We present a comprehensive comparison of spin and energy dynamics in quantum and classical spin models on different geometries, ranging from one-dimensional chains, over quasi-one-dimensional ladders, to two-dimensional square lattices. Focusing on dynamics at formally infinite temperature, we particularly consider the autocorrelation functions of local densities, where the time evolution is governed either by the linear Schrödinger equation in the quantum case or the nonlinear Hamiltonian equations of motion in the case of classical mechanics. While, in full generality, a quantitative agreement between quantum and classical dynamics can therefore not be expected, our large-scale numerical results for spin-$1/2$ systems with up to $N=36$ lattice sites in fact defy this expectation. Specifically, we observe a remarkably good agreement for all geometries, which is best for the nonintegrable quantum models in quasi-one or two dimensions, but still satisfactory in the case of integrable chains, at least if transport properties are not dominated by the extensive number of conservation laws. Our findings indicate that classical or semiclassical simulations provide a meaningful strategy to analyze the dynamics of quantum many-body models, even in cases where the spin quantum number $S=1/2$ is small and far away from the classical limit $S\to \infty$.

Chiral materials, where no improper symmetry operations such as inversion are present, are systems prone to the appearance of a skyrmion lattice. Recently it has been shown theoretically that not only ferromagnets (FMs) but also antiferromagnets (AFMs) can host such kind of phases. In this work we study a new candidate for AFM skyrmions, ${\mathrm{EuIr}}_2{\mathrm{P}}_2$, by means of magnetization and specific heat measurements on poly and single crystals. X-ray diffraction confirms a trigonal chiral crystal structure, where europium ions form helices along the $c$ direction. In spite of predominantly FM interactions, ${\mathrm{Eu}}^{2+}$ ions order antiferromagnetically at $T_{N_1}=5$ K in what seems to be an incommensurate amplitude-modulated magnetic state where the moments are oriented mainly along the $c$ direction. A second magnetic transition takes place at $T_{N_2}=2.9$ K, involving the ordering of an in-plane component of the Eu moment likely resulting in an equal-moment structure. Specific heat data show a tail above $T_{N_1}$. Accordingly the magnetic entropy at $T_{N_1}$ is strongly reduced in comparison to the expected $Rln8$ value. This evidences a significant amount of frustration. A simple analysis based on a Heisenberg model indicates that the observed properties imply the presence of several relevant interactions, with competing FM and AFM ones resulting in frustration. Thus ${\mathrm{EuIr}}_2{\mathrm{P}}_2$ is a new interesting magnetic system, where chirality and frustration might result in unconventional magnetic textures.

For more than a decade the HSE06 hybrid exchange-correlation functional developed by Heyd, Scuseria and Ernzerhof has provided a tool for reliable defect level calculations in density functional theory for which postprocessing tools are not necessary, in contrast to previous calculations using semilocal density functionals. One of the main reasons for its reliability is the high precision of HSE06 for band gap calculations. Recently, other functionals from the meta-generalized gradient approximation (meta-GGA) class have been used extensively to calculate the electronic properties of solids. In particular, band gaps can be accurately evaluated with the modified Becke-Johnson (MBJ) potential, and relaxed atomic structures close to experimental findings can be obtained with the strongly constrained and appropriately normed (SCAN) exchange-correlation functional. Both approaches are computationally cheaper than HSE06, and we consider here their performance for defect level calculations. We compare results for the $\epsilon (+/0)$ transition levels of seven donors and $\epsilon (0/-)$ transition levels of four acceptors in group IV semiconductors. We conclude that in certain situations where HSE06 cannot be applied because of excessive computational costs, SCAN and MBJ might provide a good alternative.

We develop a phonon-magnon interaction model for the two-dimensional honeycomb ferromagnet and calculate the band structure of the hybrid phonon-magnon excitation. When the phonon (either acoustic or optical) energy overlaps with the magnon energy, the degeneracies at the crossing points are lifted by the phonon-magnon interaction, leading to topological band inversion. We show that the Berry curvatures and Chern numbers are nonzero around the phonon-magnon band-crossing areas but vanish throughout the rest of the Brillouin zone. We calculate the thermal Hall conductance enabled by the phonon-magnon interaction, which is also an indicator of nontrivial topological properties. In addition, we show that band topologies can be manipulated by varying spin-exchange coupling strengths and Dzyaloshinskii-Moriya interactions strengths.

The magnetic skyrmion, a tiny magnetic texture that holds promise as the next-generation information carrier, has been widely studied in recent years. A fine tunability of skyrmion density is required for its real applications in novel memory and logic devices. Here, we report on the manipulation of skyrmion density at room temperature in a Pt/Co/Ta/MgO system composed of multiple repetitions with perpendicular magnetic anisotropy. Néel-type skyrmions are observed by performing Lorentz transmission electron microscopy and magnetic force microscopy. The influence of structure repetition on skyrmions is experimentally investigated and further understood by micromagnetic simulations. The variation of skyrmion density with repetition number is mainly attributed to magnetic anisotropy. Meanwhile, thermal annealing is utilized to regulate the skyrmion density, where skyrmion-related properties exert a competitive effect. Our findings provide alternative means to manipulate skyrmion density, further allowing for optimized engineering of skyrmion-based devices.

We demonstrate that a machine learning technique with a simple feedforward neural network can sensitively detect two successive phase transitions associated with the Berezinskii-Kosterlitz-Thouless (BKT) phase in $q$-state clock models simultaneously by analyzing the weight matrix components connecting the hidden and output layers. We find that the method requires only a data set of the raw spatial spin configurations for the learning procedure. This data set is generated by Monte Carlo thermalizations at selected temperatures. Neither prior knowledge of, for example, the transition temperatures, number of phases, and order parameters nor processed data sets of, for example, the vortex configurations, histograms of spin orientations, and correlation functions produced from the original spin-configuration data are needed, in contrast with most of previously proposed machine learning methods based on supervised learning. Our neural network evaluates the transition temperatures as $T_2/J=0.921$ and $T_1/J=0.410$ for the paramagnetic-to-BKT transition and BKT-to-ferromagnetic transition in the eight-state clock model on a square lattice. Both critical temperatures agree well with those evaluated in the previous numerical studies.

Topological Weyl semimetals have been attracting broad interest. Recently, a new type of Weyl point with topological charge of four, termed as charge-four Weyl point (C-4 WP), was proposed in spinless systems. Here, we show the minimum symmetry requirement for C-4 WP is point-group $T$ together with $\mathcal{T}$ symmetry or point-group $O$. We establish a minimum tight-binding model for C-4 WP on a cubic lattice with time-reversal symmetry and without spin-orbit coupling effect. This lattice model is a two-band one, containing only one pair of C-4 WPs with opposite chirality around the Fermi level. Based on both the low-energy effective Hamiltonian and the minimum lattice model, we investigate the electronic, optical, and magnetic properties of C-4 WP. Several chirality-dependent properties are revealed, such as chiral Landau bands, quantized circular photogalvanic effect and quadruple-helicoid surface arc states. Furthermore, we predict that under symmetry breaking, various exotic topological phases can evolve out of C-4 WPs. Our paper not only reveals several interesting phenomena associate with C-4 WPs, but also provides a simple and ideal lattice model of C-4 WP, which will be helpful for the subsequent study on C-4 WPs.

We consider $\mathrm{SU}\left(N\right)$-symmetric Ginzburg-Landau models coupled to a noncompact Abelian gauge field focusing on the case $N>2$ at finite temperature. We show that, at least for sufficiently large gauge-field coupling constants, these models have two phase transitions. The intermediate phase between the symmetric and low-temperature phases is a state with composite neutral order and no Meissner effect. In this neutral phase the system spontaneously breaks only the symmetry associated with phase differences and density differences between components. For $N>2$, in contrast to the $\mathrm{SU}\left(2\right)$ case, the neutral state cannot be mapped onto an $\mathrm{O}\left(M\right)$ model. We term this state the $\mathrm{SU}{\left(N\right)}_{\mathrm{n}}$ phase.

Elemental gallium can exist in several phases under ambient pressure. The stable $\alpha$ phase has a superconducting transition temperature, $T_c$, of 0.9 K. By contrast, the $T_c$ of the metastable $\beta$ phase is around 6 K. To understand the significant improvement in $T_c$ in the $\beta$ phase, we first calculate the electronic structure, phonon dispersion, and the electron-phonon coupling of gallium in the $\alpha$ and $\beta$ phases. Next, we solve the Eliashberg equations to obtain the superconducting gaps and the transition temperatures. Using these results, we relate the increased $T_c$ in the $\beta$ phase to structural differences between the phases that affect the electronic and phonon properties. The structure motif of the $\alpha$ phase is ${\mathrm{Ga}}_2$ dimers, which form strong covalent bonds leading to bonding and antibonding states that reduce the density of states at the Fermi level. The $\beta$-Ga structure consists of arrays of Ga chains that favor strong coupling between the lattice vibrations and the electronic states near the Fermi level. The increased density of states and strong coupling to the phonons for the $\beta$-Ga chains compared to the $\alpha {\mathrm{Ga}}_2$ dimers enhance superconductivity in the $\beta$-Ga phase.

We study the electron temperature profiles for an inhomogeneous electron flow in the hydrodynamic regime. We assume that the inhomogeneity is due to a weakly nonuniform distribution of the momentum relaxation time within a spherically constricted area. We show that the temperature profile dramatically depends on the drive strength and the viscosity of the electron liquid. In the absence of viscosity, a Landauer-dipole-like temperature distribution, asymmetrically deformed along the current by the inelastic electron-phonon scattering, emerges around the inhomogeneity. We find that both the Landauer-dipole temperature profile and its asymmetry in the direction of the driving electric field exist in all dimensionalities and are, therefore, universal features of inhomogeneous hydrodynamic electron flow. We further demonstrate that the electron viscosity suppresses the thermal Landauer dipole and leads to the appearance of a “hot spot” exactly at the center of the constriction. We also calculate the phonon temperature distribution, which can be directly measured in experiments on thermal nanoimaging.

Transition metal dichalcogenides (TMDs) are layered materials which show excellent potential for nanoelectronic and optoelectronic applications. However, as many of the exciting features of these materials are controlled by anharmonic effects, a proper understanding of the phonon properties and anharmonicity associated with these materials is essential for the proposed applications to be realized. We present here a comprehensive study on the phonon properties of two different TMDs, viz., $\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{Mo}{\mathrm{Te}}_2$, as a function of temperature, laser excitations, and polarization, as well as flake thickness. This paper includes the measurement of anharmonicity in the first-order and higher order Raman scattering processes. Variations in anharmonicity with the thickness of $\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{Mo}{\mathrm{Te}}_2$ have been explained in terms of their phonon symmetries, electron-phonon coupling, and phonon-phonon interactions. Further, the effect of the underlying substrate on the anharmonic properties of in-plane and out-of-plane phonons has also been estimated from Raman measurements, thus elucidating the intrinsic phonon properties of two-dimensional layered materials.

We discuss the applicability of elementary band representations (EBRs) to diagnose spatial- and time-reversal-symmetry protected topological phases in interacting insulators in terms of their single-particle Green's functions. We do so by considering an auxiliary noninteracting system $H_{\text{T}}\left(\mathbf{k}\right)=-G^{-1}(0,\mathbf{k})$, known as the topological Hamiltonian, whose bands can be labeled by EBRs. This labeling is robust if neither (i) the gap in the spectral function at zero frequency closes, (ii) the Green's function has a zero at zero frequency, or (iii) the Green's function breaks a protecting symmetry. We demonstrate the use of EBRs applied to the Green's function on the one-dimensional Su-Schrieffer-Heeger model with Hubbard interactions, which we solve by exact diagonalization for a finite number of unit cells. Finally, the use of EBRs for the Green's function to diagnose so-called symmetry-protected topological phases is discussed, but remains an open question.

Isolated many-body quantum systems quenched far from equilibrium can eventually equilibrate, but it is not yet clear how long they take to do so. To answer this question, we use exact numerical methods and analyze the entire evolution, from perturbation to equilibration, of a paradigmatic disordered many-body quantum system in the chaotic regime. We investigate how the equilibration time depends on the system size and observables. We show that if dynamical manifestations of spectral correlations in the form of the correlation hole (“ramp”) are taken into account, the time for equilibration scales exponentially with system size, while if they are neglected, the scaling is better described by a power law with system size, although with an exponent larger than what is expected for diffusive transport.

Three-, four-, and sixfold excitations have significantly extended the subjects of condensed-matter physics. There is an urgent need for a realistic material that can have coexisting three-, four-, and sixfold excitations. However, these materials are uncommon because these excitations in electronic systems are usually broken by spin-orbit coupling (SOC) and are normally far from the Fermi level. Unlike the case in electronic systems, phonon systems with a negligible SOC effect, not constrained by the Pauli exclusion principle, provide a feasible platform to realize these excitations in a wide frequency range. Hence, in this work, we demonstrate by first-principles calculations and symmetry analysis that perfect three-, four-, sixfold excitations appear in the phonon dispersion rather than the band structures of ${\mathrm{Zr}}_3{\mathrm{Ni}}_3{\mathrm{Sb}}_4$, which is a well-known indirect-gap semiconductor with an ${\mathrm{Y}}_3{\mathrm{Au}}_3{\mathrm{Sb}}_4$-type structure. This material features a threefold-degenerate quadratic contact triple-point phonon, fourfold-degenerate Dirac point phonon, and sixfold degenerate point phonon. Moreover, these nodal point phonons are very robust to uniform strain. Two obvious phonon surface arcs of the (001) plane are extended in the whole Brillouin zone, which will facilitate their detection in future experimental studies. The current work provides an ideal model to investigate rich excitations in a single material.

We report magnetic proximity effect, valley splitting (VS), and magneto-optical properties of polar $(\mathrm{TiBrI}/\mathrm{Cr}{\mathrm{I}}_3)$ and nonpolar ($\mathrm{Ti}{X}_2/\mathrm{Cr}{\mathrm{I}}_3$, $X=\mathrm{Br},\mathrm{I}$) magnetic van der Waals heterostructures. To properly handle many-body effects, the band structure and excitonic effects are considered on the same footing by carrying out first-principles calculations together with resolving the Bethe-Salpeter equation. We find that an atypical type-III band alignment leads to a sizable magnetic proximity effect as well as giant VS (126 meV). In addition, they can be largely tuned by the polarity of TiXY crystal structure and stacking configuration. Moreover, such a giant magnetic proximity effect drives a switch of spin-band (spin-up and spin-down) ordering of TiBrI, not only in the conduction band, but also surprisingly in the valence band in the vicinity of $K$ or $K$′ points, which brings out a significant change in exciton emissions. Our results open an avenue for spintronics and nano-optics applications.

The energy level alignment at the metal/organic interface greatly affects the charge injection/extraction efficiency of electrodes in organic semiconductor devices. The charge carrier in the vicinity of the metal surface should be stabilized by the screening effect of the metal surface, thereby resulting in the narrowing of the energy gap (highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap) and modifying the energy level alignment at the metal/organic interface. However, this metal screening effect has not been fully clarified because there has been no precise way to quantitatively evaluate the experimental values. In this study, we employed ultraviolet photoelectron spectroscopy (UPS), metastable atom electron spectroscopy (MAES), and low-energy inverse photoelectron spectroscopy (LEIPS) to examine the quasi–layer-by-layer grown film of perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) on the atomically flat metal surface of Ag(111) and Au(111). By applying a procedure we established recently, we precisely evaluated the energy of the metal screening effect. The results demonstrate that the screening effect of the metal surface modifies the charge injection/collection barrier at the metal/organic interface by as much as 0.25 eV. We found that the PTCDA thickness dependent screening effect is precisely reproduced by the image charge model.

The two-dimensional electron gas with spin-orbit interactions (SOIs) of Rashba and Dresselhaus types is known to form an anisotropic system with a Van Hove singularity in the density of states. Moreover, the “amplitude” and the energy position of this singularity depend on the ratio of the constants of Rashba $\alpha$ and Dresselhaus $\beta$ SOIs, $\gamma =\beta /\alpha$. Here the dependencies of the conductivity and spin susceptibility tensors on the position of the Fermi level are calculated for a wide range of $\gamma$. It is shown that if only the lower spin subband is filled the diagonal elements of the conductivity tensor have dips that appear when the Fermi level passes the singularity point both for $\gamma <1$ and $\gamma >1$. The amplitude of these features and their energy position depend on $\gamma$ and, in particular, for the state of persistent spin helix $\gamma =1$ they disappear. When only the lower spin subband is filled, the off-diagonal elements of the conductivity tensor are nonzero, that is, there is a Hall voltage due to the anisotropy of the Fermi surface and the scattering. In the region of filling of two spin subbands the ratio of diagonal and nondiagonal components of the spin susceptibility tensor is equal to $\gamma$ and in the conductivity tensor, the off-diagonal terms vanish.

Recent studies have shown that the ferromagnetic intralayer order in $\mathrm{Cr}{\mathrm{I}}_3$ is weakened by electrostatic electron doping, with magnetization and Curie temperature decreasing linearly with doping density. The linear doping dependence observed in $n$-type $\mathrm{Cr}{\mathrm{I}}_3$ is puzzling because it requires a “fine-tuned” nonlinear decrease of the spin-wave gap upon electron doping. Here, using first-principles-based simulations, we reveal that electron doping of $\mathrm{Cr}{\mathrm{I}}_3$ induces a quantum phase transition to a magnetic state characterized by spontaneous spin-flip formation at the atomic scale. The electron localization in the presence of the spin-flips “renormalizes” the energy gap for collective spin excitations, which explains the puzzling doping effect on the two-dimensional magnetism of $\mathrm{Cr}{\mathrm{I}}_3$.

Hydrogen-rich compounds are being extensively explored theoretically and experimentally as potential hydrogen storage materials. In this work, we predicted a hydrogen-rich compound rhodium trihydride ($\mathrm{Rh}{\mathrm{H}}_3$) with a high volumetric hydrogen density of 212.5 g/L by means of ab initio calculations. The $\mathrm{Rh}{\mathrm{H}}_3$ with Pnma symmetry is thermodynamically stable and accessible through synthesis above 40 GPa. The compound is dynamically and mechanically stable at ambient pressure. Further calculation suggests a probable dehydrogenation temperature $T_{\mathrm{des}}$ of $65{}^{\circ }\mathrm{C}$ at ambient pressure with decomposition route to $\mathrm{Rh}+{\mathrm{H}}_2$. High volumetric hydrogen density and moderate dehydrogenation temperature place $\mathrm{Rh}{\mathrm{H}}_3$ as one of the best hydrogen storage materials. Our work encourages the experimental synthesis of $\mathrm{Rh}{\mathrm{H}}_3$ at high pressure.