Since tantalum arsenide (TaAs) has been experimentally verified as a Weyl semimetal, intensive research has been devoted to study of the unique properties of the material. Despite this, the ultrafast dynamics of TaAs is still not very well understood. In this work, we study the relaxation dynamics in TaAs using transient reflection spectroscopy. From the transient reflection measurement, we observe either a single (fast) or a dual (fast and slow) relaxation, depending on the probing wavelength. The additional relaxation channel is attributed to an asymmetric population of photoexcited electrons and holes.

As is well known, the single-site anisotropy vanishes in the spin-$\frac{1}{2}$ compounds as a consequence of the fundamental Kramers degeneracy. We argue, rather generally, that a similar property holds for the magnetically induced electric polarization $\mathit{P}$, which should depend only on the relative orientation of spins in the bonds but not on the direction of each individual spin. Thus, for insulating multiferroic compounds, $\mathit{P}$ can be decomposed in terms of pairwise isotropic, antisymmetric, and anisotropic symmetric contributions, which can be rigorously derived in the framework of the superexchange (SE) theory, in analogy with the spin Hamiltonian. The SE theory also allows us to identify the microscopic mechanism that stands behind each contribution. The most controversial and intriguing one—concerning the form, appearances, and implications for the properties of real compounds—is the antisymmetric or spin-current mechanism. In this work, we propose that, within the SE theory, the disputed magnetoelectric (ME) properties of tetragonal ${\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{Ge}}_2{\mathrm{O}}_7$, representing the lattice of magnetic ${\mathrm{Cu}}^{2+}$ ions in the tetrahedral environment, can be explained solely by the spin-current mechanism, while other contributions are either small or forbidden by symmetry. First, after analysis of the symmetry properties of the SE Hamiltonian and corresponding parameters of electric polarization, we explicitly show how the cycloidal spin order induces the experimentally observed electric polarization in the direction perpendicular to the tetragonal plane, which can be naturally explained by the spin-current mechanism operating in the out-of-plane bonds. Then, we unveil the previously overlooked ME effect, where the application of the magnetic field perpendicular to the plane not only causes the incommensurate-commensurate transition, but also flips the electric polarization into the plane due to the spin-current mechanism operating in the neighboring bonds within this plane. In both cases, the magnitude and direction of $\mathit{P}$ can be controlled by rotating the spin pattern in the tetragonal plane. Our analysis is based on a realistic spin model, which was rigorously derived from first-principles electronic structure calculations and supplemented with a new algorithm for the construction of localized Wannier functions obeying the crystallographic symmetry of ${\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{Ge}}_2{\mathrm{O}}_7$.

The magnetization of $\mathrm{Sm}{\mathrm{Fe}}_{11}\mathrm{Ti}$ single crystals has been measured along the principal crystallographic directions in steady (14 T) and pulsed (43 T) magnetic fields. The fourfold symmetry axis [001] is an easy magnetization direction. The magnetization curves measured in directions perpendicular to [001] are remarkable in two ways: (i) They do not depend on orientation of $\mathit{H}$ within the basal plane; (ii) at low temperature they are $\mathsf{S}$ shaped, with an inflection point at about 0.6 times saturation magnetization. These two facts enable us to conclude that three out of five crystal field parameters of $\mathrm{Sm}{\mathrm{Fe}}_{11}\mathrm{Ti}$ are negligibly small; only $A_2^0$ and $A_6^0$ are essentially nonzero. A comparison with an isomorphous compound ${\mathrm{DyFe}}_{11}\mathrm{Ti}$ reveals a dramatic disparity of their crystal fields, especially as regards $A_4^4$, nearly zero in $\mathrm{Sm}{\mathrm{Fe}}_{11}\mathrm{Ti}$ but outstandingly large in ${\mathrm{DyFe}}_{11}\mathrm{Ti}$.

The crystal structure and the magnetic properties of the ${\mathrm{Co}}_{2.5}{\mathrm{Cr}}_{0.5}{\mathrm{BO}}_5$ ludwigite have been investigated by x-ray diffraction, magnetization, and specific heat experiments. Cr ions mainly occupy sites 4 of the ludwigite lattice, substituting approximately half of the ${\mathrm{Co}}^{3+}$. It changes the interatomic distances and favors a high spin state for the remaining ${\mathrm{Co}}^{3+}$ ions. Doping the homometallic ${\mathrm{Co}}_3{\mathrm{BO}}_5$ with magnetic Cr drastically increases the magnetic transition temperature from 42 K, for the undoped compound, to 76 K for ${\mathrm{Co}}_{2.5}{\mathrm{Cr}}_{0.5}{\mathrm{BO}}_5$. The latter contains three different magnetic ions, ${\mathrm{Co}}^{2+}, {\mathrm{Co}}^{3+}$ and ${\mathrm{Cr}}^{3+}$ in high spin states, as evidenced by magnetization measurements. The specific position of Cr in the structure (sites 4) gives rise, according to calculations of the exchange interactions and the Goodenough-Kanamori rules, to a few frustrated magnetic interactions. This is responsible for the high ferrimagnetic ordering temperature of 76 K, when compared to that of the pure compound. The experimental results imply a magnetic structure for the system that we show is consistent with the known interactions and the Goodenough-Kanamori rules. Low temperature specific heat and magnetization measurements reveal that the two-dimensional nature of the magnetism ${\mathrm{Co}}_3{\mathrm{BO}}_5$ when doped with Cr acquires a three-dimensional character with a high temperature ferrimagnetic order.

Single crystals of $\mathrm{Nb}{\mathrm{Ge}}_2$ which crystallize in a noncentrosymmetric hexagonal structure with chirality are synthesized and their superconductivity is investigated. Type-I superconductivity is confirmed by dc magnetization, a field-induced second-to first-order phase transition in specific heat, and a small Ginzburg-Landau parameter ${\kappa }_{\text{GL}}=0.12$. The isothermal magnetization measurements show that there is a crossover from type-I to type-II/1 superconductivity with decreasing temperature and an unusually enhanced surface superconducting critical field ($H_{c3}$) is discovered. The band structure calculations indicate the presence of Kramer-Weyl nodes near the Fermi level. These observations demonstrate that $\mathrm{Nb}{\mathrm{Ge}}_2$ is an interesting and rare example involving the possible interplay of type-I superconductivity, noncentrosymmetric structures, and topological properties.

The $\eta$-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989)]. These states are not many-body scar states in the Hubbard model because they occupy unique symmetry sectors defined by the so-called $\eta$-pairing SU(2) symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [J. E. Hirsch, Physica C 158, 326 (1989)], where the $\eta$-pairing states survive without the $\eta$-pairing symmetry and become true scar states. We also discuss similarities between the $\eta$-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [M. Schecter and T. Iadecola, Phys. Rev. Lett. 123, 147201 (2019)], and systematically arrive at all nearest-neighbor terms that preserve such scar towers in one dimension. We also generalize these terms to arbitrary bipartite lattices. Our study of the spin-1 XY model also leads us to several scarred models, including a spin-1/2 $J_1-J_2$ model with Dzyaloshinskii-Moriya interaction, in realistic quantum magnet settings in one and two dimensions.

As a novel type of fermionic state, the hybrid nodal loop with the coexistence of both type-I and type-II band crossings has attracted intense research interest. However, it remains a challenge to realize the hybrid nodal loop in both two-dimensional (2D) materials and in ferromagnetic (FM) materials. Here, we propose a FM hybrid nodal loop in a 2D CrN monolayer. We show that the material has a high Curie temperature ($>600$ K) FM ground state, with the out-of-plane [001] magnetization. It shows a half-metallic band structure with two bands in the spin-up channel crossing each other near the Fermi level. These bands produce both type-I and type-II band crossings, which form a fully spin-polarized hybrid nodal loop. We find the nodal loop is protected by the mirror symmetry and robust against spin-orbit coupling. An effective Hamiltonian characterizing the hybrid nodal loop is established. We further find the configuration of the nodal loop can be shifted under external perturbations such as strain. Most remarkably, we demonstrate that both type-I and type-II Weyl nodes can be realized from such FM hybrid nodal loop by simply shifting the magnetization from out of plane to in plane. Our work provides an excellent candidate to realize a FM hybrid nodal loop and Weyl fermions in 2D material, and is also promising for related topological applications with their intriguing properties.

We study the impact of next-nearest-neighbor (NNN) hopping on the low-energy collective excitations of strongly correlated doped antiferromagnetic cuprate spin chains. Specifically, we use exact diagonalization and the density matrix renormalization group method to study the single-particle spectral function, the dynamical spin and charge structure factors, and the Cu $L$-edge resonant inelastic x-ray scattering (RIXS) intensity of the doped $t\text{−}t\prime \text{−}J$ model for a set of $t\prime$ values. We find evidence that the spin and charge degrees of freedom of the doped holes are not strictly separated anymore as $|t\prime |$ increases and identify the consequences of this in the dynamical response functions. The inclusion of NNN hopping couples the spinon and holon excitations, resulting in the formation of a spin polaron, where a ferromagnetic spin-polarization cloud dresses the doped carrier. The spin polaron manifests itself as additional spectral weight in the dynamical correlation functions, which appear simultaneously in the spin- and charge-sensitive channels. We also demonstrate that RIXS can provide a unique view of the spin polaron, due to its sensitivity to both the spin and charge degrees of freedom.

In the envelope-function approximation, interband transitions produced by electric fields are neglected. However, electric fields may lead to a spatially local $\left(k\text{−}\mathrm{independent}\right)$ coupling of band (internal, pseudospin) degrees of freedom. Such a coupling exists between heavy-hole and light-hole (pseudo)spin states in III-V semiconductors, such as GaAs, or in group IV semiconductors (germanium, silicon,...) with broken inversion symmetry. Here, we calculate the electric-dipole (pseudospin-electric) coupling for holes in GaAs from first principles. We find a transition dipole of 0.5 debye, a significant fraction of that for the hydrogen-atom $1s\to 2p$ transition. In addition, we derive the Dresselhaus spin-orbit coupling that is generated by this transition dipole for heavy holes in an asymmetric quantum well. A quantitative microscopic description of this pseudospin-electric coupling may be important for understanding the origin of spin splitting in quantum wells, spin coherence/relaxation $(T_2^{*}/T_1)$ times, spin-electric coupling for cavity-QED, electric-dipole spin resonance, and spin nonconserving tunneling in double quantum dot systems.

$\mathrm{Si}\left(111\right)\text{−}(5\times 2)\text{−}\mathrm{Au}$ represents a prototype system for an adsorbate-induced spontaneous symmetry break by formation of quasi-one-dimensional atomic chains that are metallic. Surprisingly, the geometric structure of these chains is still under debate. In this paper, we show that examination of the unoccupied band structure by plasmon spectroscopy in combination with low energy electron diffraction contains sufficient information to discriminate between suggested models, favoring an optimal concentration of 6 atoms per $(5\times 2)$ unit cell. Furthermore, we tested the stability of this structure and found that higher concentrations of Au tend to destabilize the single-domain structure on the slightly misoriented Si(111) surface, favoring formation of $(\sqrt{3}\times \sqrt{3})R{30}^{\circ }\text{−}\mathrm{ordered}$ islands with a local concentration of 1 ML already at a surplus of 0.08 ML. The precise role of Au atoms at concentrations exceeding 0.60 ML that seem to stabilize formation of three domains, however, must remain open.

We investigate the dynamical interaction between an electron crystal trapped above the surface of liquid helium and surface waves (‘ripplons') excited by its motion. At rest, the electron system is ‘dressed’ by static ripplons to form ‘ripplopolaron’ states. As the electrons move, resonant ripplon scattering results in a growth of the ripplopolaron effective mass, on timescales comparable with the inverse of the ripplon frequency ($\sim 100$ ns). Under sufficient driving force, the electron system decouples from the surface waves and moves at high velocity, before decelerating sharply when the electron solid and surface excitations recouple to form a ‘new’ ripplopolaron system. The mass of the newly formed ripplopolarons is similar to that in the initial static case.

In this article, we study the energy spectrum of fractals which has block-hierarchical structure. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it numerically by calculation of level-spacing distributions. Our approach provides qualitative explanation for various spectral properties of self-similar graphs within the theory of dynamical systems, including the power-law level-spacing distribution, smooth density of states, and effective chaotic regime.

In the vicinity of the magic angle in twisted bilayer graphene (TBG), many exotic correlated states, such as superconductivity, ferromagnetism, and topological phases, are observed because the two low-energy Van Hove singularities (VHSs) become exceedingly narrow, i.e., become flatbands. Heterostrain, strain in van der Waals structures where each layer is strained independently, can modify the single-particle band structure of the TBG and lead to various properties. Here, we show that heterostrain in a TBG near the magic angle generates a zero-energy flatband between the two VHSs. Doping the TBG to partially fill the zero-energy flatband, we observe a correlation-induced valley-polarized gap of ∼10 meV. By applying perpendicular magnetic fields, a large and linear response of the gap to magnetic fields is observed, attributing to the large orbital magnetic moments in TBG. The measured orbital magnetic moment per moiré unit cell is $\sim 15{\mu }_B$ in the TBG, which is well consistent with our calculations.

The electron self-energy for long-range Coulomb interactions plays a crucial role in understanding the many-body physics of interacting electron systems (e.g., in metals and semiconductors) and has been studied extensively for decades. In fact, it is among the oldest and the most-investigated many-body problems in physics. However, there is a lack of an analytical expression for the self-energy $Re{\mathrm{\Sigma }}^{\left(R\right)}(\varepsilon ,T)$ when energy $\varepsilon$ and temperature $k_{\mathsf{B}}T$ are arbitrary with respect to each other (while both being still small compared with the Fermi energy). We revisit this problem and calculate analytically the self-energy on the mass shell for a two-dimensional electron system with Coulomb interactions in the high density limit $r_s\ll 1$, for temperature $r_s^{3/2}\ll k_{\mathsf{B}}T/E_{\mathsf{F}}\ll r_s$ and energy $r_s^{3/2}\ll \left|\varepsilon \right|/E_{\mathsf{F}}\ll r_s$. We provide the exact high-density analytical expressions for the real and imaginary parts of the electron self-energy with arbitrary value of $\varepsilon /k_{\mathsf{B}}T$, to the leading order in the dimensionless Coulomb coupling constant $r_s$, and to several higher than leading orders in $k_{\mathsf{B}}T/r_s{E}_{\mathsf{F}}$ and $\varepsilon /r_s{E}_{\mathsf{F}}$. We also obtain the asymptotic behavior of the self-energy in the regimes $\left|\varepsilon \right|\ll k_{\mathsf{B}}T$ and $\left|\varepsilon \right|\gg k_{\mathsf{B}}T$. The higher-order terms have subtle and highly nontrivial compound logarithmic contributions from both $\varepsilon$ and $T$, explaining why they have never before been calculated in spite of the importance of the subject matter.

The ground-state phase diagram is obtained for an antiferromagnetic spin-1 anisotropic biquadratic model. With the help of symmetry and duality transformations, three symmetry-protected trivial phases and one dimerized symmetry-breaking phase are found. Local and nonlocal order parameters are identified to characterize these phases. Quantum phase transitions between the symmetry-protected phases belong to the Gaussian universality class with central charge $c=1$, and quantum phase transitions from the symmetry-protected trivial phases to the dimerized phase belong to the Ising universality class with central charge $c=1/2$. In addition, the model admits three characteristic lines of factorized ground states, which are located in the symmetry-protected trivial phases instead of a symmetry-breaking phase, in sharp contrast to other known cases.

The nonequilibrium excitonic insulator (NEQ-EI) is an excited state of matter characterized by a finite density of coherent excitons and a time-dependent macroscopic polarization. The stability of this exciton superfluid as the density grows is jeopardized by the increased screening efficiency of the looser excitons. In this work we put forward a Hartree plus screened exchange scheme to predict the critical density at which the transition toward a free electron-hole plasma occurs. The dielectric function is calculated self-consistently using the NEQ-EI polarization and found to vanish in the long-wavelength limit. This property makes the exciton superfluid stable up to relatively high densities. Numerical results for the ${\mathrm{MoS}}_2$ monolayers indicate that the NEQ-EI phase survives up to densities of the order of ${10}^{12}{\mathrm{cm}}^{-2}$.

The optical spectra of two-dimensional (2D) materials exhibit sharp absorption peaks that are commonly identified with exciton and trions (or charged excitons). In this paper, we show that excitons and trions in doped 2D materials can be described by two coupled Schrödinger-like equations—one two-body equation for excitons and another four-body equation for trions. In electron-doped 2D materials, a bound trion state is identified with a four-body bound state of an exciton and an excited conduction-band electron-hole pair. In doped 2D materials, the exciton and trion states are the not the eigenstates of the full Hamiltonian and their respective Schrödinger equations are coupled due to Coulomb interactions. The strength of this coupling increases with the doping density. Solutions of these two coupled equations can quantitatively explain all the prominent features experimentally observed in the optical absorption spectra of 2D materials, including the observation of two prominent absorption peaks and the variation of their energy splittings and spectral shapes and strengths with the electron density. The optical conductivity obtained in our paper satisfies the optical conductivity sum rule exactly. A superposition of exciton and trion states can be used to construct a solution of the two coupled Schrödinger equations and this solution resembles the variational exciton-polaron state, thereby establishing the relationship between our approach and Fermi polaron physics.

Using density functional theory based electronic structure calculations, we carry out detailed investigation on geometric and electronic properties of group-III atom (B, Al, and Ga) based monolayers, namely borophene, aluminene, and gallinene, in ${\beta }_{12}$ configuration which is one of the stable structures for borophene. The results of our calculations indicate that all these monolayers form energetically stable systems and these are all metallic in nature since they possess finite density of states at the Fermi level. Analysis of optimized geometric structures reveals that while borophene in ${\beta }_{12}$ structure stabilizes in planar structure, the geometries of the remaining monolayers are nonplanar. In the case of borophene, there is a signature of crossing of two linear bands (which form Dirac cones) at about 2 eV and 0.5 eV above the Fermi level. Similar features have also been observed in electronic band structures of both aluminene and gallinene. Interestingly, one of the Dirac cones in these monolayers lies much closer to the Fermi level compared to the borophene case. The Fermi velocities around these Dirac cones are also higher and comparable to that in graphene. We further study the effect of isoelectronic substitution at one of the inequivalent sites (C site) of the ${\beta }_{12}$ configuration for these three monolayers. Our results show that borophene still retains its planar geometry following the substitution. Interestingly, in all these cases, crossing of linearly dispersing bands (Dirac cones) is observed nearer to the Fermi level compared to the pristine systems. Our study suggests that isoelectronic substitutions may be useful in tuning the electronic properties, in particular linear dispersion, of monolayer systems.

We calculate the quasiparticle properties of $\mathrm{Mo}{\mathrm{S}}_2$ monolayer at $T=0$ considering the dynamical electron-electron interaction effect within random-phase-approximation (RPA). The calculations are carried out for an electron-doped slab of $\mathrm{Mo}{\mathrm{S}}_2$ monolayer using a minimal massive Dirac Hamiltonian and the quasi-two-dimensional nature of the Coulomb interaction in this system is taken into account considering a modified interaction of Keldysh type. Having calculated the real and imaginary parts of the retarded self-energy, we find the spectral function and discuss the impact of extrinsic variables such as the dielectric medium and the charge carrier density on the appearance and position of the quasiparticle peaks. We also report the results of the renormalization constant and the effective Fermi velocity calculations in a broad range of the coupling constant and carrier density. We show that the effective Fermi velocity obtained solving the self-consistent Dyson equation has an absolutely different behavior from the one found from the on-shell approximation. Our results show that the nonlocal dielectric screening of the monolayer tends to stabilize the Fermi liquid picture in $\mathrm{Mo}{\mathrm{S}}_2$ monolayer and that the interaction strength parameter of this system is a multivariable function of the coupling constant, carrier density, and also the screening length.

We performed inelastic x-ray scattering experiments on solid and liquid Li to determine the static density response function $\chi (q,0)$, where $q$ is wave vector. The experimentally determined $\chi (q,0)$ allows meaningful comparison of the response function with that of the electron gas model; $\chi (q,0)$ exhibits the $2k_F$ singularity predicted in the electron gas model. The screening electron density induced by a positive point charge is calculated, and it shows Friedel oscillations both in solid and liquid Li. Moreover, we found that the Friedel oscillations become weak upon melting.