# Publications

The terahertz photoconductivity of 100 μm and 20 μm Hall bars fabricated from narrow AlAs quantum wells (QWs) of different widths is investigated in this paper. The photoresponse is dominated by collective magnetoplasmon excitations within the body of the Hall structure. We observed a radical change of the magnetoplasma spectrum measured precisely for AlAs QWs of widths ranging from 4 nm to 15 nm. We have shown that the observed behavior is a vivid manifestation of valley transition taking place in the two-dimensional electron system. Remarkably, we show that the photoresponse for AlAs QWs with a width of 6 nm features two resonances, indicating simultaneous occupa- tion of strongly anisotropic X xy valleys and isotropic X z valley in the QW plane. Our results pave the way for realizing valley-selective layered heterostructures, with potential applications in valleytronics.

We consider a small itinerant ferromagnet exposed to an external magnetic field and strongly driven by a thermally induced spin current. For this model, we derive the quasi-classical equations of motion for the magnetization where the effects of a dynamical non-equilibrium distribution function are taken into account self-consistently. We obtain the Landau-Lifshitz-Gilbert equation supplemented by a spin-transfer torque term of Slonczewski form. We identify a regime of persistent precessions in which we find an enhancement of the thermoelectric current by the pumping current.

Helical edge modes of 2D topological insulators are supposed to be protected from time-reversal invariant elastic backscattering. Yet substantial deviations from the perfect conductance are typically observed experimentally down to very low temperatures. To resolve this conundrum we consider the effect of a single magnetic impurity with arbitrary spin on the helical edge transport. We consider the most general structure of the exchange interaction between the impurity and the edge electrons. Moreover, for the first time, we take into the account the local anisotropy for the impurity and show that it strongly affects the backscattering current in a wide range of voltages and temperatures. We show that the sensitivity of the backscattering current to the presence of the local anisotropy is different for half-integer and integer values of the impurity spin. In the latter case the anisotropy can significantly increase the backscattering correction to the current.

The celebrated Jordan–Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension. Here we extend this spin–fermion mapping to arbitrary *tree* structures, which enables mapping between fermionic and spin systems with nearest-neighbor coupling. The mapping is achieved with the help of additional spins at the junctions between one-dimensional chains. This property allows for straightforward simulation of Majorana braiding in spin or qubit systems.

Landau level splitting in a two-dimensional electron gas (2DEG) confined in an ultrapure GaN/AlGaN heterostructure grown by molecular beam epitaxy on bulk GaN is verified spectroscopically. The Landau level fan reconstructed from magneto-photoluminescence (PL) data yields an effective mass of 0.24*m*0 for the 2D electrons. Narrow excitonic PL line widths < 100 *μ*eV, an atomically flat surface of the layer stack, as well as the absence of the 2DEG in the dark environment, are important ancillary experimental findings while focusing on magneto-PL investigations of the heterostructure. Simultaneously recorded Shubnikov-de Haas and magneto-PL intensity oscillations under steady UV illumination exhibit an identical frequency and allow for two independent ways of determining the 2D density.

Quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states and the resistivity ρ, occurring when the Fermi level E crosses a bottom E_N of some subband of transverse quantization. We demonstrate that the character of smearing of the singularities crucially depends on the concentration of impurities. There is a crossover concentration n_c ∝ |λ|,λ ≪ 1 being the dimensionless amplitude of scattering. For n ≫ n_c the singularities are simply rounded at ε ≡ E − E_N ∼ τ ^{−1} – the Born scattering rate. For n ≪ nc the single-impurity non-Born effects in scattering become essential despite λ ≪ 1. The peak of the resistivity is asymmetrically split in a Fano-resonance manner (however with a more complex structure). Namely, for ε > 0 there is a broad maximum at ε∝λ^2 while for ε<0 there is a deep minimum at |ε|∝n^2 ≪λ^2. The behaviour of ρ below the minimum depends on the sign of λ. In case of repulsion ρ monotonically grows with |ε| and saturates for |ε| ≫ λ^2. In case of attraction ρ has sharp maximum at |ε| ∝ λ^2. The latter feature is due to resonant scattering at quasistationary bound states that inevitably arise just below the bottom of each subband for any attracting impurity.

The concept of non-ergodicity in quantum many body systems can be discussed in the context of the wave functions of the many body system or as a property of the dynamical observables, such as time-dependent spin correlators. In the former approach the non-ergodic delocalized state is defined as the one in which the wave functions occupy a volume that scales as a non-trivial power of the full phase space. In this work we study the simplest spin glass model and find that in the delocalized non-ergodic regime the spin–spin correlators decay with the characteristic time that scales as non-trivial power of the full Hilbert space volume. The long time limit of this correlator also scales as a power of the full Hilbert space volume. We identify this phase with the glass phase whilst the many body localized phase corresponds to a ’hyperglass’ in which dynamics is practically absent. We discuss the implications of these findings to quantum information problems.

We discuss magnetization curves of a toy-model trigonal and tetrahedral clusters. Nonlinearity of magnetization with local minimum of differential susceptibility resembling known magnetization plateaus of triangular-lattice and pyrochlore lattice antiferromagnets is observed at intermediate temperature range *J* ≲ *T* ≲ Θ (here, *J* is the exchange coupling constant and Θ is a Curie–Weiss temperature). This behavior is due to increased statistical weight of the states with intermediate total spin of the cluster, which is related to the “order-by-disorder” mechanism of plateau stabilization of a macroscopic frustrated magnet.

Magneto-fermionic condensate under study is a Bose-Einstein condensate of cyclotron spin-flip magnetoexcitons in a quantum Hall insulator. This condensate features unique properties such as millisecond range lifetime and hundreds of micrometers of propagation length. In this study, utilizing the photo-induced resonant reflection technique, we measured the exciton escape time. Finally, we estimated the exciton condensate propagation velocity as 25 m/s, which is much higher than a single particle propagation velocity. We also proposed a mechanism of exciton condensation.

Experimental results on the properties of a recently discovered new collective state, the magnetofermionic condensate, are summarized herein. Condensation occurs in a fermionic system, a quantum Hall insulator (filling factor ν = 2), as a result of the formation of a dense ensemble of long-lived spin cyclotron magnetoexcitons, composite bosons. At temperatures below 1 K, the exciton ensemble exhibits a sharp enhancement in its response to an external electromagnetic field due to the formation of a super-absorbing state that interacts coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level rearrange to form a new non-equilibrium radiative recombination channel. The condensate shows a sharp decrease in viscosity and the ability to spread over macroscopically large distances, on the order of a millimeter, at a speed of ≈103 cm s−1. Due to this rapid long-distance spin transfer, new opportunities in the field of spintronics have been opened up.

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 superconducting properties of the Co_{2}Cr_{1-x}Fe_{x}Al_{y}/Cu/Ni/Cu/Pb spin-valve structure the magnetic part of which comprises the Heusler alloy layer HA = Co_{2}Cr_{1-x}Fe_{x}Al_{y} with a high degree of spin polarization (DSP) of the conduction band and a Ni layer of variable thickness. The separation between the superconducting transition curves measured for the parallel (α = 0°) and perpendicular (α = 90°) orientation of the magnetization of the HA and the Ni layers reaches up to 0.5 K (α is the angle between the magnetization of two ferromagnetic layers). For all studied samples the dependence of the superconducting transition temperature T c on α demonstrates a deep minimum in the vicinity of the perpendicular configuration of the magnetizations. This suggests that the observed minimum and the corresponding full switching effect of the spin valve is caused by the long-range triplet component of the superconducting condensate in the multilayer. Such a large effect can be attributed to a half-metallic nature of the HA layer, which in the orthogonal configuration efficiently draws off the spin-polarized Cooper pairs from the space between the HA and Ni layers. Our results indicate a significant potential of the concept of a superconducting spin-valve multilayer comprising a half-metallic ferromagnet, recently proposed by A. Singh et al., Phys. Rev. X 2015, 5, 021019, in achieving large values of the switching effect.

Stochastic roughness is a widespread feature of natural surfaces and is an inherent byproduct of most fabrication techniques. In view of the rapid development of microfluidics, the important question is how this inevitable problem affects the low-Reynolds-number flows that are common for micro-devices. Moreover, one could potentially turn the flaw into a virtue and control the flow properties by means of specially ‘tuned’ random roughness. In this paper we investigate theoretically the statistics of fluctuations in fluid velocity produced by the waviness irregularities at the surface of a no-slip wall. Particular emphasis is laid on the issue of the universality of our findings.

We show that experimentally observed complex line shapes of smeared Van Hove singularities in the resistivity of a quasi-one-dimensional system may be due to non-Born effects in scattering. At low concentration of impurities with respect to scattering amplitude λ the non-Born effects are essential if the Fermi level is sufficiently close to singularity. The structure of the line shape depends on the sign of λ: for repulsion (λ>0) it is "plateau-minimum-maximum-plateau", while for attraction (λ<0) it is "plateau-maximum-minimum-maximum-plateau". In contrast with Fano-resonance scenario, complex structure of the line shape arises even in the absence of a resonant level.

We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As it was established experimentally, elastic turbulence possesses a boundary layer where the fluid velocity field can be approximated by a steady shear flow with relatively small fluctuations on the top of it. Assuming that at the bottom of the boundary layer the dissolved polymers can be considered as passive objects, we examine analytically and numerically statistics of the polymer conformation, which is highly nonuniform in the wall-normal direction. Next, imposing the condition that the passive regime terminates at the border of the boundary layer, we obtain an estimate for the ratio of the mean flow to the magnitude of flow fluctuations. This ratio is determined by the polymer concentration, the radius of gyration of polymers and their length in the fully extended state. The results of our asymptotic analysis reproduce the qualitative features of elastic turbulence at finite Weissenberg numbers.

Magnetisation measurements and ESR spectra of a doped quasi 2D antiferromagnet on a triangular lattice reveal a crucial change of the ground state spin configuration and a disappearance of a characteristic 1/3-magnetisation plateau under a doping. According to theory, this is a result of the competition between the structural and dynamic disorders. The dynamic zero-point or thermal fluctuations are known to lift the degeneracy of the mean field ground state of a triangular magnet and cause the spin configuration to be the most collinear, while the static disorder provides another selection of the ground state, with the least collinear structure. Low-level doping was found to decrease the N\'{e}el temperature and saturation field by only few percent, while the magnetisation plateau disappears completely and the spin configuration is drastically changed. ESR spectra confirm an impurity-induced change of the so-called Y-type structure to an inverted Y-structure for 15%-doping by potassium.

We compute the differential Poisson’s ratio of a suspended two-dimensional crystalline membrane embedded into a space of large dimensionality . We demonstrate that, in the regime of anomalous Hooke’s law, the differential Poisson’s ratio approaches a universal value determined solely by the spatial dimensionality , with a power-law expansion , where . Thus, the value predicted in previous literature holds only in the limit .

Spectra of magnetoplasma excitations have been investigated in two-dimensional electron systems in AlAs quantum wells (QWs) of different widths. The magnetoplasma spectrum has been found to change profoundly when the quantum well width becomes thinner than 5.5 nm, indicating a drastic change in the conduction electron energy spectrum. The transformation can be interpreted in terms of transition from the in-plane strongly anisotropic Xx−Xy valley occupation to the out-of-plane isotropic Xz valley in the QW plane. Strong enhancement of the cyclotron effective mass over the band value in narrow AlAs QWs is reported.

Spin resonance of a two-dimensional electron system confined in a GaN/AlGaN heterostructure grown by molecular beam epitaxy was resistively detected over a wide range of magnetic field and microwave frequency. Although the spin-orbit interaction is strong in this type of heterostructure at zero magnetic field, surprisingly the width of the detected spin resonance line was very narrow— down to 6.5 mT at 13.3 T. The spin depolarization time extracted from the resonance linewidth was estimated to be 2 ns. The electron g-factor was measured with high accuracy, resembling a value close to the free-electron value and its dependence on the magnetic field was studied.

The spin polarization features of an electron system and the relaxation of nonequilibrium spin excitations near an even-denominator fractional state of 3/2 in a two-dimensional electron system based on the GaAs/AlGaAs heterostructure are experimentally investigated. It is shown that the 3/2 state is a singular point in the filling factor dependence of the spin ordering of the two-dimensional electron system, at which the spin subsystem is rearranged. A giant slowing down of the relaxation of spin excitations to the ground state is revealed in a certain range of filling factors near filling factor 3/2.

Experimental and theoretical studies of a smectic-A–hexatic-B transition in freely suspended films of thickness 2–10μm of the n-pentyl-4′−n-pentanoyloxy-biphenyl-4-carboxylate (54COOBC) compound are presented. X-ray investigations revealed a discontinuous first-order transition into the hexatic phase. The temperature region of two-phase coexistence near the phase transition point diminishes with decreasing film thickness. The width of this temperature region as a function of the film thickness was derived on the basis of a Landau mean-field theory in the vicinity of a tricritical point (TCP). Close to TCP the surface hexatic-B order penetrates anomalously deep into the film interior.