The existence of pure spin currents in absence of any driving external field is commonly considered an exotic phenomenon appearing only in quantum materials, such as topological insulators. We demonstrate instead that equilibrium spin currents are a rather general property of materials with non-negligible spin-orbit coupling (SOC). Equilibrium spin currents can be present at the surfaces of a slab. Yet, we also propose the existence of global equilibrium spin currents, which are net bulk spin currents along specific crystallographic directions of solid-state materials. Equilibrium spin currents are allowed by symmetry in a very broad class of systems having gyrotropic point groups. The physics behind equilibrium spin currents is uncovered by making an analogy between electronic systems with SOC and non-Abelian gauge theories. The electron spin can be seen as analogous to the color degree of freedom in $\mathrm{SU}\left(2\right)$ gauge theories and equilibrium spin currents can then be identified with diamagnetic color currents appearing as the response to a effective non-Abelian magnetic field generated by the SOC. Equilibrium spin currents are not associated with spin transport and accumulation, but they should nonetheless be carefully taken into account when computing transport spin currents. We provide quantitative estimates of equilibrium spin currents for a number of different systems, specifically the Au(111) and Ag(111) metallic surfaces presenting Rashba-type surface states, nitride semiconducting nanostructures, and bulk materials, such as the prototypical gyrotropic medium tellurium. In doing so, we also point out the limitations of model approaches showing that first-principles calculations are needed to obtain reliable predictions. We therefore use density functional theory computing the so-called bond currents, which represent a powerful tool to deeply understand the relation between equilibrium currents, electronic structure, and crystal point group.

We have investigated the normal state Fermi-surface properties of the kagome superconductor ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ using torque magnetometry with applied fields ($H$) up to 35 T. The torque signal shows clear de Haas–van Alphen (dHvA) oscillations above 15 T. The oscillations are smooth and consist of seven distinct frequencies with values from $\sim$ 18 T to 2135 T. The presence of higher frequencies in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ is further confirmed by carrying out additional measurements using the tunnel diode oscillator technique. All frequencies measured at different tilt angles ($\theta$) of the field direction with respect to the c axis show a $1/\cos \theta$ dependence, implying that the Fermi surfaces corresponding to these frequencies are two dimensional (2D). The absence of dHvA oscillations at $\theta$ = ${90}^o$ further supports the presence of 2D Fermi surfaces. The Berry phase ($\varphi$) determined from the Landau level fan diagram for all frequencies is $\sim$ 0.4. This value is close to the theoretical value of $\varphi$ = 0.5 for a nontrivial system, which strongly supports the nontrivial topology of the Fermi surfaces of these frequencies. Several quantities characterizing the Fermi surface are calculated employing the Lifshitz-Kosevich theory. These findings are crucial for exploring the interplay between nontrivial band topology, charge-density wave, and unconventional superconductivity of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$.

We have investigated the Ce valence of an intermetallic compound ${\mathrm{Ce}}_2{\mathrm{Rh}}_2\mathrm{Ga}$ with a phase transition at $T_t=128.5$ K by means of high-energy resolution fluorescence-detected x-ray absorption spectroscopy (HERFD-XAS) and resonant x-ray emission spectroscopy (RXES) around the Ce $L_3$ edge. The HERFD-XAS spectra in the whole temperature range from 300 to 3 K exhibit weak $f^0\left({\mathrm{Ce}}^{4+}\right)$ and $f^2\left({\mathrm{Ce}}^{2+}\right)$ peaks as well as the $f^1\left({\mathrm{Ce}}^{3+}\right)$ main peak, indicating that the Ce $4f$ electrons hybridize with the conduction electrons. With decreasing temperature from 125 to 100 K across $T_t$, the $f^1$ peak is reduced, while the $f^0$ peak is enhanced. Concomitantly, the Ce $L{\alpha }_1$ RXES intensity taken at the $f^2$ peak of the HERFD-XAS spectrum decreases. These spectroscopic results indicate that the phase transition at $T_t$ of ${\mathrm{Ce}}_2{\mathrm{Rh}}_2\mathrm{Ga}$ is driven by a valence transition of the Ce ions.

Exchange-correlation kernels in density functional theory are the second-order derivatives of the exchange-correlation functionals with respect to the density matrix. For collinear functionals, the forms of kernels are well known, and their applications in calculating responses of electrons to predict properties of molecules and materials are mature. However, kernels of noncollinear functionals in closed-shell systems, except for LDA (local density approximation), are generally unknown, at least mathematically ill-defined, suffering from the indeterminate forms of 0 divided by 0. We find that such singularities in noncollinear GGA (generalized gradient approximation) kernels can be removed by introducing a proper limit process and approaching the limit after the calculations of derivatives have been done. Following this idea, mathematically well-defined noncollinear GGA kernels for closed-shell systems emerge naturally. Theoretically, these kernels are shown to be numerically stable and spin-rotational symmetry preserved. Numerical tests on excitation energies and spectroscopy parameters present reasonable results, indicating the applicability of this methodology.

Topological phases supported by quasiperiodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that for both the uncorrelated and correlated phases, the operator algebras that generate the Hamiltonians are noncommutative tori, hence the quasiperiodic chains display physics akin to the quantum Hall effect in two and higher dimensions. The robust topological edge modes are found to be strongly shaped by the interaction and, generically, they have hybrid edge-localized and chain-delocalized structures. Our findings lay the foundations for topological spin pumping using the phason of a quasiperiodic pattern as an adiabatic parameter, where selectively chosen quantized bits of magnetization can be transferred from one edge of the chain to the other.

Pyrochlore oxide ${\mathrm{Cd}}_2{\mathrm{Re}}_2{\mathrm{O}}_7$ exhibits successive structural transitions upon cooling that break its inversion symmetry. The low-temperature noncentrosymmetric metallic phases are believed to be some odd-parity multipole ordered states that are associated with a Fermi-liquid instability due to the strong spin-orbit interaction (SOI) and electronic correlation. However, their microscopic ordering pictures and the driving force of the phase transitions are still unclear. We determined the electronic structure of the lowest temperature phase of ${\mathrm{Cd}}_2{\mathrm{Re}}_2{\mathrm{O}}_7$ by combining quantum oscillation measurements with electronic structure calculations. The observed Fermi surfaces were well reproduced based on the optimized crystal structure, and we demonstrated the strong influence of the antisymmetric SOI. From the mass enhancement factor, we elucidated the strongly correlated nature of the electronic states. In addition, we visualized the microscopic picture of the $3z^2-r^2$-type metallic electric-toroidal-quadrupole (ETQ) order characterized by the Re-O bond order. These results corroborate that the metallic ETQ order is driven by a Fermi-liquid instability associated with the strong SOI and electronic correlation, as has been theoretically proposed. Our results provide the basis for exploring unconventional phenomena expected in the metallic ETQ order.

We revisit the problem of surface states in semiconductors with inverted-band structures, such as $\alpha$-Sn and HgTe. We unravel the confusion that arose over the past decade regarding the origin of the surface states, their topological nature, and the role of strain. Within a single minimalistic description, we reconcile different solutions found in the 1980s with the results obtained from modern-day numerical simulations, allowing us to unambiguously identify all branches of surface states around the $\mathrm{\Gamma }$ point of the Brillouin zone in different regimes. We also show that strain is a smooth deformation to the surface states, following the usual continuity principle of physics, and not leading to any drastic change of the physical properties in these materials, in contrast to what has recently been advanced in the literature. We consider biaxial in-plane strain that is either tensile or compressive, leading to different branches of surface states for topological insulators and Dirac semimetals, respectively. Our model can help in interpreting numerous experiments on topological surface states originating from inverted-band semiconductors.

We investigate both first-order topology, as realized through Haldane's model, and second-order topology, implemented through an additional Kekulé distortion, on the honeycomb lattice. The interplay and competition of both terms result in a phase diagram at half-filling which contains 12 distinct phases. All phases can be characterized by the first Chern number or by a quantized ${\mathbb{Z}}_Q$ Berry phase. Highlights include phases with high Chern numbers, a ${\mathbb{Z}}_6$ topological phase, but also coupled kagome-lattice Chern insulators. Furthermore, we explore the insulating phases at lower fillings and find again first- and second-order topological phases. Finally, we identify real-space structures which feature corner states not only at half but also at third and sixth fillings, in agreement with the quantized ${\mathbb{Z}}_Q$ Berry phases.

In this paper, we present a theoretical perspective concerning the scattering of electrons on a twisted light (TL) driven graphene quantum dot (GQD). Relatively recently discovered, TL is a novel type of electromagnetic field which carries a finite orbital angular momentum oriented on the propagation direction, besides its spin. This striking property of TL is due to its spatial structure. It is well known that the localization of electrons in a GQD is forbidden by the Klein tunneling, an effect that manifests by the perfect transmission of electrons through a potential barrier, regardless of its magnitude. Here we demonstrate that, for a suitable choice of the scattering regimes, there emerge scattering resonances characterized by trapping states of the incident electron inside the GQD for finite periods of time. The most interesting result is the prediction regarding the possibility to control the trapping times using a TL irradiation. Also, we mention that the investigation was performed for a frequency of the TL within the infrared spectrum.

It is usually admitted that the inverse Faraday effect (IFE) originates from the spin angular momentum (SAM) of light. In this paper, we show that part of the IFE in a metal is induced by the orbital angular momentum (OAM) of light. On the basis of a hydrodynamic model of the conduction electron gas, we describe the dependence of the IFE on the spin and orbital angular momenta as well as spin-orbit interaction in a nonparaxial light beam. We also numerically quantify the relative contributions of the SAM and OAM of light to the IFE in a thin gold film illuminated by different focused beams carrying SAM and/or OAM. The OAM of light provides an additional degree of freedom in the control of the IFE and resulting optomagnetic field, thus potentially impacting various research fields, including all-optical magnetization switching and spin-wave excitation.

The emergence of interference is observed in the resistance of a graphene annulus p-n junction device as a result of applying two separate gate voltages. The observed resistance patterns are carefully inspected, and it is determined that the position of the peaks resulting from those patterns is independent of temperature and magnetic field. Furthermore, these patterns are not attributable to Aharonov-Bohm oscillations, Fabry-Pérot interference at the junction, or moiré potentials. The device data are compared with those of another device fabricated with a traditional Hall bar geometry, as well as with quantum transport simulation data. Since the two devices are of different topological classes, the subtle differences observed in the corresponding measured data indicate that the most likely source of the observed geometric interference patterns is quantum scarring.

We investigate the microwave response of a gated two-dimensional electron system (2DES) loaded by an external on-chip resonator. We find the system response to be dominated by the excitation of relativistic plasmons. These plasmons exhibit anomalously strong coupling to the photon mode of the resonator, which manifests itself in a drastic reduction of the plasma resonant frequency and linewidth. We develop an analytical approach to explain the observed phenomenon of strong interaction of 2D plasma with light. The theory turned out to be in good agreement with the experiment.

Stacking variations in quasi-two-dimensional materials can have an important influence on material properties, such as changing the topology of the band structure. Unfortunately, the weakness of van der Waals (vdW) interactions makes it difficult to compute the stacking dependence of properties, and even in a material as simple as graphite the stacking energetics remain unclear. ${\mathrm{Mo}}_{1-x}{\mathrm{W}}_x{\mathrm{Te}}_2$ is a material in which three differently stacked phases are conveniently accessible by temperature changes: $1T^{\prime }, T_d^{*}$, and the reported Weyl semimetal phase $T_d$. The transitions proceed via layer sliding, and the corresponding interlayer shear mode (ISM) is relevant not just for the stacking energetics but also for understanding the relationship between Weyl physics and structural changes. However, the interlayer interactions of ${\mathrm{Mo}}_{1-x}{\mathrm{W}}_x{\mathrm{Te}}_2$ are not well understood, with wide variation in computed properties. We report inelastic neutron scattering of the ISM in a ${\mathrm{Mo}}_{0.91}{\mathrm{W}}_{0.09}{\mathrm{Te}}_2$ crystal. The ISM energies are generally consistent with the linear chain model, as expected given the weak interlayer interaction, though there are some discrepancies from predicted intensities. However, the interlayer force constants $K_x$ in the $T_d^{*}$ and $1T^{\prime }$ phases are substantially weaker than that of $T_d$ at 75(3) and 83(3)%, respectively. Considering that the relative positioning of atoms in neighboring layers is approximately the same regardless of overall stacking, our results suggest that longer-range influences, such as stacking-induced electronic band-structure changes, may be responsible for the substantial change in the interlayer vibrational coupling and thus the $C_{55}$ elastic constant. These findings should elucidate the stacking energetics of ${\mathrm{Mo}}_{1-x}{\mathrm{W}}_x{\mathrm{Te}}_2$ and other vdW layered materials.

The commonly employed supercell approach for defects in crystalline materials may introduce spurious interactions between the defect and its periodic images. A rich literature is available on how the interaction energies can be estimated, reduced, or corrected. A simple and seemingly straightforward approach is to extrapolate from a series of finite supercell sizes to the infinite-size limit, assuming a smooth polynomial dependence of the energy on inverse supercell size. In this work, we demonstrate by means of explict density-functional theory supercell calculations and simplified models that wave-function overlap and electrostatic interactions lead to more complex dependencies on supercell size than commonly assumed. We show that this complexity cannot be captured by the simple extrapolation approaches and that suitable correction schemes should be employed.

The topological phase transition in a Hermitian system is associated with a change in the topological invariant that characterizes the band structure of the two distinct phases. Recently, the delocalization-localization transition in a quasicrystal described by the non-Hermitian $\mathcal{PT}$-symmetric extension of the Aubry-André-Harper (AAH) Hamiltonian has been related to a topological phase transition. Interestingly, the $\mathcal{PT}$ symmetry also breaks down at the same point. In this article, we have shown that the delocalization-localization transition and the breaking of $\mathcal{PT}$ symmetry are not connected to a topological phase transition. We have studied the non-Hermitian $\mathcal{PT}$-symmetric AAH Hamiltonian in the presence of Rashba spin-orbit coupling. It has been demonstrated that except in some particular cases, the delocalization-localization and the topological transition points are not identical. In fact, it precedes the topological transition point whenever they do not coincide. However, the breaking of $\mathcal{PT}$ symmetry occurs simultaneously with the delocalization-localization transition. Moreover, we have discovered that the Lyapunov exponent, which is often used as a primary signature to characterize the delocalization-localization transition, does not always determine it correctly. The Lyapunov exponent rather identifies the topological transition point in quasicrystals.

When an optical emitter is strongly coupled to a vibrational bath the polaron transformation is often used to permit an accurate second-order Redfield master equation. However, the optical transition rates in the polaron frame are not analytic and approximations typically need to be made, which result in the loss of anything other than simple additive effects of the two baths. In this paper, we derive an intuitive analytic expression for the polaron frame optical transition rates by means of a finite-mode truncation of the vibrational bath. Using this technique, calculations of the transition rates converge for only a few modes in the truncated spectral density, and capture nonadditive effects such as population inversion of a two-level system.

We present a hybrid quantum-classical simulation of charge-polaron transport in conjugated polymers. The charge, which couples to the angular rotations of the monomers, is modeled via the time-dependent Schrödinger equation, while the monomers are treated classically via the Ehrenfest equations of motion. In addition, the system is thermalized by assuming that the monomers are subject to Brownian fluctuations modeled by the Langevin equation. Charge coupling to the monomer rotations localizes the particle into a Landau polaron, while the thermal fluctuations of the monomers causes polaron dynamics. The emergent low-energy scale of the model is the polaron reorganization energy, $E_r$, and thus $T_r=E_r/k_B$ is a convenient scale for the low-temperature dynamics. We investigate two types of dynamics; both relevant for temperatures $T<T_r$. In the lower temperature regime the system remains in the same quasidiabatic state, corresponding to activationless polaron diffusion as the polaron crawls stochastically along the chain. As the temperature is raised, however, there is a cross-over to an additional activated transfer process which corresponds to hopping between diabatic states. We show that these processes exhibit Landau-Zener type dynamics. We note that as our model is general, it equally applies to exciton-polaron (i.e., energy) transport in conjugated polymers, and to charge and exciton polaron transport in quasi one-dimensional molecular stacks.

Non-Hermiticity and dephasing, collaborating in an unusual wave-packet dynamics, realize unconventional entanglement evolution in a disordered, interacting, and asymmetric (nonreciprocal) quantum medium. Taking the Hatano-Nelson model as a concrete example, we first consider how wave packet spreads in a non-Hermitian disordered system for demonstrating that it is very different from the Hermitian case. Interestingly, a cascadelike wave-packet spreading as in the Hermitian case is suppressed in the clean limit and at weak disorder, while it revives in the vicinity of the localization-delocalization transition. Based on this observation, we then analyze how the entanglement entropy of the system evolves in the interacting non-Hermitian model, revealing its nonmonotonic evolution in time. We clarify the different roles of dephasing in the time evolution of entanglement entropy in Hermitian and non-Hermitian systems, and show that the many-body dynamics is governed by a principle different from the Hermitian case. The size dependence of the results suggests with the increase of disorder, an unusual area-volume–area-law crossover of the maximal entanglement entropy. To analyze the effects of disorder on a firm basis, using the Hermitian limit as a benchmark, we employ a quasiperiodic disorder (Aubry-André model) in the analyses.

The predictability of any characteristic functional aspect in a double perovskite system has always been compromised by its strong dependence on the inevitably present antisite disorders (ASD). Here, we aim to precisely map the quantitative and qualitative nature of ASD with the corresponding modifications in observables describing the magnetic and electronic state in epitaxial ${\mathrm{Sm}}_2{\mathrm{NiMnO}}_6$ (SNMO) double perovskite thin films. The concentration and distribution patterns of ASD are effectively controlled by optimizing growth conditions and estimated on both local and global scales utilizing extended x-ray absorption fine structure and bulk magnetometry. Depending upon the defect densities, the nature of disorder distribution can vary from homogeneous to partially segregated patches. Primarily, the effect of varying $B$-site cationic arrangement in SNMO is reflected as the competition of long-range ferromagnetic (FM) and short-scale antiferromagnetic (AFM) interactions originated from ordered Ni-O-Mn and disordered Ni-O-Ni or Mn-O-Mn bonds, respectively, which leads to a systematic shift in magnetic transition temperature and a drastic drop in saturation magnetization. In addition, we have observed that the gradual increment in the density of ASD leads to a significant deviation from the uniaxial anisotropy character, reduction in anisotropy energy, and enhancement of moment pinning efficiency. However, the observed signatures of ${\mathrm{Ni}}^{2+}+{\mathrm{Mn}}^{4+}⟶{\mathrm{Ni}}^{3+}+{\mathrm{Mn}}^{3+}$ charge disproportionation is found to be independent of cation disorder densities. This work serves as a basic route map to tune the characteristic magnetic anisotropy, magnetic phase transitions, and magnetization reversal mechanism by controlling ASD in a general double perovskite system.