The quench dynamics in type-I inversion-symmetric Weyl semimetals (WSM) is explored in this work which, due to the form of the Hamiltonian, may be readily extended to two-dimensional Chern insulators. We analyze the role of equilibrium topological properties characterized by the Chern number of the prequench ground state in dictating the nonequilibrium dynamics of the system, specifically, the emergence of dynamical quantum phase transitions (DQPT). By investigating the ground-state fidelity, it is found that a change in the signed Chern number constitutes a sufficient but not necessary condition for the occurrence of DQPTs. Depending on the ratio of the transverse and longitudinal hopping parameters, DQPTs may also be observed for quenches lying entirely within the initial Chern phase. Additionally, we analyze the zeros of the boundary partition function discovering that while the zeros generally form two-dimensional structures resulting in one-dimensional critical times, infinitesimal quenches may lead to one-dimensional zeros with zero-dimensional critical times, provided the quench distance scales appropriately with the system size. This is strikingly manifested in the nature of nonanalyticities of the dynamical free energy, revealing a logarithmic singularity. Moreover, we show that these zero-dimensional critical times may be detected only by a direct observation of the dynamical free energy. Finally, following recent advances in observing the dynamical zeros of the Loschmidt overlap through azimuthal Bloch phase vortices, we rigorously investigate the same in WSMs, demonstrating that only one-dimensional critical times arising from two-dimensional manifolds of zeros of the boundary partition function lead to dynamical vortices.

We develop a general, fully quantum mechanical theory of Raman scattering from first principles in terms of many-body correlation functions. In order to arrive at expressions that are practically useful in the context of condensed matter physics, we adopt the Lehmann-Symanzik-Zimmermann reduction formula from high-energy physics and formulate it in the language of many-body perturbation theory. This enables us to derive a general and practically useful expression for the Raman scattering rate in terms of quantities that can be computed ab initio. Our work paves the way toward a comprehensive computational approach to the calculation of Raman spectra that goes beyond the current state of the art by capturing both excitonic and nonadiabatic effects.

The ground state of the bilayer Kitaev model with the Heisenberg-type interlayer exchange interaction is investigated by means of the exact diagonalization. Calculating the ground-state energy, local quantity defined on each plaquette, and dynamical spin structure factor, we obtain results suggesting the existence of a quantum phase transition between the Kitaev quantum spin liquid (QSL) and dimer singlet states when the interlayer coupling is antiferromagnetic. On the other hand, increasing the ferromagnetic interlayer coupling, there exists no singularity in the physical quantities, suggesting that the $S=1/2$ Kitaev QSL state realized in each layer adiabatically connects to another QSL state realized in the $S=1$ Kitaev model. Thermodynamic properties are also studied by means of the thermal pure quantum state method.

Topological Hall effect (THE) caused by a noncoplanar spin texture characterized by a scalar spin chirality is often described by the Berry phase, or the associated effective magnetic field. This picture is appropriate when the coupling $M$ of conduction electrons to the spin texture is strong (strong coupling regime) and the adiabatic condition is satisfied. However, in the weak coupling regime, where the coupling $M$ is smaller than the electrons' scattering rate, the adiabatic condition is not satisfied and the Berry phase picture does not hold. In such a regime, the relation of the effective magnetic field to the spin texture can be “nonlocal,” in contrast to the “local” relation in the strong coupling case. Focusing on continuous but general spin textures, we investigate the THE in various characteristic regions in the weak coupling regime, namely, (1) diffusive and local, (2) diffusive and nonlocal, and (3) ballistic. In the presence of spin relaxation, there arise two more regions in the “weakest coupling” regime: ($1^{\prime }$) diffusive and local and ($2^{\prime }$) diffusive and nonlocal. We derived the analytic expression of the topological Hall conductivity (THC) for each region, and found that the condition for the locality of the effective field is governed by transverse spin diffusion of electrons. In region 1, where the spin relaxation is negligible and the effective field is local, the THC is found to be proportional to $M$, instead of $M^3$ of the weakest coupling regime. In the diffusive, nonlocal regions (2 and $2^{\prime }$), the effective field is given by a spin chirality formed by “effective spins” that the electrons see during their diffusive motion. Applying the results to a skyrmion lattice, we found that the THC decreases as the skyrmion density is increased in region $2^{\prime }$, reflecting the nonlocality of the effective field, and shows a maximum at the boundary to the “local” region. For general spin textures, a scaling-like argument is given to analyze the THC in the nonlocal region. These analytic results are supplemented with numerical calculations for an isolated single skyrmion as well as for periodic textures of skyrmions and merons.

Principles of machine learning are applied to spin configurations generated by Monte Carlo method on Dzyaloshinskii-Moriya ferromagnetic models hosting the skyrmion phase in two dimensions. Successful feature predictions regarding the average spin chirality, magnetization, as well as magnetic field and temperature, were possible with the machine-learning architecture consisting of convolutional and dense neural network layers. Algorithms trained solely on the $xy$ or $z$ component of the local magnetization were as effective as the one trained on the full $xyz$ component of the input spin configuration in predicting various features. The predictive capacity of the algorithm extended beyond those configurations generated by the model used to make the training configurations, but also those generated by models plagued with disorder. A “scaling procedure” for working with data generated at various length scales is developed and proven to work in a manner analogous to the real-space renormalization process.

The iron-based superconductor $\mathrm{Rb}\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{As}}_4$ undergoes a magnetic phase transition deep in the superconducting state. We investigate the calorimetric response of $\mathrm{Rb}\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{As}}_4$ single crystals of the magnetic and the superconducting phase and its anisotropy to in-plane and out-of-plane magnetic fields. Whereas the unusual cusplike anomaly associated with the magnetic transition is suppressed to lower temperatures for fields along the crystallographic $c$ axis, it rapidly transforms to a broad shoulder shifting to higher temperatures for in-plane fields. We identify the cusp in the specific-heat data as a Berezinskii-Kosterlitz-Thouless transition with fine features caused by the three-dimensional effects. The high-temperature shoulder in high magnetic fields marks a crossover from a paramagnetically disordered to an ordered state. This observation is further supported by Monte Carlo simulations of an easy-plane two-dimensional Heisenberg model and a fourth-order high-temperature expansion, both of which agree qualitatively and quantitatively with the experimental findings.

The icosahedron-based bulk boron structures have extremely chemical and structural complexity, and are usually semiconductors at ambient conditions. Here we predict bulk boron phases with a 60-atom orthorhombic unit cell from an ab initio evolutionary structure search, termed as ${\mathrm{B}}_{60}$. The metastable structures can be either a conductor or a semimetal depending on their interstitial atomic positions. In particular, an orthorhombic structure with $Pnma$ symmetry ($Pnma-{\mathrm{B}}_{60}$), consisting of ${\mathrm{B}}_{12}$ icosahedra and twisted interstitial two-atom wide boron ribbons, is identified to be a topological node-line semimetal with potential superior electronic transport. The band structure and simulated electron-diffraction pattern of $Pnma-{\mathrm{B}}_{60}$ are in satisfactory agreement with the experimental data, suggesting that it may exist in the form of nanomaterials.

We have collected neutron-diffraction data of sufficient quality for structural refinement from deuterated ice VII to over 60 GPa. At these pressures, we are approaching the onset of molecular dissociation where the water molecule should be significantly distorted. We fitted our data with both the conventional structural model for ice VII and a recently proposed “interstitial” model. We found these to be statistically indistinguishable and, therefore, adopted the conventional model in this work. Our refinements yield the first direct experimental determination of the molecular structure in this pressure regime. They show a clear elongation of the covalent bond, the rate of which rapidly increases with pressure, indicating we have entered a distinct regime on the approach to ice X. In addition, we have directly measured the pressure dependence of the separation of the two equivalent deuteron sites along the hydrogen bonds, which provides an upper bound on the hydrogen-bond centering pressure.

We present neutron-diffraction data for the cubic-heavy-fermion YbBiPt that show broad magnetic diffraction peaks due to the fragile short-range antiferromagnetic (AFM) order persist under an applied magnetic-field $\mathbf{H}$. Our results for $\mathbf{H}\perp \left[\overline{1}10\right]$ and a temperature of $T=0.14\left(1\right)\mathrm{K}$ show that the $(\frac{1}{2},\frac{1}{2},\frac{3}{2})$ magnetic diffraction peak can be described by the same two-peak line shape found for ${\mu }_{0}H=0\mathrm{T}$ below the Néel temperature of $T_{\text{N}}=0.4\mathrm{K}$. Both components of the peak exist for ${\mu }_{0}H\lesssim 1.4\text{T}$, which is well past the AFM phase boundary determined from our new resistivity data. Using neutron-diffraction data taken at $T=0.13\left(2\right)\mathrm{K}$ for $\mathbf{H}\parallel \left[001\right]$ or $\left[110\right]$, we show that domains of short-range AFM order change size throughout the previously determined AFM and non-Fermi liquid regions of the phase diagram, and that the appearance of a magnetic diffraction peak at $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ at ${\mu }_{0}H\approx 0.4\mathrm{T}$ signals canting of the ordered magnetic moment away from $\left[111\right]$. The continued broadness of the magnetic diffraction peaks under a magnetic field and their persistence across the AFM phase boundary established by detailed transport and thermodynamic experiments present an interesting quandary concerning the nature of YbBiPt's electronic ground state.

We present a computational study of antiferromagnetic transition in ${\mathrm{RuO}}_2$. The rutile structure with the magnetic sublattices coupled with $\pi /2$ rotation leads to a spin-polarized band structure in the antiferromagnetic state, which gives rise to a $d$-wave modulation of the Fermi surface in the spin-triplet channel. We argue a finite spin conductivity that changes sign in the $ab$ plane is expected in ${\mathrm{RuO}}_2$ because of this band structure. We analyze the origin of the antiferromagnetic instability and link it to presence of a nodal line close to the Fermi level.

We report a comprehensive study of the noncentrosymmetric superconductor ${\mathrm{Mo}}_3\mathrm{P}$. Its bulk superconductivity, with $T_c=5.5\mathrm{K}$, was characterized via electrical-resistivity, magnetization, and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation/relaxation ($\mu \mathrm{SR}$) and nuclear magnetic resonance (NMR) techniques. In the normal state, NMR relaxation data indicate an almost ideal metallic behavior, confirmed by band-structure calculations, which suggest a relatively high electron density of states, dominated by the Mo $4d$ orbitals. The low-temperature superfluid density, determined via transverse-field $\mu \mathrm{SR}$ and electronic specific heat, suggest a fully gapped superconducting state in ${\mathrm{Mo}}_3\mathrm{P}$, with zero-temperature gap ${\mathrm{\Delta }}_0=0.83\mathrm{meV}$, the same as the BCS gap value in the weak-coupling case, and a zero-temperature magnetic penetration depth ${\lambda }_0=126\mathrm{nm}$. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined from zero-field $\mu \mathrm{SR}$ measurements, indicates a preserved time-reversal symmetry in the superconducting state of ${\mathrm{Mo}}_3\mathrm{P}$ and, hence, spin-singlet pairing.

The three-dimensional charge density wave (CDW) compound ${\mathrm{CuV}}_2{\mathrm{S}}_4$ is known to undergo phase transitions at $\sim 91$ and $\sim 50\mathrm{K}$. Employing single-crystal x-ray diffraction on an annealed crystal, we confirm the formation of an incommensurate CDW at $T_{\text{CDW}}\approx 91\mathrm{K}$, and we establish the nature of the transition at $T_{\text{lock-in}}\approx 50\mathrm{K}$ as a lock-in transition toward a threefold superstructure. As-grown crystals develop the same incommensurate CDW as the annealed crystal does, but they fail to go through the lock-in transition. Instead, the length of the modulation wave vector continues to decrease down to low temperatures in as-grown crystals. These findings are corroborated by distinct temperature dependencies of the electrical resistivity, magnetic susceptibility, and specific heat measured on as-grown and annealed crystals. A superspace model for the crystal structure of the incommensurate CDW suggests that the formation of extended vanadium clusters is at the origin of the CDW. In the lock-in phase, short and long V-V distances persist, but clusters now percolate the entire crystal. The lowering toward orthorhombic symmetry appears to be responsible for the precise pattern of short and long V-V distances. However, the orthorhombic lattice distortion is nearly zero for the annealed crystal, while it is visible for the as-grown material, again suggesting the role of lattice defects in the latter.

We have applied the model-mapped random phase approximation (RPA) [H. Sakakibara et al., J. Phys. Soc. Jpn. 86, 044714 (2017)] to the cuprate superconductors ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{HgBa}}_2{\mathrm{CuO}}_4$, resulting in two-orbital Hubbard models. All the model parameters are determined based on first-principles calculations. For the model Hamiltonians, we perform fluctuation exchange calculation. Results explain relative height of $T_c$ observed in experiment for ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{HgBa}}_2{\mathrm{CuO}}_4$. In addition, we give some analyses for the interaction terms in the model, especially comparisons with those of the constrained RPA.

Recently, the oxide semiconductor $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ nanoplates with an ultrahigh mobility demonstrated superior ultrafast photoelectronic properties of which physical origins are hotly studied theoretically and experimentally. Here we grew the $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystals via the chemical vapor transport method. The $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystal exhibits an ultrahigh Hall mobility $(\sim 2.24\times {10}^5\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}\mathrm{at}2\mathrm{K})$ and a giant magnetoresistance $\left(\mathrm{MR}\sim 0.9\times {10}^4\%\mathrm{at}9\mathrm{T}\mathrm{and}2\mathrm{K}\right)$ that are comparable with those in $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ nanoplates. MR data clearly shows Shubnikov–de Haas (SdH) oscillations. Systematic analysis of SdH oscillation verifies that the electrical carrier in $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ is a conventional Schrödinger fermion and that the Fermi surface of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ is quasi-two-dimensional-like. Remarkably, the resistivity of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ is quadratically dependent on temperature from 2 to 300 K, inferring the electron-electron scattering in $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$. Kohler's rule analysis of temperature-dependent MR verifies only electron-electron scattering dominated by the electrical and magnetotransport properties of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$. Combining first-principle calculations and empirical Landau Fermi liquid theory, we substantiate that the Fermi surface of the electron in $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ is an elongated ellipsoid, as well as that the electron-electron interaction and screening length of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ are estimated as 7.49 eV and 5.53 Å, respectively. These values are quite large among the conventional doped semiconductors. Our study may shed more light on the physical origin of the ultrafast photoelectric response of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$.

An analytical model for investigations of multipole coupling effects in the finite and infinite nanoparticle arrays supporting electromagnetic resonances is presented and discussed. This model considers the contributions of both electric and magnetic modes excited in the nanoparticles, including electric and magnetic dipoles and electric and magnetic quadrupoles. The magnetic quadrupole propagator (Green's tensor) that describes the electromagnetic field generated by a point magnetic quadrupole source in all wave zones is derived. As an example, we apply the developed model to study infinite two-dimensional rectangular periodic arrays of spherical silicon nanoparticles supporting the dipole and quadrupole resonant responses. The correctness and accuracy of the analytical model are confirmed by the agreement of its results with the results of full-wave numerical simulations. Using the developed model, we show the electromagnetic coupling between electric dipole and magnetic quadrupole moments as well as between magnetic dipole and electric quadrupole moments even for the case of an infinite rectangular periodic array of spherical nanoparticles. The strong suppression of the dipole or quadrupole moment due to the coupling effects is demonstrated and discussed for spherical nanoparticle arrays. The analytical expressions for the reflection and transmission coefficients written with the effective dipole and quadrupole polarizabilities are derived for normal light incidences and zero-order diffraction. The derived expressions are applied to explain the lattice anapole (invisibility) states when the incident light is transmitted unperturbed through the silicon nanoparticle array. The important role of dipole and quadrupole excitations in scattering compensation resulting in the lattice anapole effect is explicitly demonstrated. The presented approach can be used for designing metasurfaces and further utilizing them in developing ultrathin functional optical elements.

There are two types of previously known three-dimensional Dirac semimetals (DSs)—topological DSs and nonsymmorphic DSs. Here, we present a three-dimensional DS that exhibits features of both topological and nonsymmorphic DSs. We introduce a minimal tight-binding model for the space group 100 that describes a layered crystal made of two-dimensional planes in the $p4g$ wallpaper group. Using this model, we demonstrate that double glide mirrors allow a noncentrosymmetric three-dimensional DS that hosts both symmetry-enforced Dirac points at time-reversal invariant momenta and twofold-degenerate Weyl nodal lines on a glide-mirror-invariant plane in momentum space. The proposed DS allows for rich topological physics manifested in both topological surface states and topological phase diagrams, which we discuss in detail. We also perform first-principles calculations to predict that the proposed DS is realized in a set of existing materials $\mathrm{BaLa}X\mathrm{B}{Y}_5$, where $X=\text{Cu}$ or Au, and $Y=\text{O}$, S, or Se.

Finding fingerprints of disordered Weyl semimetals (WSMs) is an unsolved task. Here we report such findings in the level statistics and the fractal nature of electron wave function around Weyl nodes (WNs) of disordered WSMs. The nearest-neighbor level spacing follows a new universal distribution $P_c\left(s\right)=C_1{s}^{2}exp[-C_2{s}^{2-{\gamma }_0}]$ originally proposed for the level statistics of critical states in the integer quantum Hall systems or normal dirty metals (diffusive metals) at metal-to-insulator transitions, instead of the Wigner-Dyson distribution for diffusive metals. Numerically we find ${\gamma }_0=0.62\pm 0.07$. In contrast to the Bloch wave functions of clean WSMs that uniformly distribute over the whole space of $\left(D=3\right)$ at large length scale, the wave function of disordered WSMs at a WN occupies a fractal space of dimension $D=2.18\pm 0.05$. Away from the WN, wave function is a fractal at a length scale below a correlation length diverging at the WN as $\xi \propto {\left|E\right|}^{-\nu }$ with $\nu =0.89\pm 0.05$. Beyond the length scale, the wave function is homogeneous. In the ergodic limit, the level number variance ${\mathrm{\Sigma }}_2$ around Weyl nodes increases linearly with the average level number $N,{\mathrm{\Sigma }}_2=\chi N$, where $\chi =0.2\pm 0.1$ is independent of system sizes and disorder strengths.

We study Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions for magnetic impurities on graphene in situations where the electronic spectrum is in the form of Landau levels. Two such situations are considered: nonuniformly strained graphene, and graphene in a real magnetic field. RKKY interactions are enhanced by the lowest Landau level, which is shown to form electron states binding with the spin impurities and add a strong nonperturbative contribution to pairwise impurity spin interactions when their separation $R$ is no more than the magnetic length. Beyond this, interactions are found to fall off as $1/R^3$ due to perturbative effects of the negative-energy Landau levels. Based on these results, we develop simple mean-field theories for both systems, taking into account the fact that typically the density of states in the lowest Landau level is much smaller than the density of spin impurities. For the strain field case, we find that the system is formally ferrimagnetic, but with very small net moment due to the relatively low density of impurities binding electrons. The transition temperature is nevertheless enhanced by them. For real fields, the system forms a canted antiferromagnet if the field is not so strong as to pin the impurity spins along the field. The possibility that the system in this latter case supports a Kosterlitz–Thouless transition is discussed.

In the presence of crossed electric and magnetic fields, a graphene ribbon has chiral states running along sample edges and along boundaries between $p$-doped and $n$-doped regions. We here consider the scattering of edge states into interface states, which takes place wherever the $pn$ interface crosses the sample boundary, as well as the reverse process. For a graphene ribbon with armchair boundaries, the evolution of edge states into interface states and vice versa is governed by the conservation of valley isospin. Although valley isospin is not conserved in simplified models of a ribbon with zigzag boundaries, we find that arguments based on isospin conservation can be applied to a more realistic modeling of the graphene ribbon, which takes account of the lifting of electron-hole degeneracy. The valley isospin of interface states is an important factor determining the conductance of a graphene $pn$ junction in a quantizing magnetic field.