Selenium is the only easily vitrified elementary substance. Numerous experimental studies of glassy Se ($g$-Se) at high pressures show a large spread in the data on the compressibility and electrical resistivity of $g$-Se. Furthermore, H. Liu et al. [Proc. Natl. Acad. Sci. USA 105, 13229 (2008)] have arrived at the surprising conclusion that the volume of glass increases during pressure-induced crystallization. We have performed high-precision measurements of the specific volume and electrical resistivity of glassy selenium ($g$-Se) at high hydrostatic pressures up to 9 GPa. The measured bulk modulus at normal pressure is $B=\left(9.05\pm 0.15\right)$ GPa and its pressure derivative is $B_P^{\prime }=6.4\pm 0.2$. In the pressure range $\mathrm{P}<3$ GPa, glassy selenium has an anomalously large negative second derivative of the bulk modulus. The electrical resistivity of $g$-Se decreases almost exponentially with increasing pressure and reaches 20 $\mathrm{\Omega }$ cm at a pressure of 8.75 GPa. The inelastic behavior and weak relaxation of the volume for $g$-Se begin at pressures above 3.5 GPa; the volume and logarithm of the electrical resistivity relax significantly (logarithmically with the time) at pressures above 8 GPa. Bulk measurements certainly indicate that the volume of $g$-Se glass in the crystallization pressure range is larger than the volumes of both appearing crystalline phases (by 2% and 4%). Therefore, the “volume expansion phenomenon” suggested in [H. Liu et al., Proc. Natl. Acad. Sci. USA 105, 13229 (2008)] is not observed, and the pressure-induced crystallization of glassy selenium is consistent with the laws of thermodynamics.

We report on the experimental observation of topologically protected edge waves in a two-dimensional elastic hexagonal lattice. The lattice is designed to feature $K$-point Dirac cones that are well separated from the other numerous elastic wave modes characterizing this continuous structure. We exploit the arrangement of localized masses at the nodes to break mirror symmetry at the unit-cell level, which opens a frequency band gap. This produces a nontrivial band structure that supports topologically protected edge states along the interface between two realizations of the lattice obtained through mirror symmetry. Detailed numerical models support the investigations of the occurrence of the edge states, while their existence is verified through full-field experimental measurements. The test results show the confinement of the topologically protected edge states along predefined interfaces and illustrate the lack of significant backscattering at sharp corners. Experiments conducted on a trivial waveguide in an otherwise uniformly periodic lattice reveal the inability of a perturbation to propagate and its sensitivity to backscattering, which suggests the superior waveguiding performance of the class of nontrivial interfaces investigated herein.

Fully spin-polarized hole current is theoretically proposed to be generated by photoexcitation in the impurity states of the $\mathrm{Mo}{\mathrm{S}}_2$ monolayer with sulfur partially substituted by copper. To understand the dynamics of the photogenerated spin hole current, we perform a time-domain ab initio nonadiabatic molecular dynamics investigation with different initial excitation and temperature. First, the spin hole relaxes in a band-by-band manner. Therefore a longer lifetime can be achieved if the initial hole is generated at the lower edge of the impurity bands. Second, the phonon excitation is found to affect the spin hole dynamics significantly. When the temperature is decreased from 100 to 50 K, the hole relaxation across the band gap is strongly suppressed by the phonon bottleneck, which is due to the reduction of the phonon occupations. Our results show that the initial hole generation and phonon excitation are two key factors determining the dynamics of the photogenerated spin hole, which provide insights into the design of optimal spintronic devices.

Spin accumulation generated by the anomalous Hall effect (AHE) in mesoscopic ferromagnetic $\mathrm{N}{\mathrm{i}}_{81}\mathrm{F}{\mathrm{e}}_{19}$ (permalloy, Py) films is detected electrically by a nonlocal method. The reciprocal phenomenon, the inverse spin Hall effect (ISHE), can also be generated and detected all electrically in the same structure. For accurate quantitative analysis, a series of nonlocal AHE/ISHE structures and supplementary structures are fabricated on each sample substrate to account for statistical variations and to accurately determine all essential physical parameters in situ. By exploring Py thicknesses of 4, 8, and 12 nm, the Py spin diffusion length ${\lambda }_{\mathrm{Py}}$ is found to be much shorter than the film thicknesses. The product of ${\lambda }_{\mathrm{Py}}$ and the Py spin Hall angle ${\alpha }_{\mathrm{SH}}$ is determined to be independent of thickness and resistivity: ${\alpha }_{\mathrm{SH}}{\lambda }_{\mathrm{Py}}=(0.066\pm 0.009)\mathrm{nm}$ at 5 K and $(0.041\pm 0.010)\mathrm{nm}$ at 295 K. These values are comparable to those obtained from mesoscopic Pt films.

We present measurements of the spin Hall effect (SHE) in AuW and AuTa alloys for a large range of W or Ta concentrations by combining experiments on lateral spin valves and ferromagnetic-resonance/spin-pumping techniques. The main result is the identification of a large enhancement of the spin Hall angle (SHA) by the side-jump mechanism on Ta impurities, with a SHA as high as $+0.5$ (i.e., $50\%$) for about 10% of Ta. In contrast, the SHA in AuW does not exceed $+0.15$ and can be explained by intrinsic SHE of the alloy without significant extrinsic contribution from skew or side-jump scattering by W impurities. The AuTa alloys, as they combine a very large SHA with a moderate resistivity (smaller than $85\mu \mathrm{\Omega }\text{cm}$), are promising for spintronic devices exploiting the SHE.

We present the phase diagram of a 2D isotropic triangular Heisenberg antiferromagnet in a magnetic field. We consider spin-$S$ model with nearest-neighbor ($J_1$) and next-nearest-neighbor ($J_2$) interactions. We focus on the range of $1/8<J_2/J_1<1$, where the ordered states are different from those in the model with only nearest-neighbor exchange. A classical ground state in this range is infinitely degenerate in any field. The actual order is then determined by quantum fluctuations via “order from disorder” phenomenon. We argue that the phase diagram is rich due to competition between competing quantum states which break either orientational or sublattice symmetry. At small and high fields, the ground state is a canted stripe state, which breaks orientational symmetry, but at intermediate fields the ordered states break sublattice symmetry. The most noticeable of such states is “three up, one down” state in which spins in three sublattices are directed along the field and in one sublattice opposite to the field. In such a state, magnetization is quantized at exactly one half of the saturation value. We identify gapless states, which border the “three up, one down” state and discuss the transitions between these states and the canted stripe state.

We report a study on the superconducting pairing mechanism of FeSe via the pair-breaking effects induced by ${\mathrm{H}}^{+}$ irradiation combined with low-temperature specific heat measurements. A multigap structure with nodes or gap minima is suggested in a clean FeSe by the specific heat results. The suppression of critical temperature $T_c$ with increasing the defect density manifests a two-step behavior. When the increase in the residual resistivity is small, $\mathrm{\Delta }{\rho }_0\lesssim 4.5\mu \mathrm{\Omega }\mathrm{cm}$, $T_c$ is gradually suppressed with increasing the density of the scattering centers, suggesting the presence of symmetry-unprotected nodes or gap minima. However, for $\mathrm{\Delta }{\rho }_0\gtrsim 4.5\mu \mathrm{\Omega }\mathrm{cm}$, $T_c$ is almost independent of the scattering, which indicates that the nodes or gap minima are lifted and the order parameter becomes almost isotropic without a sign change. Thus, the superconductivity in FeSe is found to be realized in a symmetry-unprotected nodal or highly anisotropic $s_{++}$ state.

We study Anderson localization in a generalized discrete-time quantum walk—a unitary map related to a Floquet driven quantum lattice. It is controlled by a quantum coin matrix which depends on four angles with the meaning of potential and kinetic energy, and external and internal synthetic flux. Such quantum coins can be engineered with microwave pulses in qubit chains. The ordered case yields a two-band eigenvalue structure on the unit circle, which becomes completely flat in the limit of vanishing kinetic energy. Disorder in the external magnetic field does not impact localization. Disorder in all the remaining angles yields Anderson localization. In particular, kinetic-energy disorder leads to logarithmic divergence of the localization length at spectral symmetry points. Strong disorder in potential and internal magnetic field energies allows one to obtain analytical expressions for spectrally independent localization length, which is highly useful for various applications.

We calculate the oxygen $K$-edge x-ray magnetic circular dichroism (XMCD) spectra of ${\mathrm{CrO}}_2$ to investigate the origin of light-element XMCD. The XMCD spectra evaluated by using a multiple scattering theory are interpreted in terms of the spin-orbit interaction (SOI) at each atomic site. We find that the SOI at the nearest-neighbor Cr atoms dominantly contributes to the oxygen $K$-edge XMCD. Since it has been speculated that XMCD originates from the spin polarization and the SOI at the x-ray-absorbing atom, the present finding may lead to modification of the previously speculated mechanism underlying $K$-edge XMCD. We also perform calculations with a small ${\mathrm{CrO}}_2$ cluster to examine how the O-$p$ and Cr-$d$ states are hybridized and how oxygen atoms acquire orbital angular momentum density. Strong $K$-edge XMCD features reflect the character of the $d$ states of neighboring magnetic atoms and do not directly connect to the orbital magnetic moments of light-element $p$ states.

The structural, magnetic, and electronic properties of ${\mathrm{NdFe}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_3$ have been studied in a comprehensive manner using various experimental and theoretical methods. Mn/Fe sublattice of the compound orders into a G-type antiferromagnetic phase close to 250 K where the magnetic structure belongs to ${\mathrm{\Gamma }}_1$ irreducible representation ($G_y$) unlike ${\mathrm{\Gamma }}_4$ ($G_x$) representation observed in most of the orthoferrites and orthochromites. The magnetic structure undergoes a complete spin reorientation transition with temperature between 75 and 25 K where the magnetic structure exists as a sum of two irreducible representations (${\mathrm{\Gamma }}_1+{\mathrm{\Gamma }}_2$). At 1.5 K, the antiferromagnetic structure belongs entirely to ${\mathrm{\Gamma }}_2$ representation ($G_z$) with a small ferromagnetic component ($F_x$) due to Nd. The unusual spin reorientation and correlation between magnetic ground state and electronic structure have been investigated using phenomenological theory and first-principles calculations within GGA+$U$ and GGA+$U$+SO formalisms.

We present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being evaluated in real time, avoid the analytic continuation issues typically encountered in Monte Carlo calculations. Our results show that inchworm Monte Carlo methods have now reached a state where they can be used as dynamical mean field impurity solvers and the dynamical sign problem can be overcome. As nonequilibrium problems can be simulated at the same cost, we envisage the main use of these methods as dynamical mean field solvers for time-dependent problems far from equilibrium.

We develop methods to probe the excitation spectrum of topological phases of matter in two spatial dimensions. Applying these to the Fibonacci string nets perturbed away from exact solvability, we analyze a topological phase transition driven by the condensation of non-Abelian anyons. Our numerical results illustrate how such phase transitions involve the spontaneous breaking of a topological symmetry, generalizing the traditional Landau paradigm. The main technical tool is the characterization of the ground states using tensor networks and the topological properties using matrix-product-operator symmetries. The topological phase transition manifests itself by symmetry breaking in the entanglement degrees of freedom of the quantum transfer matrix.

We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for ${\mathrm{LaTiO}}_3$, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.

The search for new materials based on computational screening relies on methods that accurately predict, in an automatic manner, total energy, atomic-scale geometries, and other fundamental characteristics of materials. Many technologically important material properties directly stem from the electronic structure of a material, but the usual workhorse for total energies, namely density-functional theory, is plagued by fundamental shortcomings and errors from approximate exchange-correlation functionals in its prediction of the electronic structure. At variance, the $GW$ method is currently the state-of-the-art ab initio approach for accurate electronic structure. It is mostly used to perturbatively correct density-functional theory results, but is, however, computationally demanding and also requires expert knowledge to give accurate results. Accordingly, it is not presently used in high-throughput screening: fully automatized algorithms for setting up the calculations and determining convergence are lacking. In this paper, we develop such a method and, as a first application, use it to validate the accuracy of $G_0{W}_0$ using the PBE starting point and the Godby-Needs plasmon-pole model ($G_0{W}_0^{\mathrm{GN}}$@PBE) on a set of about 80 solids. The results of the automatic convergence study utilized provide valuable insights. Indeed, we find correlations between computational parameters that can be used to further improve the automatization of $GW$ calculations. Moreover, we find that $G_0{W}_0^{\mathrm{GN}}$@PBE shows a correlation between the PBE and the $G_0{W}_0^{\mathrm{GN}}$@PBE gaps that is much stronger than that between $GW$ and experimental gaps. However, the $G_0{W}_0^{\mathrm{GN}}$@PBE gaps still describe the experimental gaps more accurately than a linear model based on the PBE gaps. With this paper, we hence show that $GW$ can be made automatic and is more accurate than using an empirical correction of the PBE gap, but that, for accurate predictive results for a broad class of materials, an improved starting point or some type of self-consistency is necessary.

A quasiparticle band structure of a single layer $2H\text{−}{\mathrm{NbSe}}_2$ is reported by using first-principles $GW$ calculation. We show that a self-energy correction increases the width of a partially occupied band and alters its Fermi surface shape when comparing those using conventional mean-field calculation methods. Owing to a broken inversion symmetry in the trigonal prismatic single layer structure, the spin-orbit interaction is included and its impact on the Fermi surface and quasiparticle energy bands are discussed. We also calculate the doping dependent static susceptibilities from the band structures obtained by the mean-field calculation as well as $GW$ calculation with and without spin-orbit interactions. A complete tight-binding model is constructed within the three-band third nearest neighbor hoppings and is shown to reproduce our $GW$ quasiparticle energy bands and Fermi surface very well. Considering variations of the Fermi surface shapes depending on self-energy corrections and spin-orbit interactions, we discuss the formations of charge density wave (CDW) with different dielectric environments and their implications on recent controversial experimental results on CDW transition temperatures.

The magnetic anisotropy, exchange couplings, and spin-driven ferroelectricity in recently discovered multiferroic oxide $\alpha -{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ have been investigated using first-principles calculation and symmetry analysis. Density functional theory (DFT) calculations predict easy $a$-axis anisotropy, while applying an on-site Hubbard correction (DFT + $U$) converts the easy axis into $b$ direction. These results can explain the discrepancy of easy axis between previous theoretical prediction and experimental results. The third-nearest-neighbor exchange interaction is proved to be dominant for the antiferromagnetic structure. The nearest-neighbor Dzyaloshinskii-Moriya interaction plays an important role in the origins of spin canting, and the canted magnetic moments are oriented predominantly along the $c$ axis. Although the spin-dependent $p-d$ hybridization mechanism induces a sizable electric polarization, the observed large polarization can be mainly attributed to the exchange-striction mechanism including spin-lattice coupling.

Dirac and Weyl fermions appear as quasiparticle excitations in many different condensed-matter systems. They display various quantum transitions which represent unconventional universality classes related to the variants of the Gross-Neveu model. In this paper we study the bosonized version of the standard Gross-Neveu model—the Gross-Neveu-Yukawa theory—at three-loop order, and compute critical exponents in $4-\epsilon$ dimensions for a general number of fermion flavors. Our results fully encompass the previously known two-loop calculations, and agree with the known three-loop results in the purely bosonic limit of the theory. We also find the exponents to satisfy the emergent superscaling relations in the limit of a single-component fermion, order by order up to three loops. Finally, we apply the computed series for the exponents and their Padé approximants to several phase transitions of current interest: metal-insulator transitions of spin-1/2 and spinless fermions on the honeycomb lattice, emergent supersymmetric surface field theory in topological phases, as well as the disorder-induced quantum transition in Weyl semimetals. Comparison with the results of other analytical and numerical methods is discussed.

We describe a theoretical approach to finding spontaneously symmetry-broken electronic phases due to strong electronic interactions when using recently developed slave-particle (slave-boson) approaches based on occupation numbers. We describe why, to date, spontaneous symmetry breaking has proven difficult to achieve in such approaches. We then provide a total energy based approach for introducing auxiliary symmetry-breaking fields into the solution of the slave-particle problem that leads to lowered total energies for symmetry-broken phases. We point out that not all slave-particle approaches yield energy lowering: the slave-particle model being used must explicitly describe the degrees of freedom that break symmetry. Finally, our total energy approach permits us to greatly simplify the formalism used to achieve a self-consistent solution between spinon and slave modes while increasing the numerical stability and greatly speeding up the calculations.

Since the up-conversion phenomenon in rare-earths (REs) doped ${\mathrm{NaYF}}_4$ is strongly affected by the crystal electric field (CF), determining the CF parameters, wave functions, and scheme of the energy levels of the RE $J$ multiplets could be crucial to improve and tune the up-conversion efficiency. In this work, the temperature and magnetic field dependent magnetization of ${\mathrm{NaY}}_{1-x}{\left[\mathrm{Er}\left(\mathrm{Yb}\right)\right]}_x{\mathrm{F}}_4$ hexagonal nanoparticles (NPs) is reported. The data were best fit using the appropriated CF Hamiltonian for the $J=15/2(J=7/2)$ ground state multiplet of ${\mathrm{Er}}^{3+}({\mathrm{Yb}}^{3+}$) ions. The $B_2^0, B_4^0, B_6^0$, and $B_6^6$ CF parameters were considered in the Hamiltonian for RE ions located at the hexagonal ${\mathrm{C}}_{3h}$ point symmetry site of the ${\mathrm{NaYF}}_4$ host lattice. These results allowed us to predict an overall CF splitting of $\sim 214$ ($\sim 356$ K) for ${\mathrm{Er}}^{3+}$ (${\mathrm{Yb}}^{3+}$) and the wave functions and their energy levels for the $J=15/2$ ($J=7/2$) ground state multiplet which are in good agreement with the low temperature electron spin resonance experiments. Besides, our measurements allowed us to calculate all the excited CF $J$ multiplets that yield to a good estimation of the up-conversion light emission linewidth. The nonlinear optical light emission of the studied ${\mathrm{NaY}}_{1-x}{\left[\mathrm{Er}\right(\mathrm{Yb}\left)\right]}_x{\mathrm{F}}_4$ hexagonal NPs was also compared with the most efficient up-conversion codoped ${\mathrm{NaY}}_{1-x-y}{\mathrm{Er}}_x{\mathrm{Yb}}_y{\mathrm{F}}_4$ hexagonal NPs.