# Publications

We investigate the coherent vortex produced by two-dimensional turbulence excited in a finite box. We establish analytically the mean velocity profile of the vortex for the case where the bottom friction is negligible and express its characteristics via the parameters of pumping. Our theoretical predictions are verified and confirmed by direct numerical simulations in the framework of two-dimensional weakly compressible hydrodynamics with zero boundary conditions.

We explore correlations of eigenstates around the many-body localization (MBL) transition in their dependence on the energy difference (frequency) ω and disorder W. In addition to the genuine many-body problem, XXZ spin chain in random field, we consider localization on random regular graphs that serves as a toy model of the MBL transition. Both models show a very similar behavior. On the localized side of the transition, the eigenstate correlation function β(ω) shows a power-law enhancement of correlations with lowering ω; the corresponding exponent depends on W. The correlation between adjacent-in-energy eigenstates exhibits a maximum at the transition point W_c, visualizing the drift of W_c with increasing system size towards its thermodynamic-limit value. The correlation function β(ω) is related, via Fourier transformation, to the Hilbert-space return probability. We discuss measurement of such (and related) eigenstate correlation functionson state-of-the-art quantum computers and simulators.

We introduce a simple physical picture to explain the process of molecular sorting, whereby specific proteins are concentrated and distilled into submicrometric lipid vesicles in eukaryotic cells. To this purpose, we formulate a model based on the coupling of spontaneous molecular aggregation with vesicle nucleation. Its implications are studied by means of a phenomenological theory describing the diffusion of molecules toward multiple sorting centers that grow due to molecule absorption and are extracted when they reach a sufficiently large size. The predictions of the theory are compared with numerical simulations of a lattice-gas realization of the model and with experimental observations. The efficiency of the distillation process is found to be optimal for intermediate aggregation rates, where the density of sorted molecules is minimal and the process obeys simple scaling laws. Quantitative measures of endocytic sorting performed in primary endothelial cells are compatible with the hypothesis that these optimal conditions are realized in living cells.

Charge transport in doped quantum paraelectrics (QPs) presents a number of puzzles, including a pronounced T^2 regime in the resistivity. We analyze charge transport in a QP within a model of electrons coupled to a soft transverse optical (TO) mode via a two-phonon mechanism. For T above the soft-mode frequency but below some characteristic scale (E_0), the resistivity scales with the occupation number of phonons squared, i.e., as T^2. The T^2 scattering rate does not depend on the carrier number density and is not affected by a crossover between degenerate and nondegenerate regimes, in agreement with the experiment. Temperatures higher than E_0 correspond to a nonquasiparticle regime, which we analyze by mapping the Dyson equation onto a problem of supersymmetric quantum mechanics. The combination of scattering by two TO phonons and by a longitudinal optical mode explains the data quite well.

We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between the phases of the order parameter and of the anomalous Green functions.

We compute the absolute Poisson’s ratio and the bending rigidity exponent of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality , . We demonstrate that, in the regime of anomalous Hooke’s law, the absolute Poisson’s ratio approaches material independent value determined solely by the spatial dimensionality : where . Also, we find the following expression for the exponent of the bending rigidity: . These results cannot be captured by self-consistent screening approximation.

We report low temperature electron spin resonance experimental and theoretical studies of an archetype S=1/2 strong-rung spin ladder material (C5H12N)2CuBr4. Unexpected dynamics is detected deep in the Tomonaga-Luttinger spin liquid regime. Close to the point where the system is half-magnetized (and believed to be equivalent to a gapless easy plane chain in zero field) we observed orientation-dependent spin gap and anomalous g-factor values. Field theoretical analysis demonstrates that the observed low-energy excitation modes in magnetized (C5H12N)2CuBr4 are solitonic excitations caused by Dzyaloshinskii-Moriya interaction presence.

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.

We consider the structure of a coherent vortex formed around a solid rotating disc in two-dimensional turbu- lent flow. We find the average velocity profile of the coherent vortex for different rotation velocities

We examine coherent vortices appearing as a result of the inverse cascade of two-dimensional turbulence in a finite box in the case of pumping with arbitrary correlation time in the quasilinear regime. We demonstrate that the existence of the vortices depends on the ratio between the values of the bottom friction coefficient α and the viscous damping of the flow fluctuations at the pumping scale.

The plasma oscillations in new advanced two-dimensional electron systems (2DESs) based on the heterostructures ZnO/MgZnO, AlAs/AlGaAs, and GaAs/AlGaAs are studied and compared. The relaxation times and the effective masses in samples with various electron densities in these 2DESs are found by microwave plasma spectroscopy. The specific features of the plasma oscillations in the AlAs/AlGaAs quantum wells that are induced by the filling of several valleys with electrons are revealed. The possibility of adjusting a plasmon spectrum via changing the electron concentrations in valleys is demonstrated.

We consider a nonequilibrium cross-response phenomenon, where a driven magnetization gives rise to electric shot noise (but no d.c. current). This effect is realized on a nanoscale, with a small metallic ferromagnet which is tunnel coupled to two normal metal leads. The driving gives rise to a precessing magnetization. The geometrically generated noise is related to a nonequilibrium electron distribution in the ferromagnet. Our protocol provides a channel for detecting and characterizing ferromagnetic resonance.

It is shown that the anomalous elasticity of membranes affects the profile and thermodynamics of a bubble in van der Waals heterostructures. Our theory generalizes the nonlinear plate theory as well as the membrane theory of the pressurised blister test to incorporate the power-law scale dependence of the bending rigidity and Young's modulus of a two-dimensional crystalline membrane. This scale dependence, caused by long-range interaction of relevant thermal fluctuations (flexural phonons), is responsible for the nonlinear Hooke law observed recently in graphene. It is shown that this anomalous elasticity affects the dependence of the maximal height of the bubble as a function of its radius and temperature. We determine the characteristic temperature above which the anomalous elasticity is important. It is suggested that, for graphene-based van der Waals heterostructures, the predicted anomalous regime is experimentally accessible at room temperature.

Magnetic impurities with sufficient anisotropy could account for the observed strong deviation of the edge conductance of 2D topological insulators from the anticipated quantized value. In this work we consider such a helical edge coupled to dilute impurities with an arbitrary spin S and a general form of the exchange matrix. We calculate the backscattering current noise at finite frequencies as a function of the temperature and applied voltage bias. We find that, in addition to the Lorentzian resonance at zero frequency, the backscattering current noise features Fano-type resonances at nonzero frequencies. The widths of the resonances are controlled by the spectrum of corresponding Korringa rates. At a fixed frequency the backscattering current noise has nonmonotonic behavior as a function of the bias voltage.

The interplay of interactions and disorder in two-dimensional (2D) electron systems has actively been studied for decades. The paradigmatic approach involves starting with a clean Fermi liquid and perturbing the system with both disorder and interactions. Instead, we start with a clean non-Fermi liquid near a 2D ferromagnetic quantum critical point and consider the effects of disorder. In contrast with the disordered Fermi liquid, we find that our model does not suffer from runaway flows to strong coupling and the system has a marginally stable fixed point with perfect conduction.

An experimental technique based on time-resolved Kerr rotation allows a comparison of the spin stiffnesses of different spin-polarized and depolarized states in a two-dimensional electron system. With this technique, a new spin-correlated phase that has no known analogues was discovered. The new spin-depolarized phase is characterized by high spin stiffness equal to that of a spin-polarized quantum Hall ferromagnet

Internodal dynamics of quasiparticles in Weyl semimetals manifest themselves in hydrodynamic, transport, and thermodynamic phenomena and are essential for potential valleytronic applications of these systems. In an external magnetic field, coherent quasiparticle tunnelling between the nodes modifies the quasiparticle dispersion and, in particular, opens gaps in the dispersion of quasiparticles at the zeroth Landau level. We study magnetotransport in a Weyl semimetal taking into account mechanisms of quasiparticle scattering, both affected by such gaps and independent of them. We compute the longitudinal resistivity of a disordered Weyl semimetal with two nodes in a strong magnetic field microscopically and demonstrate that in a broad range of magnetic fields, it has a strong angular dependence, ρ(η)∝C1+C2cos2η, where η is the angle between the field and the separation between the nodes in momentum space. The first term is determined by the coherent internodal tunnelling and is important only at angles η close to π/2. This contribution depends exponentially on the magnetic field, ∝exp−B0/B. The second term is weakly dependent on the absolute value of the magnetic field for realistic concentrations of the impurities in a broad interval of fields.

The mesoscopic Stoner instability is an intriguing manifestation of symmetry breaking in isolated metallic quantum dots, underlined by the competition between single-particle energy and Heisenberg exchange interaction. Here we study this phenomenon in the presence of tunnel coupling to a reservoir. We analyze the spin susceptibility of electrons on the quantum dot for different values of couplings and temperature. Our results indicate the existence of a “quantum phase transition” at a critical value of the tunneling coupling, which is determined by the Stoner-enhanced exchange interaction. This quantum phase transition is a manifestation of the suppression of the Coleman-Weinberg mechanism of symmetry breaking, induced by coupling to the reservoir.

We studied electron spin resonance in a quantum magnet NiCl2−4SC(NH2)2, demonstrating a field-induced quantum phase transition from a quantum-disordered phase to an antiferromagnet. We observe two branches of the antiferromagnetic resonance of the ordered phase, one of them has a gap, and the other is a Goldstone mode with zero frequency at a magnetic field along the fourfold axis. This zero-frequency mode acquires a gap at a small tilting of the magnetic field with respect to this direction. The upper gap was found to be reduced in the Br-substituted compound Ni(Cl1−xBrx)2−4SC(NH2)2 with x=0.21. This reduction is unexpected because of the previously reported rise in the main exchange constant in a substituted compound. Furthermore, a nonresonant diamagnetic susceptibility χ′ was found for the ordered phase in a wide frequency range above the quasi-Goldstone mode. This dynamic diamagnetism is as large as the dynamic susceptibility of the paramagnetic resonance. We speculate that it originates from a two-magnon absorption band of the low-frequency dispersive magnon branch.

To meet increasingly demanding technological needs in modern security and industrial applications involving rapid close-range screening, we have developed a 100- GHz linear scanner. Having incorporated a novel approach in terahertz sensing and an advanced IMPATT-diode signal generating technique, the proposed system offers an efficient non-destructive testing (NDT) solution that is absolutely safe, fast, highly portable, and cost-effective. The test results demonstrate outstanding capability of the scanner to provide continuous, high-throughput security screening of mail. The system can perform real-time imaging with effective resolution approaching 5 mm at conveyor speeds of up to 15 m/s.

Clean quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states ν and resistivity ρ, occurring when the Fermi level crosses the bottom of some transversal quantization subband. However, taking the scattering on impurities into the account should smear the singularities. As we have shown in our previous work [Phys. Rev. B **99**, 035414 (2019)], for the case of clean conducting tubes, the character of smearing strongly depends on the impurity concentration n. For n≫nc, the singularities are simply rounded, while for n≪nc, the initial peak is asymmetrically split into two for the case of attracting impurities, nc being a crossover concentration. In this work, we extend our consideration to “strips”—quasi-one-dimensional structures in 2D conductors. Here also for n≪nc, an original Van Hove singularity is asymmetrically split into two peaks. However, in contrast to the tube case, the amplitudes of scattering at impurities depend on their positions and these peaks are inhomogeneously broadened. The strongest broadening occurs in the left peak, arising, for attracting impurities, due to the scattering at the quasistationary levels that form a relatively broad impurity band with a weak quasi-Van Hove feature on its lower edge. Different parts of ρ(ɛ) are dominated by different groups of impurities: close to the minimum the most effective scatterers, paradoxically, are the “weakest” impurities located close to nodes of the electronic wave function. The quasi-Van Hove feature at the left maximum is dominated by the strongest impurities located close to antinodes.