{R}$ point. The predicted topological properties are verified by surface state and Chern number analysis. Additionally, we predict that a measurable thermal Hall conductivity can be associated with the emergence of the Weyl points, the position and number of which can be tuned by modifying the Dzyaloshinskii-Moriya interaction in the system.

We present a full description of the nonergodic properties of wave functions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization lengths: the largest one describes localization along rare branches and diverges with a critical exponent ${\nu }_{\parallel }=1$ at the transition. The second length, which describes localization along typical branches, reaches at the transition a finite universal value (which depends only on the connectivity of the graph), with a singularity controlled by a new critical exponent ${\nu }_{\perp }=1/2$. We show numerically that these two localization lengths control the finite-size scaling properties of key observables: wave-function moments, correlation functions, and spectral statistics. Our results are identical to the theoretical predictions for the typical localization length in the many-body localization transition, with the same critical exponent. This strongly suggests that the two transitions are in the same universality class and that our techniques could be directly applied in this context.

We uncover an unexpected family of in-gap chiral edge states in noninverted spin-1 Dirac quantum dots. The system represents a topologically trivial confinement configuration where such edge states are not expected according to the conventional wisdom. In particular, for a massive type of confining potential, two distinct situations can arise: with or without mass sign change, corresponding to a quantum dot with or without band inversion, respectively. The former case is conventional, where topologically protected chiral edge modes can arise in the gap. For the latter, contrary to the belief that there should be no one-way current-carrying edge channels, we find the surprising emergence of such edge states and the spin-1 analog of Majorana modes. These states are strikingly robust and immune to backscattering. In the presence of a magnetic field, the edge states result in peculiar Fock-Darwin states originated from Landau-level confinement. The unexpected phenomenon is also validated in systems with bulk-topology regularization through (1) a properly regularized continuum model and (2) an experimentally accessible tight-binding dice lattice system.

Recent evidence from magnetic torque, electron spin resonance, and second harmonic generation indicate that the prototypical quantum spin liquid candidate, herbertsmithite, has a symmetry lower than its x-ray refined trigonal space group. Here we consider known and possible distortions of this mineral class, along with related copper kagome oxides and fluorides, relate these to possible valence bond patterns, and comment on their relevance to the physics of these interesting materials.

Amorphous systems have rapidly gained attention as promising platforms for topological matter. In this work, we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By carrying out a finite-size scaling analysis of topological invariants averaged over discrete and continuum random geometries, we discover critical properties of Chern and ${\mathbb{Z}}_2$ glass transitions. Even for short-range hopping models, the Chern glass phase may persist down to the fundamental lower bound given by the classical percolation threshold. While the topological indices accurately satisfy the postulated one-parameter scaling, they do not generally flow to the closest integer value in the thermodynamic limit. Furthermore, the value of the critical exponent describing the diverging localization length varies continuously along the phase boundary and is not fixed by the symmetry class of the Hamiltonian. We conclude that the critical behavior of amorphous topological systems exhibit characteristic features not observed in disordered systems, motivating a wealth of interesting research directions.

We study Josephson junctions based on second-order topological superconductors (SOTSs) which can be realized in quantum spin Hall insulators with a large inverted gap in proximity to unconventional superconductors. We find that tuning the chemical potential in the superconductor strongly modifies the induced pairing of the helical edge states, resulting in topological phase transitions. In a corresponding Josephson junction, a $0-\pi$ transition is realized by tuning the chemical potentials in the superconducting leads. This striking feature is stable in junctions with respect to different sizes, doping the normal region, and the presence of disorder. Our transport results can serve as novel experimental signatures of SOTSs. Moreover, the $0-\pi$ transition constitutes a fully electric way to create or annihilate Majorana bound states in the junction without any magnetic manipulation.

When two lasers are applied to a noncentrosymmetric material, it can generate light at the difference of the incoming frequencies $\mathrm{\Delta }\omega$, a phenomenon known as difference frequency generation (DFG), well characterized in semiconductors. In this work, we derive a general expression for DFG in metals, which we use to show that the DFG in chiral topological semimetals under circular polarized light is quantized in units of $e^3/h^2$ and independent of material parameters, including the scattering time $\tau$, when $\mathrm{\Delta }\omega \gg {\tau }^{-1}$. In this regime, DFG provides a simpler alternative to measure a quantized response in metals compared to previous proposals based on single frequency experiments. Our general derivation unmasks, in addition, a free-carrier contribution to the circular DFG beyond the semiclassical one. This contribution can be written as a Fermi surface integral, features strong frequency dependence, and oscillates with a $\pi /2$ shift with respect to the quantized contribution. We make predictions for the circular DFG of chiral and nonchiral materials using generic effective models, and ab initio calculations for TaAs and RhSi. Our work provides a complete picture of the DFG in the length gauge approach, in the clean, noninteracting limit, and highlights a plausible experiment to measure topologically quantized photocurrents in metals.

We demonstrate efficient intrinsic spin-to-charge current conversion in a two-dimensional electron gas using an all-epitaxial single-crystal heterostructure of $\mathrm{LaSrMn}{\mathrm{O}}_3/\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$, which can suppress spin scattering and give us an ideal environment to investigate intrinsic spin-charge conversion. With decreasing temperature to 20 K, the spin-to-charge conversion efficiency is drastically enhanced to $+6.7\mathrm{nm}$. Our band-structure calculation well reproduces this behavior and predicts further enhancement by controlling the density and relaxation time of the carriers.