We review the internal connection between quantum coherence (QC) and quantum phase transitions (QPTs). We propose two quantities $L_{\text{QC}}$ and $S_{\text{QC}}$ to detect QPTs of different orders by analyzing the spectrum of QC. Our results show that the two quantities not only can detect different types of QPT but can also exhibit a remarkable robustness against thermal fluctuations. In comparison with other detectors, such as quantum entanglement and QD, $L_{\text{QC}}$ and $S_{\text{QC}}$ can show more effective and reliable behaviors in characterizing a QPT at zero and finite temperatures. In light of this property and the fundamental role of QC in quantum information processing, QC spectrum-related $L_{\text{QC}}$ and $S_{\text{QC}}$ have considerable importance in detecting QPTs at a real finite-temperature experimental environment.

We present an approach to identify topological order based on unbiased infinite projected entangled-pair states simulations, i.e., where we do not impose a virtual symmetry on the tensors during the optimization of the tensor network ansatz. As an example we consider the ground state of the toric code model in a magnetic field exhibiting $Z_2$ topological order. The optimization is done by an efficient energy minimization approach based on a summation of tensor environments to compute the gradient. We show that the optimized tensors, when brought into the right gauge, are approximately $Z_2$ symmetric, and they can be fully symmetrized a posteriori to generate a stable topologically ordered state, yielding the correct topological entanglement entropy and modular S and U matrices. To compute the latter we develop a variant of the corner-transfer matrix method, which is computationally more efficient than previous approaches based on the tensor renormalization group.

We report on the experimental and theoretical investigation of magnetic-field-induced second harmonic generation (SHG) and two-photon absorption of excited exciton states ($n⩾3$) of the yellow series in the cuprous oxide ${\mathrm{Cu}}_2\mathrm{O}$. In this centrosymmetric material, SHG can occur due to constructive interplay of electric dipole and electric quadrupole/magnetic dipole transitions for light propagating along the low-symmetry directions [111] or [112]. By application of a magnetic field in Voigt configuration, SHG gets also allowed for excitation along the [110] axis and even the high-symmetry cubic direction [001]. Combining a symmetry analysis and a microscopic theory, we uncover the two key contributions to the magnetic-field-induced SHG: the Zeeman effect and the magneto-Stark effect. We demonstrate systematic dependencies of the SHG intensity on the linear polarization angles of the ingoing fundamental laser and the outgoing SHG beam, complementary to the paper by Rommel et al. [Phys. Rev. B 101, 115202 (2020)]. In general, the resulting contour plots in combination with a symmetry analysis allow one to determine uniquely the character of involved transitions. Moreover, we can separate in magnetic field the Zeeman and the magneto-Stark effect through appropriate choice of the experimental geometry and polarization configuration. We present a microscopic theory of the second harmonic generation of excitons in a centrosymmetric cubic semiconductor taking into account the symmetry and the band structure of cuprous oxide. Based on the developed microscopic theory, we identify the main contributions to the second-order nonlinear susceptibility of $S, P$, and $D$ excitons. We analyze the redistribution of SHG intensities between the excitonic states both in the absence and presence of the magnetic field and show good agreement with the experimental data. With increasing exciton principal quantum number, the magneto-Stark effect overpowers the influence of the Zeeman effect.

Recently, second harmonic generation (SHG) for the yellow exciton series in cuprous oxide was demonstrated [Phys. Rev. B 98, 085203 (2018)]. Assuming perfect $O_{\mathrm{h}}$ symmetry, SHG is forbidden along certain high-symmetry axes. Perturbations can break this symmetry and forbidden transitions may become allowed. We investigate theoretically the effect of external magnetic fields on the yellow exciton lines of cuprous oxide. We identify two mechanisms by which an applied magnetic field can induce a second harmonic signal in a forbidden direction. First of all, a magnetic field by itself generally lifts the selection rules. In the Voigt configuration, an additional magneto-Stark electric field appears. This also induces certain SHG processes differing from those induced by the magnetic field alone. Complementary to the paper by Farenbruch et al. [Phys. Rev. B 101, 115201 (2020)], we perform a full numerical diagonalization of the exciton Hamiltonian including the complex valence-band structure. Numerical results are compared with experimental data.

X-ray absorption spectra of vanadium pentoxide (${\mathrm{V}}_2{\mathrm{O}}_5$) at the vanadium $K$ and $L$ edges are studied with multiple scattering calculations and good agreement with experiment is obtained when the full-potential and multichannel extensions of multiple scattering theory are used. The spectral shapes are analyzed in terms of the local electronic structure at the vanadium sites and they reveal strong anisotropy and final-state correlation effects. The strong polarization dependence of the spectra is explained by the low-symmetry ligand field and vanadyl bonding. The effect of oxygen vacancies, the major intrinsic defect type of ${\mathrm{V}}_2{\mathrm{O}}_5$, is investigated. Clear spectral changes are found for vanadium atoms next to an oxygen vacancy, which may serve as a fingerprint of defects in electron energy loss spectroscopy.

Perovskite oxides $AB{\mathrm{O}}_3$ containing heavy B-site elements are a class of candidate materials to host topological metals with a large spin-orbit interaction. In contrast to the band insulator $\mathrm{BaSn}{\mathrm{O}}_3$, the semimetal $\mathrm{BaPb}{\mathrm{O}}_3$ is proposed to be a typical example with an inverted band structure, the conduction band of which is composed of mainly the $\mathrm{O}\text{−}2p$ orbital. In this paper, we exemplify a band-gap modification by systematic structural, optical, and transport measurements in $\mathrm{BaS}{\mathrm{n}}_{1-x}\mathrm{P}{\mathrm{b}}_x{\mathrm{O}}_3$ films. A sudden suppression of the conductivity and an enhancement of the weak antilocalization effect at $x=0.9$ indicate the presence of a singular point in the electronic structure as a signature of the band inversion. Our findings provide an intriguing platform for combining topological aspects and electron correlation in perovskite oxides based on band-gap engineering.

We calculate the shift in emission frequency of the trion and biexciton (relative to that of the single exciton) for nanocrystals (NCs) of inorganic perovskites ${\mathrm{CsPbBr}}_3$ and ${\mathrm{CsPbI}}_3$. The calculations use an envelope-function $\mathbf{k}·\mathbf{p}$ model combined with self-consistent Hartree-Fock and a treatment of the intercarrier correlation energy in the lowest (second) order of many-body perturbation theory. The carriers in the trion and biexciton are assumed to have relaxed nonradiatively to the ground state at the band edge before emission occurs. The theoretical trion shifts for both ${\mathrm{CsPbBr}}_3$ and ${\mathrm{CsPbI}}_3$ are found to be in fair agreement with available experimental data, which include low-temperature single-dot measurements, though are perhaps systematically small by a factor of order 1.5, which can plausibly be explained by a combination of a slightly overestimated dielectric constant and omitted third- and higher-order terms in the correlation energy. Taking this level of agreement into account, we estimate that the ground-state biexciton shift for ${\mathrm{CsPbBr}}_3$ is a redshift of order 10–20 meV for NCs with an edge length of 12 nm. This value is intermediate among the numerous high-temperature measurements on NCs of ${\mathrm{CsPbBr}}_3$, which vary from large redshifts of order 100 meV to blueshifts of several meV.

We present a model for the triplet-triplet annihilation in organic phosphorescent host-guest systems that considers the effect of the energetic disorder on the kinetics of the annihilation. Nonequilibrium (time-dependent) transport of the triplets that arises from the progressive relaxation of triplets in the energy landscape is taken into account in the model. Triplet excitons are considered to move between the guest sites (dye molecules) via the thermally activated tunneling mechanism; the annihilation step, however, takes place through the Förster mechanism. Based on the model developed, and by calculating the time evolution of the triplet concentration, we investigate the effect of the various parameters on the effective annihilation coefficient. At low dye concentrations, it is shown that relaxation of the triplets is not completed during their lifetimes, and therefore, the annihilation process occurs entirely in the nonequilibrium. We also address the competition between two pathways for the annihilation process: single-step, long-range annihilation, and diffusion-assisted annihilation. By a quantitative comparison with experimental data reported in the literature, we demonstrate certain conditions in which there is a considerable contribution from the diffusion to the total annihilation rate. The model presented in this work can also be used for the excitons that diffuse by the Förster mechanism.

Recent experiments showed that hydrogenation of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ leads to a dramatic change of the magnetic anisotropy (MA) from strongly uniaxial type to easy-plane type with easy axis and easy plane orthogonal to each other. We applied first-principles calculations aiming to understand the microscopic origin of the drastic MA change and distinguish between discontinuous and continuous scenarios of the transformation. The calculations combined with symmetry analysis revealed that the hydrogenation leads to the instability of both uniaxial and easy-plane states caused by the reduced symmetry of the atomic lattice. The obtained noncollinear noncoplanar magnetic states have the features of both apparently competing magnetic structures, which indicates the validity of the continuous scenario of the transformation. An insight into the active interatomic interactions shows that Dzyaloshinskii-Moriya interaction contributes to magnetic transformations and must be taken into account on the same footing as MA.

The solid-to-liquid phase transition for krypton and xenon is studied by means of parallel-tempering Monte Carlo simulations based on an accurate description of the atomic interactions within a many-body ansatz using relativistic coupled-cluster theory. These high-level data were subsequently fitted to computationally efficient extended Lennard-Jones and extended Axilrod-Teller-Muto types of interaction potentials. Solid-state calculations demonstrate that the many-body decomposition of the interaction energy converges well for the heavier rare gas solids, leading to solid-state properties in good agreement with experiment. The results show that it suffices to include two- and three-body interactions only for the melting simulation. The melting of the bulk is simulated for cells with cubic periodic boundary conditions, as well as within a finite cluster approach. For the latter, melting of spherical magic number clusters with increasing cluster size is studied, and the melting temperatures are obtained from extrapolation to the bulk. The calculated melting temperatures for the cluster extrapolation (the periodic approach values corrected for superheating are set in parentheses) are $T_m=113.7$ K (110.9 K) and $T_m=160.8$ K (156.1 K) for krypton and xenon, respectively. Both are in very good agreement with corresponding experimental values of 115.75 and 161.40 K.

The sliding of the room-temperature charge density wave (CDW) in the monoclinic phase of $\mathrm{Nb}{\mathrm{S}}_3$ under rf power is studied. The threshold field, $E_{\mathrm{t}}$, and Shapiro steps’ width, δE, show aperiodic Bessel-type oscillations as a function of rf voltage. Here we demonstrate experimentally that, if presented as a function of CDW path length in each half period of the rf voltage, $E_{\mathrm{t}}$ and δE show periodic oscillations, the period being equal to the CDW wavelength. The result is found to be universal for different compounds and gives clear understanding of the synchronization effects in terms of forced oscillations of a particle in a periodic potential.

The optical properties of Sn-doped ${\mathrm{Bi}}_{1.1}{\mathrm{Sb}}_{0.9}{\mathrm{Te}}_2\mathrm{S}$, the most bulk-insulating topological insulator thus far, have been examined at different temperatures over a broad frequency range. No Drude response is detected in the low-frequency range down to $30{\mathrm{cm}}^{-1}$, corroborating the excellent bulk-insulating property of this material. Intriguingly, we observe a sharp peak at about $2200{\mathrm{cm}}^{-1}$ in the optical conductivity at 5 K. Further quantitative analyses of the line shape and temperature dependence of this sharp peak, in combination with first-principles calculations, suggest that it corresponds to a van Hove singularity arising from Mexican-hat-shaped inverted bands. Such a van Hove singularity is a pivotal ingredient of various strongly correlated phases.

We study the anomalous Hall effect (AHE) of single-crystalline ${\mathrm{Co}}_3{\mathrm{Sn}}_{2-x}{\mathrm{In}}_x{\mathrm{S}}_2$ over a large range of indium concentration $x$ from 0 to 1. Their magnetization reduces progressively with increasing $x$ while their ground state evolves from a ferromagnetic Weyl semimetal into a nonmagnetic insulator. Remarkably, after systematically scaling the AHE, we find that their intrinsic anomalous Hall conductivity (AHC) features an unexpected maximum at around $x=0.15$. The change of the intrinsic AHC corresponds with the doping evolution of Berry curvature and the maximum arises from the magnetic topological nodal-ring gap. Our experimental results show a larger AHC in a fundamental nodal-ring gap than that of Weyl nodes.

Incommensurate charge density waves (CDW) have the extraordinary ability to display non-Ohmic behavior when submitted to an external field. The mechanism leading to this nontrivial dynamics is still not well understood, although recent experimental studies tend to prove that it is due to solitonic transport. Solitons could come from the relaxation of the strained CDW within an elastic-to-plastic transition. However, the nucleation process and the transport of these charged topological objects have never been observed at the local scale until now. In this paper, we use in situ scanning x-ray microdiffraction with micrometer resolution of a ${\mathrm{NbSe}}_3$ sample designed to have sliding and nonsliding areas. Direct imaging of the charge density wave deformation is obtained using an analytical approach based on the phase gradient to disentangle the transverse from the longitudinal components over a large surface $\left(90\mu \text{m}\right)$. We show that the CDW dissociates itself from the host lattice in the sliding regime and displays a large transverse deformation, ten times larger than the longitudinal one and strongly dependent on the amplitude and the direction of the applied currents. This deformation continuously extends across the macroscopic sample dimensions, over a distance 10 000 times greater than the CDW wavelength despite the presence of strong defects while remaining strongly pinned by the lateral surfaces. This two-dimensional quantitative study highlights the prominent role of the shear effect, which should be significant in the nucleation of solitons.

Plutonium (Pu), in which the $5f$ valence electrons always wander the boundary between localized and itinerant states, exhibits quite complex crystal structures and unprecedentedly anomalous properties with respect to temperature and alloying. Understanding its chemical and physical properties, especially its $5f$ electronic structure is one of the central and unsolved topics in condensed matter theory. In the present work, the electronic structures of the six allotropes of Pu (including its $\alpha , \beta , \gamma , \delta , {\delta }^{\prime }$, and $\epsilon$ phases) at ambient pressure are studied comprehensively by means of the density functional theory in combination with the single-site dynamical mean-field theory. The band structures, total and partial density of states, valence state histograms, $5f$ orbital occupancies, x-ray branching ratios, and self-energy functions are carefully studied. It is suggested that the $\alpha , \beta$, and $\gamma$ phases of Pu are typical Racah metals in which the atomic multiple effect dominates near the Fermi level. The calculated results reveal that not only the $\delta$ phase, but also all the six allotropes are archetypal mixed-valence metals with remarkable atomic eigenstate fluctuation. As a consequence, the $5f$ occupancy $n_{5f}$ is around 5.1–5.4, which varies with respect to the atomic volume and electronic correlation strength of Pu. The $5f$ electronic correlation in Pu is moderately orbital-dependent. Moreover, the $5f$ electrons in the ${\delta }^{\prime }$ phase are the most correlated and localized.

Cubic perovskite oxides are emerging high-mobility transparent conducting oxides (TCOs), but Ge-based TCOs had not been known until the discovery of metastable cubic ${\mathrm{SrGeO}}_3$. $0.5\times 0.4\times 0.2\text{−}\mathrm{m}{\mathrm{m}}^3$ large single crystals of the cubic ${\mathrm{SrGeO}}_3$ perovskite were successfully synthesized employing the high-pressure flux method. The phonon spectrum is determined from the IR optical reflectance and Raman-scattering analysis to evaluate the electron transport governed by optical phonon scattering. A calculated room-temperature mobility on the order of $3.9\times {10}^2\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ is obtained, identifying cubic ${\mathrm{SrGeO}}_3$ as one of the most promising TCOs. Employing classical phonon theory and a combined experimental-theoretical approach, a comprehensive analysis of the intrinsic electron mobility in the cubic perovskite semiconductors ${\mathrm{SrGeO}}_3$, ${\mathrm{BaSnO}}_3$, and ${\mathrm{SrTiO}}_3$ is provided based on the magnitude of polarization and eigenfrequency of optically active phonons.

The electrical conductivity of epitaxial $\mathrm{BaTi}{\mathrm{O}}_3$ films was studied by small-signal impedance spectroscopy at temperatures of 10–720 K using Pt-$\mathrm{BaTi}{\mathrm{O}}_3-\mathrm{SrRu}{\mathrm{O}}_3$ capacitors. The $\sim 150$-nm-thick $\mathrm{BaTi}{\mathrm{O}}_3$ films possessed different lattice strains and degrees of oxygen deficiency. A crossover between the low-temperature hopping of small polarons and the high-temperature semiconductor- to metal-type behavior was demonstrated in all films. It was suggested that the small electron polarons originate from self-trapping at Ti in the stoichiometric tensile-strained film and from trapping at Ti next to the oxygen vacancy in the oxygen-deficient films. The conduction-band transport was ascribed to the thermally activated release of the trapped electrons. It was pointed out that the electronic release can mimic the motion of oxygen vacancies, which are actually immobile.

We use resonant inelastic x-ray scattering (RIXS) at the Ir $L_3$ edge to study the effect of hole doping upon the $J_{\text{eff}}=\frac{1}{2}$ Mott-insulating state in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, via Rh replacement of the Ir site. The spin-wave gap, associated with XY-type spin-exchange anisotropy, collapses with increasing Rh content, prior to the suppression of the Mott-insulating state and in contrast to electron doping via La substitution of the Sr site. At the same time, despite heavy damping, the $d-d$ excitation spectra retain their overall amplitude and dispersion character. A careful study of the spin-wave spectrum reveals that deviations from the $J_1-J_2-J_3$ Heisenberg used to model the pristine system disappear at intermediate doping levels. These findings are interpreted in terms of a modulation of Ir-Ir correlations due to the influence of Rh impurities upon nearby Ir wave functions, even as the single-band $J_{\text{eff}}=\frac{1}{2}$ model remains valid up to full carrier delocalization. They underline the importance of the transition metal site symmetry when doping pseudospin systems such as ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$.