Hall resistance Rxy is commonly suggested to be linear-in-magnetic-field B, provided the field is small. We argue here that at low temperatures this linearity is broken due to weak localization/antilocalization phenomena in inhomogeneous systems, while in a uniform medium the linear-in-field dependence of Rxy(B) is preserved. We calculate the Hall resistance for different two-component media using a mean-field approach and show that this nonlinearity is experimentally observable.

Electron spin relaxation in a spin-polarized quantum Hall state is studied. Long spin-relaxation times that are at least an order of magnitude longer than those measured in previous experiments were observed and explained within the spin-exciton relaxation formalism. The absence of any dependence of the spin-relaxation time on the electron temperature and on the spin-exciton density, and a specific dependence on the magnetic field indicate a definite relaxation mechanism—spin-exciton annihilation mediated by spin-orbit coupling and a smooth random potential.

We investigate the impact of Coulomb correlations on the low-energy collective excitations in two-dimensional electron systems in the quantum Hall state ν = 2. The collective excitations are studied using inelastic light scattering in the set of MgZnO/ZnO heterostructures with high-mobility two-dimensional electrons. The study focuses on the lowest-energy collective excitations in the paramagnetic state ν = 2, the cyclotron spin-flip magnetoexcitons (CSFMs), which are associated with inter-Landau-level transitions with a simultaneous spin flip. The Coulomb contribution to the CSFM energy is measured independently of the Zeeman term as a function of electron density. It is established that in the range of electron concentrations corresponding to theWigner-Seitz parameter rs ∼ 5–7, the combination of the Coulomb and Zeeman contributions leads to a softening of the CSFM. This softening accompanies spontaneous switching of the spin configuration in the ν = 2 quantum Hall system from paramagnetic to ferromagnetic. Theoretical estimates are given for the correlation energy terms of the CSFM responsible for its softening and a concomitant ferromagnetic transition.

Shot-noise measurements are widely used for the characterization of nonequilibrium configurations in electronic conductors. The recently introduced quantum tomography approach was implemented for the studies of electronic wave functions of few-electron excitations created by periodic voltage pulses in phase-coherent ballistic conductors based on the high-quality GaAs two-dimensional electron gas. Still relying on the manifestation of Fermi correlations in noise, we focus on the simpler and more general approach beneficial for local measurements of energy distribution (ED) in electronic systems with arbitrary excitations with well-defined energies and random phases. Using biased diffusive metallic wire as a test bed, we demonstrate the power of this approach and extract the well-known double-step ED from the shot noise of a weakly coupled tunnel junction. Our experiment paves the way for local measurements of generic nonequilibrium configurations applicable to virtually any conductor.

We present the results of temperature- and polarization-dependent high-resolution optical spectroscopy studies of DyFe3(BO3)4 performed in spectral ranges 40-300cm-1 and 3000-23000cm-1. The crystal-field (CF) parameters for the Dy3+ ions in the P3121 (P3221) phase of DyFe3(BO3)4 are obtained from calculations based on the analysis of the measured f-f transitions. Recently, quadrupole helix chirality and its domain structure was observed in resonant x-ray diffraction experiments on DyFe3(BO3)4 using circularly polarized x rays [T. Usui, Y. Tanaka, H. Nakajima, M. Taguchi, A. Chainani, M. Oura, S. Shin, N. Katayama, H. Sawa, Y. Wakabayashi, and T. Kimura, Nat. Mater. 13, 611 (2014)10.1038/nmat3942]. Using the obtained set of the CF parameters, we calculate temperature dependencies of the electronic quadrupole moments of the Dy3+ ions induced by the low-symmetry (C2) CF component and show that the quadrupole helix chirality can be explained quantitatively. We also consider the temperature dependencies of the bulk magnetic dc-susceptibility and the helix chirality of the single-site magnetic susceptibility tensors of the Dy3+ ions in the paramagnetic P3121 (P3221) phase and suggest the neutron and resonant x-ray diffraction experiments in a magnetic field to reveal the helix chirality of field-induced magnetic moments.

We study a one-dimensional anisotropic XXZ spin-1/2 model with ferromagnetic sign of the coupling and z−z exchange constant Jz=ΔJ, where Δ<1, and J is the coupling within the XY spin plane. We calculate the damping of low-energy excitations with ω≪T due to their scattering from thermal excitation bath with temperature T≪J, taking into account nonzero curvature of the excitation spectrum, ε(q)=uq+δε(q). We calculate also longitudinal spin-spin correlation function ⟨Sz(x,t)Sz(0,0)⟩ at x≈ut and find the shape of the spreading “wave packet”.

Electron spin resonance (ESR) experiments in the quasi-one-dimensional (quasi-1D) S=12 antiferromagnet K2CuSO4Cl2 reveal the opening of a gap in the absence of magnetic ordering, as well as an anisotropic shift of the resonance magnetic field. These features of the magnetic excitation spectrum are explained by a crossover between a gapped spinon-type doublet ESR formed in a 1D antiferromagnet with uniform Dzyaloshinskii-Moriya interaction and a Larmor-type resonance of a quasi-1D Heisenberg system.

We consider the spin-orbit-induced spin Hall effect and spin swapping in diffusive superconductors. By employing the non-equilibrium Keldysh Green’s function technique in the quasiclassical approximation, we derive coupled transport equations for the spectral spin and particle distributions and for the energy density in the elastic scattering regime. We compute four contributions to the spin Hall conductivity, namely, skew scattering, side-jump, anomalous velocity, and the Yafet contribution. The reduced density of states in the superconductor causes a renormalization of the spin Hall angle. We demonstrate that all four of these contributions to the spin Hall conductivity are renormalized in the same way in the superconducting state. In its simplest manifestation, spin swapping transforms a primary spin current into a secondary spin current with swapped current and polarization directions. We find that the spin-swapping coefficient is not explicitly but only implicitly affected by superconducting correlations through the renormalized diffusion coefficients. We discuss experimental consequences for measurements of the (inverse) spin Hall effect and spin swapping in four-terminal geometries. In our geometry, below the superconducting transition temperature, the spin-swapping signal is increased an order of magnitude while changes in the (inverse) spin Hall signal are moderate.

The spin Hall effect for polaritons (SHEP) in a transition metal dichalcogenides (TMDC) monolayer embedded in a microcavity is predicted. We demonstrate that two counterpropagating laser beams incident on a TMDC monolayer can deflect a superfluid polariton flow due to the generation the effective gauge vector and scalar potentials. The components of polariton conductivity tensor for both noninteracting polaritons without Bose-Einstein condensation (BEC) and for weakly interacting Bose gas of polaritons in the presence of BEC and superfluidity are obtained. It is shown that the polariton flows in the same valley are splitting: the superfluid components of the A and B polariton flows propagate in opposite directions along the counterpropagating beams, while the normal components of the flows slightly deflect in opposite directions and propagate almost perpendicularly to the beams. The possible experimental observation of SHEP in a microcavity is proposed.

We investigate a possibility of pair electron-electron (e−e) collisions in a ballistic wire with spin-orbit coupling and only one populated mode. Unlike in a spin-degenerate system, a combination of spin splitting in momentum space with a momentum-dependent spin precession opens up a finite phase space for pair e−e collisions around three distinct positions of the wire's chemical potential. For a short wire, we calculate the corresponding resonant contributions to the conductance, which have different power-law temperature dependencies, and, in some cases, vanish if the wire's transverse confinement potential is symmetric. Our results may explain the recently observed feature at the lower conductance plateau in InAs wires.

Anomalous behavior of spin stiffness is revealed in ZnO-based two-dimensional electron systems (2DESs) with strong Coulomb interaction and Wigner-Seitz parameter r_s > 6. The spin stiffness is extracted directly from the quadratic k-dispersion of spin excitons at ν = 1 probed by inelastic light scattering. The resulting values are found to be dramatically rescaled compared to the case of weakly interacting 2DESs—spin stiffness turned out to be of the order of the cyclotron energy with the effective mass of Fermi-liquid quasiparticles. This result is also confirmed by the exact diagonalization simulations.

Half-metals have fully spin-polarized charge carriers at the Fermi surface. Such polarization usually occurs due to strong electron-electron correlations. Recently [Phys. Rev. Lett. 119, 107601 (2017)] we have demonstrated theoretically that adding (or removing) electrons to systems with Fermi surface nesting also stabilizes the half-metallic states even in the weak-coupling regime. In the absence of doping, the ground state of the system is a spin or charge density wave, formed by four nested bands. Each of these bands is characterized by charge (electron/hole) and spin (up/down) labels. Only two of these bands accumulate charge carriers introduced by doping, forming a half-metallic two-valley Fermi surface. Analysis demonstrates that two types of such half-metallicity can be stabilized. The first type corresponds to the full spin polarization of the electrons and holes at the Fermi surface. The second type, with antiparallel spins in electronlike and holelike valleys, is referred to as a “spin-valley half-metal” and corresponds to the complete polarization with respect to the spin-valley operator. We analyze spin and spin-valley currents and possible superconductivity in these systems. We show that spin or spin-valley currents can flow in half-metallic phases.

We discuss theoretically frustrated Heisenberg spiral magnets in magnetic field **H**. We demonstrate that small
anisotropic spin interactions (single-ion biaxial anisotropy or dipolar forces) select the plane in which spins rotate
(spiral plane) and can lead to the spiral plane flop upon in-plane field increasing. Expressions for the critical
fields *Hflop* are derived. It is shown that measuring of *Hflop* is an efficient and simple method of quantifying the
anisotropy in the system (as the measurement of spin-flop fields in collinear magnets with axial anisotropy). Corresponding recent experiments are considered in spiral magnets some of which are multiferroics of spin origin.

A low-temperature magnetic resonance study of the quasi-two-dimensional antiferromagnet Cu(en)(H2O)2SO4 (en = C2H8N2) was performed down to 0.45 K. This compound orders antiferromagnetically at 0.9 K. The analysis of the resonance data within the hydrodynamic approach allowed us to identify anisotropy axes and to estimate the anisotropy parameters for the antiferromagnetic phase. Dipolar spin-spin coupling turns out to be the main contribution to the anisotropy of the antiferromagnetic phase. The splitting of the resonance modes and its nonmonotonous dependence on the applied frequency were observed below 0.6 K in all three field orientations. Several models are discussed to explain the origin of the nontrivial splitting, and the existence of inequivalent magnetic subsystems in Cu(en)(H2O)2SO4 is chosen as the most probable source.

It is generally accepted that quantized vortices formed in coherent bosonic fluids are “excitations” and as such do not arise in a one-mode condensate at zero temperature. To excite them, one needs either inhomogeneities (impurities, rotation, etc.) or essentially finite fluctuations. Here, we predict a perfectly spontaneous formation of vortices even at zero temperature, which takes place in a homogeneous cavity-polariton system under one-mode optical excitation at normal incidence. In spite of the absence of equilibrium and U(1) invariance, this system shows a counterpart of the Berezinskii-Kosterlitz-Thouless crossover between single vortices and coupled vortex-antivortex states ranging from small dipoles to rectilinear filaments with long-range ordering.

The interplay of the electron exchange interaction and spin-orbit coupling results in spontaneous supercurrents near magnetic insulator islands, which are placed on the top of a two-dimensional (2D) superconductor, and whose magnetization is parallel to 2D electron gas. It is shown that in contrast to the well-studied situation, where such an effect involves only topologically trivial spatial variations of the superconducting order parameter, one should take into account supercurrent vortices. The latter are spontaneously generated around the island’s boundary of an arbitrary shape, and they result in screening of the Zeeman field. This problem has been considered for electrons subject to a strong Rashba spin-orbit coupling, including Dirac systems as well. In the latter case, vortices can carry Majorana zero modes.

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes N below the correlation volume Nξ and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length ξ ∼ ln Nξ that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast “diffusion,” which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate d → ∞ limit of the Anderson model in d spatial dimensions.

We report the discovery of a GeV-associated phenomenon which is strong (up to an order) stochastic reversible enhancements of photoluminescence intensity in a single GeV diamond synthesized with the high-pressure, high-temperature technique. We were lucky to observe this effect with only one crystal among dozens of similar microdiamonds. Each rise and fall of the intensity above its stable moderate level may be referred to as a superflare with smooth dynamics of the transients which develop on the timescale of seconds. These flares tend to recur infinitely at ambient conditions under cw-laser excitation above a certain input power threshold. To explain this phenomenon we propose a theory of intrinsic optical instabilities which develop in a dense ensemble of quantum emitters.

A tight-binding model of 8-Pmmn borophene, a two-dimensional boron crystal, is developed. We confirm that the crystal hosts massless Dirac fermions and the Dirac points are protected by symmetry. Strain is introduced into the model, and it is shown to induce a pseudomagnetic field vector potential and a scalar potential. The dependence of the potentials on the strain tensor is calculated. The physical effects controlled by the pseudomagnetic field are discussed.