We introduce the spin entanglement entropy (EE) to characterize spin excitations. The scalings of EEs are elaborated as $lnN, lnN+D_k$, and $2lnN+D$ for the single-magnon states, two-magnon bound states, and two-magnon continuum, respectively, based on the Bethe ansatz solutions of the ferromagnetic spin chain with $N$ sites. The $lnN$ divergence for the bound states reveals that the two magnons emerge as a new quasiparticle. More importantly, the nonzero intercepts ($D_k,D$) embody the many-body effects of two-magnon states. In particular, an exact relation between the intercept of EEs and an observable quantity, the two-magnon distance, is established for the bound states. In such a case, we quantify the two-magnon confinement in a spin system by the increasing entanglement with the distance as a particle physics analog. Moreover, the EEs can also be used to study the evolution of the excitations. When the bound states are immersed in the continuum in the alternating chain, they undergo an oscillating confinement-deconfinement crossover, shown by the oscillations of the EEs and two-magnon distance with the chain length.

In this paper, we demonstrate that the standard theory of thermoelasticity fails in describing stress dependence of laser-exited ultrasound in real dielectric and especially conductive materials. A theoretical model of thermoelasticity considering the thermal perturbation of nonstationary defect states with relaxation is presented and analyzed. To explain the obtained experimental data for metals, it is necessary to also consider a change in the pressure of the electron gas due to the defect perturbation. The proposed model is used to describe linear and nonlinear behavior of the laser ultrasonic signals near a hole in a dielectric ceramic and a metal alloy submitted to a uniform compression. The model introduces an effective dynamic coefficient of thermal expansion for real stressed materials. The obtained results provide an opportunity to estimate mechanical stresses in different materials. In this paper, we describe the calibration of the laser ultrasonic signals on stress in combination with hole drilling. The approach also allows us to estimate relaxation times of the laser-excited defects in stressed materials.

The mechanical behavior of two-dimensional (2D) materials across 2D phase changes is unknown, and the finite temperature ($T$) elasticity of paradigmatic SnSe monolayers—ferroelectric 2D materials turning paraelectric as their unit cell turns from a rectangle into a square—is described here in a progressive manner. To begin with, their $\mathrm{zero}\text{−}T$ total energy landscape gives way to (Boltzmann-like) averages from which the elastic behavior is determined. These estimates are complemented with results from the strain-fluctuation method, which employs the energy landscape or ab initio molecular dynamics data. All approaches capture the coalescence of elastic moduli $\langle C_{11}\left(T\right)\rangle =\langle C_{22}\left(T\right)\rangle$ due to the structural transformation. The broad evolution and sudden changes of elastic parameters $\langle C_{11}\left(T\right)\rangle$, $\langle C_{22}\left(T\right)\rangle$, and $\langle C_{12}\left(T\right)\rangle$ of these atomically thin phase-change membranes establishes a heretofore overlooked connection among 2D materials and soft matter.

Recently discovered magnetic topological insulators $T{\mathrm{Bi}}_2{\mathrm{Te}}_4 (T=\mathrm{Mn},\mathrm{Fe})$ crystallize into the $R\overline{3}m$ rhombohedral structure and exhibit the antiferromagnetic order. Here, we discuss the lattice dynamics of these compounds to confirm the stability of these systems. We show that the phonon dispersion does not contain soft modes, so both compounds are dynamically stable in the $R\overline{3}m$ phase. We perform theoretical analyses of the mode activity at the $\mathrm{\Gamma }$ point for the discussed compounds. In the case of the Raman active modes, our results are in agreement with the experimentally observed frequencies. Finally, we also discuss the possibility of the realization of chiral phonons.

An unusual temperature-induced spin reorientation transition from ${\mathrm{\Gamma }}_2(F_x, C_y, G_z)-{\mathrm{\Gamma }}_{23}-{\mathrm{\Gamma }}_3(C_x, F_y, A_z)$ in orthoferrite ${\mathrm{Sm}}_{0.5}{\mathrm{Y}}_{0.5}{\mathrm{FeO}}_3$ is observed in the range 282–312 K through magnetic susceptibility measured on oriented single crystals. The ${\mathrm{\Gamma }}_2-{\mathrm{\Gamma }}_{23}-{\mathrm{\Gamma }}_3$ transition is distinctly different from the spin configurations commonly observed in $R{\mathrm{FeO}}_3$ orthoferrites, and we corroborate the finding with results from Raman spectroscopic investigations. Observation of magnon spectra and the vivid correlation between spin reorientation and changes in $B_{2g}$ and $B_{3g}$ phonon modes unveil strong spin-phonon coupling prevalent in ${\mathrm{Sm}}_{0.5}{\mathrm{Y}}_{0.5}{\mathrm{FeO}}_3$ crystal.

We characterize some of the distinctive hallmarks of magnon-magnon interaction mediated by the intracavity field of a microwave cavity, along with their testable ramifications. In general, we foreground two widely dissimilar parameter domains that bring forth the contrasting possibilities of level splitting and level crossing. The former is observed in the regime of strong magnon-photon couplings, particularly when the three modes bear comparable relaxation rates. This character is marked by the appearance of three distinguishable and nonconverging polariton branches in the spectral response to a cavity drive. However, when the bare modes are resonant and the couplings are perfectly symmetrical, one of the spectral peaks gets wiped out. This anomalous extinction of polaritonic response can be traced down to the existence of a conspicuous dark mode alongside two frequency-shifted bright modes. In an alternate parameter regime, where the magnon modes are weakly coupled to the cavity, features of level attraction unfold, subject to a large relaxation rate for the cavity mode. Concurrently, for antisymmetric detunings to the magnon modes, a transmission window springs into existence, exhibiting transparency in the limit of negligible dissipation from the magnons. The emergence of level attraction can be reconciled with a theoretical model that embodies the dynamics of the magnon-magnon subsystem when the cavity field decays rapidly into its steady state. In this limit, we identify a purely dissipative coupling between the magnon modes.

The spin Hall effect of a Dirac Hamiltonian system is studied using semiclassical analyses and the Kubo formula. In this system, the spin Hall conductivity is dependent on the definition of spin current. All components of the spin Hall conductivity vanish when spin current is defined as the flow of the spin angular momentum. In contrast, the off-diagonal components of the spin Hall conductivity are nonzero and scale with the carrier velocity (and the effective $g$ factor) when spin current consists of the flow of spin magnetic moment. We derive the analytical formula of the conductivity, carrier mobility, and the spin Hall conductivity to compare with experiments. In experiments, we use Bi as a model system that can be characterized by the Dirac Hamiltonian. Te and Sn are doped into Bi to vary the electron and hole concentration, respectively. We find the spin Hall conductivity $\left({\sigma }_{\mathrm{SH}}\right)$ takes a maximum near the Dirac point and decreases with increasing carrier density $\left(n\right)$. The sign of ${\sigma }_{\mathrm{SH}}$ is the same regardless of the majority carrier type. The spin Hall mobility, proportional to ${\sigma }_{\mathrm{SH}}/n$, increases with increasing carrier mobility with a scaling coefficient of $\sim$1.4. These features can be accounted for quantitatively using the derived analytical formula. The results demonstrate that the giant spin magnetic moment, with an effective $g$ factor that approaches 100, is responsible for the spin Hall effect in Bi.

The band structure of noninteracting fermions in the honeycomb lattice exhibits the Dirac cones at the corners of the Brillouin zone. As a consequence, fermions in this lattice manifest a semiconducting behavior below some critical value of the on-site attraction $U_c$. However, above $U_c$, the superconducting phase can occur. We discuss an interplay between the semiconductor-superconductor transition and the possibility of realization of the spin-polarized superconductivity (the so-called Sarma phase). We show that the critical interaction can be tuned by the next-nearest-neighbor (NNN) hopping in the absence of the magnetic field. Moreover, a critical value of the NNN hopping exists, defining a range of parameters for which the semiconducting phase can emerge. In the weak-coupling limit case, this quantum phase transition occurs for the absolute value of the NNN hopping equal to one third of the hopping between the nearest neighbors. Similarly, in the presence of the magnetic field, the Sarma phase can appear but only in a range of parameters for which initially the semiconducting state is observed. Both of these aspects are attributed to the Lifshitz transition, which is induced by the NNN hopping as well as the external magnetic field.

We investigate dimerized quantum spin systems using the spin functional renormalization group approach proposed by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)] which directly focuses on the physical spin correlation functions and avoids the representation of the spins in terms of fermionic or bosonic auxiliary operators. Starting from decoupled dimers as initial condition for the renormalization group flow equations, we obtain the spectrum of the triplet excitations as well as the magnetization in the quantum paramagnetic, ferromagnetic, and thermally disordered phases at all temperatures. Moreover, we compute the full phase diagram of a weakly coupled dimerized spin system in three dimensions, including the correct mean-field critical exponents at the two quantum critical points.

Thermoelectricity was discovered almost two centuries ago in bismuth. The large and negative Seebeck coefficient of this semimetal remains almost flat between 300 K and 100 K. This striking feature can be understood by considering the ratio of electron and hole mobilities and the evolution of their equal densities with temperature. The large and anisotropic magneto-Seebeck effect in bismuth, on the other hand, has not been understood up to the present day. Here, we report on a systematic study of the thermopower of bismuth from room temperature down to 20 K upon application of a magnetic field of 13.8 T in the binary-bisectrix plane. The amplitude of the Seebeck coefficient depends on the orientation of the magnetic field and the anisotropy changes sign with decreasing temperature. The magneto-Seebeck effect becomes nonmonotonic at low temperatures. When the magnetic field is oriented along the binary axis, the Seebeck coefficient is not the same for positive and negative fields. This so-called Umkehr effect arises because the high symmetry axes of the Fermi surface ellipsoids are neither parallel to each other nor to the high symmetry axes of the lattice. The complex evolution of thermopower can be accounted for in a large part of the ($T,B,\mathrm{\Theta }$) space by a model based on semiclassical transport theory and incorporating Landau quantization. The employed energy dependence of the scattering time is compatible with electron-acoustic phonon scattering. We find that the transverse Nernst response plays an important role in setting the amplitude of the longitudinal magneto-Seebeck effect. Furthermore, Landau quantization significantly affects thermoelectricity up to temperatures as high as 120 K.

Recently, both charge density wave (CDW) and superconductivity have been observed in the kagome compounds $A{\mathrm{V}}_3{\mathrm{Sb}}_5$. However, the nature of the CDW that results in many novel charge modulations is still under hot debate. Based on the first-principles calculations, we discover two kinds of CDW states in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$, namely, the trimerized-hexamerized $2\times 2$ phase and the dimerized $4\times 1$ phase. Our phonon spectrum and electronic Lindhard function calculations reveal that the most intensive structural instability in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ originates from a combined in-plane vibration mode of V atoms through the electron-phonon coupling, rather than the Fermi surface nesting effect. More importantly, a metastable $4\times 1$ phase with the V-V dimer pattern and twofold symmetric bow-tie-shaped charge modulation is revealed in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. Further analyses demonstrate that both the in-plane phonon instability and $c$ direction interaction play important roles during the $4\times 1$ phase formation, which provides key understanding for the mechanism of the $4\times 1$ CDW and relative novel phenomena in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$.

We theoretically study the electronic structure of magic-angle twisted bilayer graphene with disordered moiré patterns. By using an extended continuum model incorporating nonuniform lattice distortion, we find that the local density of states of the flat band is hardly broadened, but splits into upper and lower subbands in most places. The spatial dependence of the splitting energy is almost exclusively determined by the local value of the effective vector potential induced by heterostrain, whereas the variation of local twist angle and local moiré period give relatively minor effects on the electronic structure. We explain the exclusive dependence on the local vector potential by a pseudo Landau level picture for the magic-angle flat band, and we obtain an analytic expression of the splitting energy as a function of the strain amplitude.

The exchange interaction in a singlet-triplet qubit defined by two-electron states in the double-quantum-dot system (“two-electron singlet-triplet qubit”) typically varies monotonically with the exchange interaction and thus carries no sweet spot. Here we study a singlet-triplet qubit defined by four-electron states in the double-quantum-dot system (“four-electron singlet-triplet qubit”). We demonstrate, using configuration-interaction calculations, that in the four-electron singlet-triplet qubit the exchange energy as a function of detuning can be nonmonotonic, suggesting existence of sweet spots. We further show that the tuning of the sweet spot and the corresponding exchange energy by perpendicular magnetic field can be related to the variation of orbital splitting. Our results suggest that a singlet-triplet qubit with more than two electrons can have advantages in the realization of quantum computing.

${}^3{P}_2$ superfluids realized in neutron stars are the largest topological quantum matters in our universe. We establish the existence and stability of non-Abelian half-quantum vortices (HQVs) in ${}^3{P}_2$ superfluids with strong magnetic fields. Using a self-consistent microscopic approach, we find that a singly quantized vortex is energetically destabilized into a pair of two non-Abelian HQVs owing to the strongly spin-orbit-coupled pairing. We find a topologically protected Majorana fermion on each HQV, thereby providing twofold non-Abelian anyons characterized by both Majorana fermions and a non-Abelian first homotopy group.

Discriminant indicators with generalized inversion symmetry are computed only from data at the high-symmetry points. They allow a systematic search for exceptional points. In this paper, we propose discriminant indicators for two- and three-dimensional systems with generalized $n$-fold rotational symmetry ($n=4$, 6). As is the case for generalized inversion symmetry, the indicator taking a nontrivial value predicts the emergence of exceptional points and loops without ambiguity of the reference energy. A distinct difference from the case of generalized inversion symmetry is that the indicator with generalized $n$-fold rotational symmetry ($n=4$, 6) can be computed only from data at two of four high-symmetry points in the two-dimensional Brillouin zone. Such a difference is also observed in three-dimensional systems. Furthermore, we also propose how to fabricate a two-dimensional system with generalized fourfold rotational symmetry for an electrical circuit.

A reentrant localization transition was predicted recently in a one-dimensional quasiperiodic lattice with dimerized hopping between the nearest-neighbor sites [Roy et al., Phys. Rev. Lett. 126, 106803 (2021)]. It was shown that the interplay between the hopping dimerization and a staggered quasiperiodic disorder manifests two localization transitions through two intermediate phases, resulting in four critical points as a function of the quasiperiodic potential. In this paper, we study the critical nature of the states across the localization transitions by computing the mass exponents and the corresponding fractal dimensions of the states through a multifractal analysis. Moreover, we analyze the phenomenon of this reentrant localization transition by examining the spectral properties of the eigenstates. By performing a systematic finite-size scaling analysis for a fixed value of the hopping dimerization, we obtain accurate critical disorder strengths for different transitions and the associated critical exponents. Further, we complement the critical nature of the energy spectrum by computing the Hausdorff dimensions.

Quasi-one-dimensional iron chalcogenides possess various magnetic states depending on the lattice distortion, electronic correlations, and presence of defects. We present neutron diffraction and inelastic neutron scattering experiments on the spin ladder compound ${\mathrm{BaFe}}_{2-\delta }{\mathrm{S}}_{1.5}{\mathrm{Se}}_{1.5}$ with $\sim$6% iron vacancies. The data reveal that long-range magnetic order is absent, while the characteristic magnetic excitations that correspond to both the stripe- and block-type antiferromagnetic correlations are observed. First-principles calculations support the existence of both stripe- and block-type antiferromagnetic short-range orders in the experimental sample. The disappearance of long-range magnetic order may be due to the competition between these two magnetic orders, which is greatly enhanced for a certain concentration of iron vacancies, which we calculate to be about 6%, consistent with the measured iron vacancy concentration. Our results highlight how iron vacancies in the iron-based spin ladder system strongly influence the magnetic ground state.

We study the two-dimensional motion of a magnetic skyrmion driven by a ratchetlike polarized electric current that is periodic in both space and time. Some general cases are considered in each of which in the low-temperature and adiabatic limit, regardless of the details of the driving current, the time and statistical average velocity along any direction is topologically quantized as a Chern number multiplied by a basic unit. We make two approaches, one based on identifying the drift direction and the other based on the non-Hermitian adiabatic perturbation theory developed for the Fokker-Planck operator. Both approach apply in the case of periodicity along the direction of the driving current and homogeneity in the transverse direction for which the analytical result is confirmed by our numerical simulation on the constituent spins, and a convenient experiment is proposed.