Energy band nodal structures (nodal points/lines/surfaces) in the Brillouin zone (BZ) have received immense research interest in the past decade, while their complete classification is still lacking. Here, we focus on all the 1651 magnetic space groups (MSGs) and 528 magnetic layer groups (MLGs) to provide a dataset of all symmetry-diagonalizable strictly and nearly nodal structures emanating from band nodes (BNs) at symmetric $k$ points. Using our dataset, one can quickly know their $k·p$ models. Based on the $k·p$ models, we find that charge-4 Weyl nodal point, thought to only exist in the spinless setting before, can exist in the spinful setting. Our dataset can also be applied to quickly identify the associated nodal structures, which can be composed of several nodal lines or/and surfaces given a BN. In this way, we identify nodal lines which are flexible but only fixed at one point in the BZ. Our classification includes both spinful and spinless settings with the latter applicable for bosons like phonons and electronic materials with negligible spin-orbit coupling. We show that the same as BNs, the nodal structures, especially the nearly nodal surfaces, are also ubiquitous. Finally, we predict hundreds of ever-synthesized magnetic materials with essential extended nodal lines or surfaces and one charge-4 Weyl magnetic material.

A magnetic toroidal moment is a fundamental electronic degree of freedom in the absence of both spatial inversion and time-reversal symmetries and gives rise to novel multiferroic and transport properties. We elucidate essential model parameters of the nonlinear transport in the space-time $\left(\mathcal{PT}\right)$ symmetric collinear antiferromagnetic metals accompanying a magnetic toroidal moment. By analyzing the longitudinal and transverse components of the second-order nonlinear conductivity on a two-dimensionally stacked zigzag chain based on the nonlinear Kubo formula, we show that an effective coupling between the magnetic toroidal moment and the antisymmetric spin-orbit interaction is an essential source of the nonlinear conductivity. Moreover, we find that the nonreciprocal longitudinal current and nonlinear transverse current in a multiband system are largely enhanced just below the transition temperature of the antiferromagnetic ordering. We also discuss the relevance of the nonlinear conductivity to the linear magnetoelectric coefficient and conductivity. Our result serves as a guide for exploring the microscopic essence and clarifying the parameter dependence of the nonlinear conductive phenomena in ferrotoroidal metals.

Phase transitions occur in a wide range of physical systems and are characterized by the abrupt change of a physical observable in response to the variation of an external control parameter. Phase transitions are not restricted to equilibrium situations but can also be found in nonequilibrium settings, both for classical and quantum mechanical systems. Here, we investigate a nonequilibrium phase transition in a single-electron micromaser consisting of a microwave cavity that is driven by the electron transport in a double quantum dot. For weak electron-photon couplings, only a tiny fraction of the transferred electrons are accompanied by the emission of photons into the cavity, which essentially remains empty. However, as the coupling is increased, many photons are suddenly emitted into the cavity. Employing ideas and concepts from full counting statistics and Lee-Yang theory, we analyze this nonequilibrium phase transition based on the dynamical zeros of the factorial moment generating function of the electronic charge transport statistics, and we find that the phase transition can be predicted from short-time measurements of the higher-order factorial cumulants. These results pave the way for further investigations of critical behavior in open quantum systems.

Achievement of low spin-relaxation rate is an important goal for spintronics development. We study the spin-relaxation rate arising from a low concentration of magnetic impurities in armchair graphene nanoribbons (AGNR). Large suppression in the spin-relaxation rate, exhibited as dip structures, is found when the Fermi energy approaches a subband band edge. This suppression originated from the quasi-one-dimensional density of states and is manifested via the singular features in the AGNR same-site Green's function $G_{\mathcal{II}}$, where $\mathcal{I}$ denotes site locations of magnetic impurities. Analytic analysis of the spin-relaxation rate in the close vicinity of a subband band edge is performed to further reveal the physical nature of the suppression. The robustness of the suppression feature in the spin-relaxation rate is demonstrated by systematically increasing the number of magnetic impurities involved in a coherent multiple scattering with the electrons. Major peaks in the spin-relaxation rate are analyzed in light of their connection with spin-flipped resonances. Competition between magnetic impurities with similar resonance energies is found to lead to suppression in the spin-relaxation rate. Our calculations have taken into account the hydrogen-passivation effects at the AGNR edges when the hopping constant between edge carbons is modified.

Emergent excitation continua in frustrated magnets are a fingerprint of fractionalization, characteristic of quantum spin-liquid states. Recent evidence from Raman scattering for a coupling between such continua and lattice degrees of freedom in putative Kitaev magnets may provide insight into the nature of the fractionalized quasiparticles. Here we study the renormalization of optical phonons coupled to the underlying ${\mathbb{Z}}_2$ quantum spin liquid. We show that phonon line shapes acquire an asymmetry, observable in light scattering and originating from two distinct sources, namely, the dispersion of the Majorana continuum and the Fano effect. Moreover, we find that the phonon lifetimes increase with increasing temperature due to thermal blocking of the available phase space. Finally, in contrast to low-energy probes, optical phonon renormalization is rather insensitive to thermally excited gauge fluxes and barely susceptible to external magnetic fields.

We present the theoretical results for the Majorana band structure and thermal transport properties in the Kitaev honeycomb model under a staggered magnetic field in addition to a uniform one. The Majorana band structure is asymmetrically modulated in momentum space, and the valley degree of freedom is activated and controlled by the magnitudes and directions of the uniform and staggered magnetic fields; as a result, the Majorana excitation is either gapped or gapless, the latter of which in general has Majorana Fermi surfaces, in contrast to the point nodes in the absence of the fields. We show that the asymmetric deformation of the Majorana band leads to a nonreciprocal thermal transport. The field dependence of the linear thermal conductivity is correlated with the magnitude of the Majorana gap, while that of the nonlinear thermal conductivity is associated with the asymmetry of the Majorana excitation spectra. We show the estimates of the thermal currents and discuss that the linear response is experimentally measurable, whereas future improvement is required for the observation of the nonlinear one. We also discuss how the thermal currents are modulated by other additional effects of the magnetic field and contributions from conventional magnons, the latter of which are expected in heterostructures to realize an internal staggered magnetic field.

A computationally efficient workflow for obtaining the low-energy symmetric tight-binding Hamiltonians for twisted multilayer systems is presented in this work. We apply this scheme to twisted bilayer graphene at the first magic angle. As the initial step, the full-energy tight-binding Hamiltonian is generated by the Slater-Koster model with parameters fitted to ab initio data at larger angles. Then, the low-energy symmetric four-band and 12-band Hamiltonians are constructed using the maximum-localization procedure subjected to crystal- and time-reversal-symmetry constraints. Finally, we compute extended Hubbard parameters for both models within the constrained random phase approximation for screening, which again respect the symmetries. Our workflow, exemplified in this work on twisted bilayer graphene, is straightforwardly transferable to other twisted multilayer materials.

Fabry-Pérot interferometry has emerged as a tool to probe anyon statistics in the quantum Hall effect. The interference phase is interpreted as a combination of a quantized statistical phase and an Aharonov-Bohm phase, proportional to the device area and the charge of the anyons propagating along the device edge. This interpretation faces two challenges. First, the edge states have a finite width and hence the device area is ill-defined. Second, multiple localized anyons may be present in states that overlap with the edge, and it may not be clear whether a second anyon traveling along the edge will go inside or outside the region with a localized anyon and therefore whether or not it should pick up a statistical phase. We show how one may overcome both challenges. In a case where only one chiral edge mode passes through the constrictions defining the interferometer, as when electrons in a constriction are in a Laughlin state with $\nu =1/(2n+1)$ or the integer state at $\nu =1$, we show that the interference phase can be directly related to the total electron charge contained in the interferometer. This holds for arbitrary electron-electron interactions and holds even if the bulk of the interferometer has a higher electron density than the region of the constrictions. In contrast to the device area or to the number of anyons inside a propagating edge channel, the total charge is well-defined. We examine, at the microscopic level, how the relation between charge and phase is maintained when there is a soft confining potential and disorder near the edge of the interferometer, and we discuss briefly the complications that can occur when multiple chiral modes can pass through the constriction.

Acoustics recently became a versatile platform for discovering novel physical effects and concepts at a relatively simple technological level. In this way, single resonators and the structure of their resonant modes play a central role and define the properties of complex acoustic systems such as acoustic metamaterials, phononic crystals, and topological structures. In this paper, we present a powerful method allowing a qualitative analysis of eigenmodes of resonators in the linear monochromatic acoustic domain based on multipole classification of eigenmodes. Using the apparatus of group theory, we explain and predict the structure of the scattered field knowing only the symmetry group of the resonator by connecting the multipolar content of incident and scattered fields. Such an approach can be utilized for developing resonators with predesigned properties avoiding time-consuming simulations. We performed full multipole symmetry classification for a number of resonators geometries and tightened it with scattering spectra profiles.

In the latest experimental success in the field of two-dimensional materials, $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{S}}_4$ nanosheets with a highly appealing efficiency for photocatalytic hydrogen evolution were synthesized [S. Zhang et al., ACS Nano 15, 15238 (2021)]. Motivated by this accomplishment, herein, we conduct first-principles-based calculations to explore the physical properties of the $\mathrm{Zn}{\mathrm{In}}_2{X}_4$ ($X$ = S, Se, Te) monolayers. The results confirm the desirable dynamical and mechanical stability of the $\mathrm{Zn}{\mathrm{In}}_2{X}_4$ monolayers. $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{S}}_4$ and $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{Se}}_4$ are semiconductors with direct band gaps of 3.94 and 2.77 eV, respectively while $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{Te}}_4$ shows an indirect band gap of 1.84 eV. The optical properties achieved from the solution of the Bethe-Salpeter equation predict the exciton binding energy of the $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{S}}_4$, $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{Se}}_4$, and $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{Te}}_4$ monolayers to be 0.51, 0.41, and 0.34 eV, respectively, suggesting the high stability of the excitonic states against thermal dissociation. Using the iterative solutions of the Boltzmann transport equation accelerated by machine learning interatomic potentials, the room-temperature lattice thermal conductivity of the $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{S}}_4$, $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{Se}}_4$, and $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{Te}}_4$ monolayers is predicted to be remarkably low as 5.8, 2.0, and 0.4 W/mK, respectively. Due to the low lattice thermal conductivity, high thermopower, and large figure of merit, we propose the $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{Se}}_4$ and $\mathrm{Zn}{\mathrm{In}}_2{\mathrm{Te}}_4$ monolayers as promising candidates for thermoelectric energy conversion systems. This study provides an extensive vision concerning the intrinsic physical properties of the $\mathrm{Zn}{\mathrm{In}}_2{X}_4$ nanosheets and highlights their characteristics for energy conversion and optoelectronics applications.

We consider the three-dimensional spin-orbit-coupled Luttinger semimetal of “spin” $3/2$ particles in presence of weak attractive interaction in the $l=1$ ($p$-wave) channel, and determine the low-temperature phase diagram for both particle- and hole dopings. The phase diagram depends crucially on the sign of the chemical potential, with two different states (with total angular momentum $j=0$ and $j=3$) competing on the hole-doped side, and three (one $j=1$ and two different $j=2$) states on the particle-doped side. The ground-state condensates of Cooper pairs with the total angular momentum $j=1,2,3$ are selected by the quartic, and even sextic terms in the Ginzburg-Landau free energy. Interestingly, we find that all the $p$-wave ground states appearing in the phase diagram, while displaying different patterns of reduction of the rotational symmetry, preserve time reversal. The resulting quasiparticle spectrum is either fully gapped or with point nodes, with nodal lines being absent.

The addition of spatial inversion asymmetry and significant spin-orbit coupling to synthetic antiferromagnets (SAFs) has led to a lot of fundamental discoveries and technological applications. Here, we experimentally demonstrate that the critical magnetic field for breaking the degeneracy of monochiral domain walls (DWs) to realize the spin-orbit torque (SOT)-induced magnetization switching can be varied in a wide range from field free to $3000\mathrm{Oe}$ in perpendicularly magnetized CoPt/Ru/CoPt SAFs with strong interlayer antiferromagnetic coupling, which strongly depends on the interfacial Dzyaloshinsky-Moriya interaction (DMI) and SOT at the bottom and top interfaces with multiple inversion asymmetries. Our DW dynamical calculations further reveal that the field-free magnetization switching is caused by SOT-induced left-handed chiral Néel DW displacement under the condition that the interfacial DMI of the upper magnetic layer has a significantly smaller value than that of the lower magnetic layer. These findings provide key insights for understanding the role of SOT and DMI in magnetization switching of magnetically coupled chiral systems and pave the way to practical applications of SAFs.

Recent experimental results of angle-resolved photoemission spectroscopy suggested that an additional strong nearest neighbor attraction in the Hubbard model might be significant for the doped cuprates. The stripe-ordered patterns, which are formed by the inhomogeneous distribution of spin, charge, and pairing correlations in ${\mathrm{CuO}}_2$ planes, are a well-known feature of the doped cuprates. By employing constrained path quantum Monte Carlo, we examine the effect of the nearest neighbor attraction on a two-dimensional repulsive Hubbard model. Within and across the stripe regions, the ground-state spin correlations and the $d$-wave pairing correlation are calculated. We found that the spin-spin correlation is the largest when the interstripe region is nearly half filled, and we also found the $d$-wave superconducting correlation of the neighboring sites is enhanced in the presence of the stripe pattern. This reveals the crucial effects of the strong nearest neighbor attraction on superconductivity in doped cuprates.

Various successful approaches using numerical annealing and renormalization groups have been conceived to study the thermodynamics of strongly correlated systems where perturbation or expansion theories fail to work. As the process of lowering the temperatures is usually involved in different manners, these approaches in general become much less efficient or accurate at the low temperatures. In this work, we propose to access the finite-temperature properties from the tensor network (TN) representing the zero-temperature partition function. We propose to “scissor” a finite part from such an infinite-size TN and “stitch” it to possess the periodic boundary condition along the imaginary-time direction. We dub this approach “TN tailoring.” Exceptional accuracy is achieved with a fine-tuning process, surpassing the previous methods including the linearized tensor renormalization group [W. Li, S.-J. Ran, S.-S. Gong, Y. Zhao, B. Xi, F. Ye, and G. Su, Phys. Rev. Lett. 106, 127202 (2011)], the continuous matrix product operator [W. Tang, H.-H. Tu, and L. Wang, Phys. Rev. Lett. 125, 170604 (2020)], etc. High efficiency is demonstrated, where the time cost is nearly independent of the target temperature, including the extremely low temperatures. The proposed idea can be extended to higher-dimensional systems of bosons and fermions.

Multiterminal Josephson junctions have aroused considerable theoretical interest recently and numerous works aim at putting the predictions of correlations among Coopers (i.e., the so-called quartets) and simulation of topological matter to the test of experiments. This paper is motivated by recent experimental investigation from the Harvard group reporting $h/4e$-periodic quartet signal in a four-terminal configuration containing a loop pierced by magnetic flux, together with inversion controlled by the bias voltage, i.e., the quartet signal can be larger at half-flux quantum than in zero magnetic field. Here, we theoretically focus on devices consisting of finite-size quantum dots connected to four superconducting leads and to a normal lead. In addition to presenting numerical calculations of the quartet signal within a simplified modeling, we reduce the device to a non-Hermitian Hamiltonian in the infinite-gap limit. Then, relaxation has the surprising effect of producing sharp peaks and log-normal variations in the voltage sensitivity of the quartet signal in spite of the expected moderate fluctuations in the two-terminal DC Josephson current. The phenomenon is reminiscent of a resonantly driven harmonic oscillator having amplitude inverse proportional to the damping rate, and of the thermal noise of a superconducting weak link, inverse proportional to the Dynes parameter. Perspectives involve quantum bath engineering multiterminal Josephson junctions in the circuits of cavity quantum electrodynamics.

The influence of spin-orbit interaction on the unoccupied electronic structure of the Re(0001) surface is investigated by spin- and angle-resolved inverse photoemission and density-functional theory calculations. In the two high-symmetry azimuths $\overline{\mathrm{\Gamma }}\overline{\text{K}}$ and $\overline{\mathrm{\Gamma }}\overline{\text{M}}$, we identify transitions into $d$-derived bulk states as well as different types of surface states. The Rashba-type spin-split hole pocket around $\overline{\mathrm{\Gamma }}$ finds continuation in empty spin-split surface states for higher ${\mathbf{k}}_{\parallel }$, thereby forming $\mathsf{W}$-shaped states whose lower parts are partially occupied. A large energy gap below and above the vacuum energy around $\overline{\mathrm{\Gamma }}$ hosts image-potential-induced surface states. The $n=1$ member of the Rydberg-like series exhibits a free-electron-like $E\left({\mathbf{k}}_{\parallel }\right)$ dispersion with an effective mass of $m^{*}/m_e=1.2\pm 0.1$. Careful spin-resolved measurements for several angles of electron incidence allow us to detect Rashba-type spin-dependent energy splittings of this state with a Rashba parameter of ${\alpha }_{\text{R}}=105\pm 33\text{meV}\AA$.

Nonanalytic points in the return probability of a quantum state as a function of time, known as dynamical quantum phase transitions (DQPTs), have received great attention in recent years, but the understanding of their mechanism is still incomplete. In our recent work [Phys. Rev. Lett. 126, 040602 (2021)], we demonstrated that one-dimensional DQPTs can be produced by two distinct mechanisms, namely semiclassical precession and entanglement generation, leading to the definition of precession (pDQPTs) and entanglement (eDQPTs) dynamical quantum phase transitions. In this manuscript, we extend and investigate the notion of p- and eDQPTs in two-dimensional systems by considering semi-infinite ladders of varying width. For square lattices, we find that pDQPTs and eDQPTs persist and are characterized by similar phenomenology as in 1D: pDQPTs are associated with a magnetization sign change and a wide entanglement gap, while eDQPTs correspond to suppressed local observables and avoided crossings in the entanglement spectrum. However, DQPTs show higher sensitivity to the ladder width and other details, challenging the extrapolation to the thermodynamic limit especially for eDQPTs. Moving to honeycomb lattices, we also demonstrate that lattices with an odd number of nearest neighbors give rise to phenomenologies beyond the one-dimensional classification.

Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge $Q$ and scaling dimension $\mathrm{\Delta }$. For the simplest states (such as the Laughlin series), the scaling dimension determines the anyonic statistics of the quasiparticle (the statistical phase $\theta =2\pi \mathrm{\Delta }$). For more complicated states (featuring counterpropagating modes or non-Abelian statistics), knowing the scaling dimension is not enough to extract the quasiparticle statistics. Nevertheless, even in those cases, knowing the scaling dimension facilitates distinguishing different candidate theories for describing the quantum Hall state at a particular filling (such as PH-Pfaffian and anti-Pfaffian at $\nu =\frac{5}{2}$). Here, we propose a scheme for extracting the scaling dimension of quantum Hall quasiparticles from thermal tunneling noise produced at a quantum point contact. Our scheme makes only minimal assumptions about the edge structure and features the level of robustness, simplicity, and model independence comparable with extracting the quasiparticle charge from tunneling shot noise.