# Publications

We show that the terahertz (THz) photoconductivity in the topological phase of Hg1–*x*Cd*x*Te-based structures exhibits the apparent *PT*- (parity-time) symmetry whereas the *P*-symmetry and the *T*-symmetry, separately, are not conserved. Moreover, it is demonstrated that the *P*- and *T*-symmetry breaking may not be related to any type of the sample anisotropy. This result contradicts the apparent symmetry arguments and means that there exists an external factor that interacts with the sample electronic system and breaks the symmetry. We show that deviations from the ideal experimental geometry may not be such a factor.

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.

We examine statistical properties of a laser beam propagating in a turbulent medium. We prove that the intensity fluctuations at large propagation distances possess a Gaussian probability density function and establish quantitative criteria for realizing the Gaussian statistics depending on the laser propagation distance, laser beam waist, laser frequency, and turbulence strength. We calculate explicitly the laser envelope pair correlation function and corrections to its higher-order correlation functions breaking Gaussianity. We discuss also statistical properties of the brightest spots in the speckle pattern.

t is known that the turbulence in a fast-rotating volume becomes effectively two- dimensional. The latter is characterized by an inverse energy cascade leading to the formation of coherent flow in finite systems. In a rotating three-dimensional vessel this flow has the form of columnar vortices. Here we develop an analytical theory describing interaction of the vortex with turbulent pulsations. This interaction results in energy transfer from small-scale eddies to the large-scale vortex. We derive the equation for the radial velocity profile of the vortex and solve it for the simplest boundary conditions. We indicate the domain of physical parameters where our theory works.

We consider two-dimensional turbulence in the presence of a condensate. The nondiagonal correlation functions of the Lagrangian accelerations are calculated, and it is shown that they have the same universality properties as the nondiagonal correlation functions of the velocity fluctuations.

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.

The recent experimental studies of extremely long-lived macroscopic ensembles of spin-cyclotron excitons (magnetoexcitons) which have to obey the Bose-Einstein statistics signal the emergence of an excitonic coherent phase. In the present paper the theory of a weakly interacting Bose gas of spin-cyclotron excitations is developed in terms of a virial correction to the single-magnetoexciton energy. The condition for coherent-incoherent phase transition is discussed. It is expected to be strongly related to the studied long-distance interexcitonic correlations. The results obtained theoretically are discussed in terms of their agreement with specific experimental data.

We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number m+1=3, with a box distribution of disorder and in the middle of the band (energy E=0), which is the model most frequently considered in the literature. As a first step, we carry out an accurate determination of the critical disorder, with the result Wc=18.17±0.01. After this, we determine the dependence of the correlation volume Nξ=mξ (where ξ is the associated correlation length) on disorder W on the delocalized side of the transition W<Wc, by means of population dynamics. The asymptotic critical behavior is found to be ξ∝(Wc−W)−1/2, in agreement with analytical prediction. We find very pronounced corrections to scaling, in similarity with models in high spatial dimensionality and with many-body localization transitions.

We consider quantum logical gates on Majorana qubits implemented in chain structures of ordinary qubits, spins, or pseudospins. We demonstrate that one can implement a two-qubit operation via local manipulations, using an extra coupler spin in a *T*-junction geometry, so that this coupler spin remains disentangled from the qubit. Furthermore, we identify a set of symmetry operations, which not only allow us to determine the resulting two-qubit gate, but also to demonstrate robustness of the resulting gate to inaccuracies in the manipulations, known for topological quantum computation.

Hydrodynamic charge transport is at the center of recent research efforts. Of particular interest is the nondissipative Hall viscosity, which conveys topological information in clean gapped systems. The prevalence of disorder in the real world calls for a study of its effect on viscosity. Here we address this question, both analytically and numerically, in the context of disordered noninteracting 2D electrons. Analytically, we employ the self-consistent Born approximation, explicitly taking into account the modification of the single-particle density of states and the elastic transport time due to the Landau quantization. The reported results interpolate smoothly between the limiting cases of a weak (strong) magnetic field and strong (weak) disorder. In the regime of a weak magnetic field our results describe the quantum (Shubnikov–de Haas type) oscillations of the dissipative and Hall viscosity. For strong magnetic fields we characterize the effects of the disorder-induced broadening of the Landau levels on the viscosity coefficients. This is supplemented by numerical calculations for a few filled Landau levels. Our results show that the Hall viscosity is surprisingly robust to disorder.

We have studied electron spin resonance (ESR) absorption spectra for the nonmagnetically diluted strong-leg spin ladder magnet (C7H10N)2Cu(1−x)ZnxBr4 (abbreviated as DIMPY) down to 450 mK. Formation of the clusters with nonzero net magnetization is confirmed; the cluster-cluster interaction is evidenced by the concentration dependence of ESR absorption. High-temperature spin-relaxation time was found to increase with nonmagnetic dilution. The ESR linewidth analysis proves that the Dzyaloshinskii-Moriya (DM) interaction remains the dominant spin-relaxation channel in diluted DIMPY. Experimental data indicate that the dilution results in the weakening of the effective DM interaction, which can be interpreted as total suppression of DM interaction in the close vicinity of impurity atom.

An unusual behavior of the exchange energy scale of a quantum Hall ferromagnet with ν=1 was found in strongly correlated two-dimensional electron systems based on MgZnO/ZnO heterostructures. The exchange contribution, entering the energy of a collective excitation, was probed by means of inelastic light scattering. It was established that, in a wide range of electron densities corresponding to the Wigner-Seitz parameter 7<rs<11, this contribution is on the order of the cyclotron energy, which is notably different from the typical scale of e2/ɛℓB that is typical for weakly interacting systems. The same trend was confirmed via numerical calculations.

Josephson junctions drive the operation of superconducting qubits and they are the key for the coupling and the interfacing of superconducting qubit components with other quantum platforms. They are the only means to introduce non linearity in a superconducting circuit and offer direct solutions to tune the properties of a superconducting qubit, thus enlarging the possible qubit layouts. Junctions performances and tunability can take advantage of using a large variety of barriers and their special functionalities. We mention pertinent results on the advances in understanding the properties of ferromagnetic junctions, which makepossible the use of these devices either as memory elements and as core circuit elements.

In this work, a class of metamaterials is proposed on the basis of ferromagnet/superconductor hybridization for applications in magnonics. These metamaterials comprise of a ferromagnetic magnon medium that is coupled inductively to a superconducting periodic microstructure. Spectroscopy of magnetization dynamics in such hybrid evidences formation of areas in the medium with alternating dispersions for spin wave propagation, which is the basic requirement for the development of metamaterials known as magnonic crystals. The spectrum allows for derivation of the impact of the superconducting structure on the dispersion: it takes place due to a diamagnetic response of superconductors on the external and stray magnetic fields. In addition, the spectrum displays a dependence on the superconducting critical state of the structure: the Meissner and the mixed states of a type II superconductor are distinguished. This dependence hints toward nonlinear response of hybrid metamaterials on the magnetic field. Investigation of the spin wave dispersion in hybrid metamaterials shows formation of allowed and forbidden bands for spin wave propagation. The band structures are governed by the geometry of spin wave propagation: in the backward volume geometry the band structure is conventional, while in the surface geometry the band structure is nonreciprocal and is formed by indirect band gaps.

The superconducting characteristics of the spin-valve Co2Cr1 - *x*Fe*x*Al*y*/Cu/Ni/Cu/Pb heterostructures are studied. It is found that the difference in the plots characterizing superconducting transitions at the parallel and perpendicular orientations of magnetizations in the ferromagnetic Heusler alloy layer (HA = Co2Cr1 - *x*Fe*x*Al*y*) with a high degree of spin polarization and in the nickel (Ni) layer can be as large as 0.5 K. For all samples, the dependence of *T**c* on the angle between the magnetization directions of the ferromagnetic layers exhibits a deep minimum near the orthogonal orientation. This minimum results from the long-range triplet components of the superconducting condensate in a ferromagnetic material. At the perpendicular orientation of the magnetizations, the Heusler alloy layer with the high degree of spin polarization absorbs the spin-polarized Cooper pairs from the spacing between the Heusler alloy and Ni layers.

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.

We explain theoretical peculiarities of the smectic-A–hexatic-B equilibrium phase coexistence in a finite-temperature range recently observed experimentally in free-standing smectic films [I. A. Zaluzhnyy *et al.*, Phys. Rev. E **98**, 052703 (2018)]. We quantitatively describe this unexpected phenomenon within Landau phase transitions theory assuming that the film state is close to a tricritical point. We found that the surface hexatic order diminishes the phase coexistence range as the film thickness decreases, shrinking it to zero at some minimal film thickness Lc, of the order of a few hexatic correlation length. We established universal laws for the temperature width of the phase coexistence range in terms of the reduced variables. Our theory is in agreement with the existing experimental data.

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.