Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multiorbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carathéodory and Schur class. Analysis, interpretation, and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. We derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the truncation of the off-diagonal self-energy elements leads to considerable approximation artifacts.

We show that the presence of a transiently excited hot electron gas in graphene leads to a substantial broadening of the C $1s$ line probed by time-resolved x-ray photoemission spectroscopy. The broadening is found to be caused by an exchange of energy and momentum between the photoemitted core electron and the hot electron gas, rather than by vibrational excitations. This interpretation is supported by a quantitative line-shape analysis that accounts for the presence of the excited electrons. Fitting the spectra to this model directly yields the electronic temperature of the system, in good agreement with electronic temperature values obtained from valence band data. Furthermore, we show how the momentum change of the outgoing core electrons leads to a detectable but very small change in the time-resolved photoelectron diffraction pattern and to a nearly complete elimination of the core level binding energy variation associated with the presence of a narrow $\sigma$ band in the C $1s$ state.

Dirac fermions in (2 + 1) dimensions with dynamically generated anticommuting SO(3) antiferromagnetic and ${\mathrm{Z}}_2$ Kekulé valence-bond solid (KVBS) masses map onto a field theory with a topological $\theta$ term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The $\theta$ term implies that a domain wall of the ${\mathrm{Z}}_2$ KVBS order parameter harbors a spin-$1/2$ Heisenberg chain, as described by a (1 + 1)-dimensional SO(3) nonlinear sigma model with $\theta$ term at $\theta =\pi$. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-$1/2$ chain at the ${\mathrm{Z}}_2$ topological defect. Surprisingly, the consequences of the topological term are seen far from the critical point such that the physics of apparently unrelated model systems are naturally understood by invoking them. This concept can be generalized to higher dimensions where (2 + 1)-dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.

Higher-order topological insulators, providing a horizon beyond the conventional bulk-interface correspondence, have zero-dimensional topological corner states at different corners, such as a right-angled corner. Here, we numerically demonstrate a hierarchy of band topology in a two-dimensional square-lattice sonic crystal. In our system, the acoustic bulk bands mimic the quantum spin Hall effect, while gapped interface states emerge in the bulk gap due to symmetry reduction and carry quantized Zak phases, which result in zero-dimensional topological corner states in the interface gap. By direct acoustic measurement, we observe that zero-dimensional topological corner states are confined at not only the right-angled corner, but also the straight-angled corner. Our results present this type of topological shape-dependent corner state, which possibly possesses potential application in controlling and localizing acoustic waves.

Solids usually become harder and tougher under compression and turn softer at elevated temperature. Recently, the compression-induced softening and heating-induced hardening dual anomaly was predicted in group VB elements such as vanadium. Here, the evidence for this counterintuitive phenomenon is reported. By using accurate high-temperature, high-pressure (HP) sound velocities measured at Hugoniot states generated by shockwaves, together with first-principles calculations, we observe not only the prominent compression-induced sound velocity reduction but also strong heating-induced sound velocity enhancement in shocked vanadium. The former corresponds to the softening in the shear modulus by compression, whereas the latter reflects the reverse hardening by heat. These experiments also unveil another anomaly in Young's modulus. Based on the experimental and theoretical data, we infer that vanadium might transition from body-centered cubic into two different rhombohedral phases at ∼79 and 116 GPa along the Hugoniot, respectively, which implies a dramatic difference in static and dynamic loading, as well as the significance of deviatoric stress and rate-relevant effects in HP phase transition dynamics.

We present a theoretical investigation of the dynamics induced by higher-frequency off-resonant light pulse excitation in the metallic phase of $\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_{2}X$ [where BEDT-TTF is bis(ethylenedithio)-tetrathiafulvalene and $X$ represents a counteranion] by solving the time-dependent Schrödinger equation numerically in the quarter-filled extended Hubbard model for the material. If the magnitude of the applied light pulse exceeds a critical value, the transition to the charge-ordered (CO) state is then induced by the light pulse excitation. In the CO state, one site forming a dimer becomes charge rich, the other site becomes charge poor, and the intradimer electric dipole moments are aligned in a particular direction. The transition is driven by photoinduced reduction of the effective transfer integrals and can therefore be regarded as a dynamical localization-related phenomenon. There are two degenerate A phase and B phase CO states that have opposite polarization directions. The photogenerated CO state is given by the superposition of the A phase and B phase CO states with equal weights, and the polarization of the photogenerated CO state is effectively zero. Transitions to either of the two polarized CO states can be induced selectively, and the polarization can be generated by excitation using light and terahertz pulses. Furthermore, the polarization can be reversed on a timescale of several tens of femtoseconds by excitation using double light and terahertz pulses, which induce the following phase transitions: metal $\to$ polarized CO state of the A (B) phase $\to$ metal $\to$ polarized CO state of the B (A) phase $\to$ metal.

We develop the effective field theoretical descriptions of spin systems in the presence of symmetry-breaking effects: the magnetic field, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. Starting from the lattice description of spin systems, we show that the symmetry-breaking terms corresponding to the above effects can be incorporated into the effective field theory as a combination of a background (or spurious) $\mathrm{SO}\left(3\right)$ gauge field and a scalar field in the symmetric tensor representation, which are eventually fixed at their physical values. We use the effective field theory to investigate mode spectra of inhomogeneous ground states, focusing on one-dimensionally noncollinear states, such as helical and spiral states. Although the helical and spiral ground states share a common feature of supporting the gapless Nambu-Goldstone modes associated with the translational symmetry breaking, they have qualitatively different dispersion relations: isotropic in the helical phase while anisotropic in the spiral phase. We clarify the reason for this qualitative difference based on the symmetry-breaking pattern. As another application, we discuss the magnon production induced by an inhomogeneous magnetic field, and find a formula akin to the Schwinger formula. Our formula for the magnon production gives a finite rate for antiferromagnets, and a vanishing rate for ferromagnets, whereas that for ferrimagnets interpolates between the two cases.

Electrides, which accommodate excess of electrons in lattice interstitials as anions, usually exhibit interesting properties and broad applications. Until now, most electrides, especially at high pressures, show semiconducting/insulating character arising from the strong localization of interstitial and orbital electrons. However, modulating their connectivity could turn them into metals and even superconductors. In this work, with the aid of first-principles particle swarm optimization, we have identified a series of pressure-induced Li-rich electrides in the Li-Te system, in which hollow ${\mathrm{Li}}_n$ polyhedra accommodate the excess of electrons. With increasing Li content, these electrides undergo an interesting structural evolution. Meanwhile, the connection type of ${\mathrm{Li}}_n$ polyhedra experiences transitions from vertex- or edge sharing, to face sharing, leading to a diverse distribution and connectivity of interstitial electrons. All identified electrides exhibit anionic electrons-dominated metallicity. More interestingly, ${\mathrm{Li}}_9\mathrm{Te}$, with the highest content of ${\mathrm{Li}}_6$ octahedra, is superconducting with a critical temperature $\left(T_{\mathrm{c}}\right)$ of 10.2 K at 75 GPa, which is much higher than typical electrides (e.g., $12\mathrm{CaO}·7{\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{Ca}}_2\mathrm{N}$, and ${\mathrm{Y}}_2\mathrm{C}$). Its superconductivity mainly originates from the coupling between hybridized electrons (anionic and atomic non-$s$-state ones) and Te-dominated phonons.

We observed asymmetric critical slowing down and asymmetric dynamical scaling exponent in the superheating and supercooling kinetic processes during the thermally-induced metal-insulator transition of MnNiSn based Heusler alloy. During the transition to the insulator phase, the critical-like features get enhanced compared to the transition back to the metal phase. These experimental findings suggest that the metastable phase in the cooling branch of hysteresis has approached close to the spinodal instability. On the other hand, the extended disorder, generated over and above the intrinsic crystal defects during heating, triggers the excess heterogeneous nucleation before reaching the spinodal point. Zero-temperature random field Ising model (ZTRFIM) simulation, inscribed for the athermal martensitic transitions, supports the argument that the disorder smears the spinodal instabilities as the correlation length is bounded by the average distance between the disorder points.

We study the properties of the one-dimensional Fibonacci chain, subjected to the placement of on-site impurities. The resulting disruption of quasiperiodicity can be classified in terms of the renormalization path of the site at which the impurity is placed, which greatly reduces the possible amount of disordered behavior that impurities can induce. Moreover, it is found that, to some extent, the addition of multiple weak impurities can be treated by superposing the individual contributions together and ignoring nonlinear effects. This means that a transition regime between quasiperiodic order and disorder exists in which some parts of the system still exhibit quasiperiodicit, while other parts start to be characterized by different localization behaviors of the wave functions. This is manifested through a symmetry in the wave-function amplitude map, expressed in terms of conumbers, and through the inverse participation ratio. For the latter, we find that its average of states can also be grouped in terms of the renormalization path of the site at which the impurity has been placed.

The creep motion of domain walls driven by external fields in magnetic thin films is described by universal features related to the underlying depinning transition. One key parameter in this description is the roughness exponent characterizing the growth of fluctuations of the domain wall position with its longitudinal length scale. The roughness amplitude, which gives information about the scale of fluctuations, however, has received less attention. Albeit their relevance, experimental reports of the roughness parameters, both exponent and amplitude, are scarce. We report here experimental values of the roughness parameters for different magnetic field intensities in the creep regime at room temperature for a Pt/Co/Pt thin film. The mean value of the roughness exponent is $\zeta =0.74$, and we show that it can be rationalized as an effective value in terms of the known universal values corresponding to the depinning and thermal cases. In addition, it is shown that the roughness amplitude presents a significant increase with decreasing field. These results contribute to the description of domain wall motion in disordered magnetic thin systems.

Coupling between spin and charge degrees of freedom in electrons is a source of various electronic and magnetic properties of solids. We theoretically study charge density waves induced by the spin-charge coupling in the presence of magnetic orderings in itinerant magnets. By performing a perturbative calculation in the weak-coupling limit of the Kondo lattice model, we derive a useful formula for the relationship between charge and spin density waves, which can be applied to any magnetic orderings, including noncollinear and noncoplanar ones composed of multiple spin density waves called multiple-$Q$ magnetic orderings. We demonstrate the predictive power for single-$Q$ and double-$Q$ states including skyrmion and meron-antimeron crystals on a square lattice, in comparison with the numerical calculations. Moreover, we show that the charge density waves contain richer information than the spin density waves, and are indeed useful in distinguishing the spin textures with similar spin structure factors. We discuss the relation to bond modulation in terms of the kinetic bond energy and the vector spin chirality. We also perform numerical calculations beyond the perturbative regime and find that the charge density waves can be enhanced when the electron filling is commensurate. Furthermore, we investigate the effect of the spin-orbit coupling, which can lead to additional charge density waves owing to effective anisotropic magnetic interactions in momentum space. Our result will provide a way to identify complex magnetic orderings and their origins from the charge modulations.

We report a systematic study of the $5d$-electron-doped system $\mathrm{Ce}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Ir}}_x\right)}_2{\mathrm{Al}}_{10}$ $(0\le x\le 0.15)$. With increasing $x$, the orthorhombic $b$ axis decreases slightly while accompanying changes in $a$ and $c$ leave the unit cell volume almost unchanged. Inelastic neutron scattering, along with thermal and transport measurements, reveal that for the Kondo semiconductor ${\mathrm{CeFe}}_2{\mathrm{Al}}_{10}$, the low-temperature energy gap, which is proposed to be a consequence of strong $c\text{−}f$ hybridization, is suppressed by a small amount of Ir substitution for Fe and that the system adopts a metallic ground state with an increase in the density of states at the Fermi level. The charge or transport gap collapses (at $x=0.04$) faster than the spin gap with Ir substitution. Magnetic susceptibility, heat capacity, and muon spin relaxation measurements demonstrate that the system undergoes long-range antiferromagnetic order below a Néel temperature $T_{\mathrm{N}}$ of 3.1(2) K for $x=0.15$. The ordered moment is estimated to be smaller than 0.07(1) ${\mu }_{\mathrm{B}}$/Ce, although the trivalent state of Ce is confirmed by Ce $L_3$-edge x-ray absorption near edge spectroscopy. It is suggested that the $c\text{−}f$ hybridization gap, which plays an important role in the unusually high ordering temperatures observed in $\mathrm{Ce}{T}_2{\mathrm{Al}}_{10}$ ($T$ = Ru and Os), may not be necessary for the onset of magnetic order with a low $T_{\mathrm{N}}$ seen here in $\mathrm{Ce}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Ir}}_x\right)}_2{\mathrm{Al}}_{10}$.

New developments in scanning tunneling spectroscopy now allow for the spatially resolved measurement of the Josephson critical current $I_c$ between a tip and a superconducting sample, a nearly direct measurement of the true superconducting order parameter. However, it is unclear how these $I_c$ measurements are correlated with previous estimates of the spectral gap taken from differential conductance measurements. In particular, recent experiments on an iron-based superconductor found almost no correlation between $I_c$ and the spectral gap obtained from differential conductance $g=dI/dV$ spectra, reporting instead a more significant correlation between $I_c$ and the coherence-peak height. Here we point out that the correlation—or the lack thereof—between these various quantities can be naturally explained by the effect of disorder on unconventional superconductivity. Using large-scale numerical simulations of a BCS $d$-wave pair Hamiltonian with many-impurity potentials, we observe that “substitutional” disorder models with weak pointlike impurities lead to a situation in which the true superconducting order parameter and $I_c$ are both uncorrelated with the spectral gap from $dI/dV$ measurements and highly correlated with the coherence-peak heights. The underlying mechanism appears to be the disorder-induced transfer of spectral weight away from the coherence peaks. On the other hand, smooth impurity potentials with a length scale larger than the lattice constant lead to a large positive correlation between the true superconducting order parameter and the spectral gap, in addition to a large correlation between the order parameter and the coherence-peak height. We discuss the applicability of our results to recent Josephson scanning tunneling spectroscopy experiments on iron-based and cuprate high-temperature superconductors.

A novel planar Hall effect (PHE) is induced by the chiral anomaly or nontrivial Berry curvature, which has been predicted in nonmagnetic Weyl/Dirac semimetals. Recent theories suggest such an effect exists in three-dimensional (3D) topological insulators even in the absence of chiral anomaly. In this paper, we present a detailed analysis of the transport properties in the quasi-1D $\mathrm{Ta}{\mathrm{Se}}_3$, a candidate of topological superconductor (TSC) predicted by the theorist. There are some interesting observations on $\mathrm{Ta}{\mathrm{Se}}_3$. (1) The electron-hole compensation has been confirmed by the Hall effect measurements around $T_{\mathrm{com}}\sim 30\mathrm{K}$, which accounts for the extremely large magnetoresistance in $\mathrm{Ta}{\mathrm{Se}}_3$. (2) The remarkable PHE and anisotropic magnetoresistance (AMR) are observed in $\mathrm{Ta}{\mathrm{Se}}_3$. Based on the detailed analysis of the PHE and AMR curves, the origin of PHE in $\mathrm{Ta}{\mathrm{Se}}_3$ is suggested to originate from the resistivity anisotropy induced by the difference of field-induced anisotropic scattering in surface Dirac fermions of various spins. (3) We observed the successive Fermi surface reconstruction induced by the temperature around $T^{*}\sim 50\mathrm{K}$, where the amplitude of intrinsic PHE drops sharply related to the suppression of the topological surface state. Meanwhile, the $d{\rho }_{xx}\left(T\right)/dT$ curve presents a broad anomaly around $T_{\mathrm{peak}}\sim 70\mathrm{K}$, which can be explained as a possible charge-density wave associated with imperfect Fermi surface nesting. PHE provides an effective method to understand the relationship between the electronic transport properties and the topological structure in quasi-1D TSC $\mathrm{Ta}{\mathrm{Se}}_3$.

Recently, Urai et al. [Phys. Rev. Lett. 124, 117204 (2020)] reported that an antiferromagnetic long-range-ordered state in $\kappa$-${\left(\mathrm{ET}\right)}_2\mathrm{Cu}\mathrm{[N}{\left(\mathrm{CN}\right)}_2\mathrm{]Cl}$ changes into a quantum spin liquid via an unconventional spin glass-like state as randomness is introduced by x-ray irradiation. Here, we focused on the spin glass-like state and conducted a detailed investigation into it using ${}^{13}\mathrm{C}$-NMR measurements on 150-h x-ray-irradiated $\kappa$-$({\mathrm{ET})}_2\mathrm{Cu}\mathrm{[N(}{\mathrm{CN})}_2\mathrm{]Cl}$. We found that the spin glass-like state is composed of two components: the major component inherits the spin structure of nonirradiated $\kappa$-$({\mathrm{ET})}_2\mathrm{Cu}\mathrm{[N(}{\mathrm{CN})}_2\mathrm{]Cl}$, whereas the minor component differs from that of nonirradiated $\kappa$-${\left(\mathrm{ET}\right)}_2\mathrm{Cu}\mathrm{[N(}{\mathrm{CN})}_2\mathrm{]Cl}$. We also found that in the spin glass-like state, spin moments fluctuate very slowly around stable directions even at low temperatures, which is very likely related to the Griffiths physics.

The asymptotics of the Kohn-Sham (KS) exact exchange potential $V_x\left(z\right)$ of a jelliumlike semi-infinite metal is investigated in the framework of the optimized-effective-potential formalism of density-functional theory. Our numerical calculations clearly show that deep into the vacuum side of the surface $V_x\left(z\right)\propto e^{2}ln\left(az\right)/z$ with $a$ being a system-dependent constant, thus, confirming the analytical calculations reported in Phys. Rev. B 81, 121106(R) (2010). A criticism of this work published in Phys. Rev. B 85, 115124 (2012) is shown to be incorrect. Our rigorous exchange-only results provide strong constraints both for the building of approximate exchange functionals and for the determination of the still unknown KS correlation potential.

We explore the electronic band structure of freestanding monolayers of chromium trihalides $\mathrm{Cr}{X}_3$, $X$ = Cl, Br, I, within an advanced ab initio theoretical approach based on the use of Green's function functionals. We compare the local density approximation with the quasiparticle self-consistent GW (QSGW) approximation and its self-consistent extension $\left(\mathrm{QS}G\widehat{W}\right)$ by solving the particle-hole ladder Bethe-Salpeter equations to improve the effective interaction $W$. We show that, at all levels of theory, the valence band consistently changes shape in the sequence $\mathrm{Cl}\to \mathrm{Br}\to \mathrm{I}$, and the valence band maximum shifts from the $M$ point to the $\mathrm{\Gamma }$ point. By analyzing the dynamic and momentum-dependent self-energy, we show that $\mathrm{QS}G\widehat{W}$ adds to the localization of the systems in comparison with QSGW, thereby leading to a narrower band and reduced amount of halogens in the valence band manifold. Further analysis shows that $X$ = Cl is most strongly correlated, and $X$ = I is least correlated (most bandlike) as the hybridization between Cr $d$ and $X$ $p$ enhances in the direction $\mathrm{Cl}\to \mathrm{Br}\to \mathrm{I}$. For ${\mathrm{CrBr}}_3$ and ${\mathrm{CrI}}_3$, we observe remarkable differences between the QSGW and $\mathrm{QS}G\widehat{W}$ valence band structures, while their eigenfunctions are very similar. We show that weak perturbations, like moderate strain, weak changes to the $d-p$ hybridization, and adding small $U$, can flip the valence band structures between these two solutions in these materials.