Igor Gornyi

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Papers by Igor Gornyi

Disordered electron liquid in double quantum well heterostructures: Renormalization group analysis and dephasing rate

Physical Review B, 2011

We report a detailed study of the influence of the electron-electron interaction on physical obse... more We report a detailed study of the influence of the electron-electron interaction on physical observables (conductance, etc.) of a disordered electron liquid in double quantum well heterostructure. We find that even in the case of common elastic scattering off electrons in both quantum wells, the asymmetry in the electron-electron interaction across and within quantum wells decouples them at low temperatures. Our results are in quantitative agreement with recent transport experiments on the gated double quantum well AlxGa1−xAs/GaAs/AlxGa1−xAs heterostructures.

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Transversal magnetoresistance in Weyl semimetals

Physical Review B, 2015

ABSTRACT We explore theoretically the magnetoresistvity of three-dimensional Weyl and Dirac semim... more ABSTRACT We explore theoretically the magnetoresistvity of three-dimensional Weyl and Dirac semimetals in transversal magnetic fields within two alternative models of disorder: (i) short-range impurities and (ii) charged (Coulomb) impurities. Impurity scattering is treated using the self-consistent Born approximation. We find that an unusual broadening of Landau levels leads to a variety of regimes of the resistivity scaling in the temperature-magnetic field plane. In particular, the magnetoresitance is non-monotonous for the white-noise disorder model. For $H\to 0$ the magnetoresistance for short-range impurities vanishes in a non-analytic way as $H^{1/3}$. In the limits of strongest magnetic fields $H$, the magnetoresistivity vanishes as $1/H$ for pointlike impurities, while it is linear and positive in the model with Coulomb impurities.

Transport of Interacting Electrons through a Double Barrier

NATO Science Series, 2000

Cyclotron resonance in antidot arrays

Physical Review B, 2002

We study the dynamical properties of an electron gas scattered by impenetrable antidots in the pr... more We study the dynamical properties of an electron gas scattered by impenetrable antidots in the presence of a strong magnetic field. We find that the lineshape of the cyclotron resonance is very different from the Lorentzian and is not characterized by the Drude scattering rate. We show that the dissipative dynamical response of skipping orbits, Sc(ω), is broadened on a scale of the cyclotron frequency ωc and has a sharp dip ∝ |ω − ωc|. For small antidots, Sc(ω) is strongly modulated with a period equal to ωc and has sharp square-root singularities for a series of resonant frequencies. For large antidots, Sc(ω) has a hard gap at ω < ωc between two sharp peaks, associated respectively with edge states and free cyclotron orbits.

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Quantum interference in HgTe structures

physica status solidi (b), 2014

ABSTRACT We study quantum transport in HgTe/HgCdTe quantum wells under the condition that the che... more ABSTRACT We study quantum transport in HgTe/HgCdTe quantum wells under the condition that the chemical potential is located outside of the band gap. We first analyze symmetry properties of the effective Bernevig–Hughes–Zhang Hamiltonian and the relevant symmetry-breaking perturbations. Based on this analysis, we overview possible patterns of symmetry breaking that govern the quantum interference (weak localization or weak antilocalization) correction to the conductivity in two-dimensional HgTe/HgCdTe samples. Further, we perform a microscopic calculation of the quantum correction beyond the diffusion approximation. Finally, the interference correction and the low-field magnetoresistance in a quasi-one-dimensional geometry are analyzed.

Comment on the paper of A. G. Groshev and S. G. Novokshonov “Negative Magnetoresistance and Hall Coefficient of a Two-Dimensional Disordered System”

by S. Novokshonov and Igor Gornyi

Physics of the Solid State, 2001

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Rippling and crumpling in disordered free-standing graphene

Physical Review B, 2015

ABSTRACT Graphene is a famous realization of elastic crystalline two-dimensional (2D) membrane. T... more ABSTRACT Graphene is a famous realization of elastic crystalline two-dimensional (2D) membrane. Thermal fluctuations of a 2D membrane tend to destroy the long-range order in the system. Such fluctuations are stabilized by strong anharmonicity effects, which preserve thermodynamic stability. The anharmonic effects demonstrate critical behaviour on scales larger than the Ginzburg scale. In particular, clean suspended flake of graphene shows a power-law increase of the bending rigidity with the system size, $\varkappa\propto L^{\eta},$ due to anharmonic interaction between in-plane and out-of-plane (flexural) phonon modes. We demonstrate that random fluctuations of membrane curvature caused by static disorder may change dramatically the scaling of the bending rigidity and lead to a non-monotonous dependence of $\varkappa$ on $L.$ We derive coupled renormalization-group equations describing combined flow of $\varkappa$ and effective disorder strength $b$, find a critical curve $b(\varkappa)$ separating flat and crumpled phases, and explore the behavior of disorder in the flat phase. Deep in the flat phase, disorder decays in a power-law way at scales larger than the Ginzburg length which therefore sets a characteristic size for the ripples---static out-of-plane deformations observed experimentally in suspended graphene. We find that in the limit $L \to \infty $ ripples are characterized by anomalous exponent $2\eta$ in contrast to dynamical fluctuations governed by $\eta$. In the near-critical regime, disorder first increase with $L$, then reaches a maximum and starts to decrease. In this case, the membrane shows fractal properties implying a multiple folding starting form a certain length scale $L_1$ and finally flattens at a much larger scale $L_2$ (which diverges at criticality). We conclude the paper by a comparison of our results with available experimental data on graphene ripples.

Collision-dominated nonlinear hydrodynamics in graphene

Physical Review B, 2015

We present an effective hydrodynamic theory of electronic transport in graphene in the interactio... more We present an effective hydrodynamic theory of electronic transport in graphene in the interactiondominated regime. We derive the emergent hydrodynamic description from the microscopic Boltzmann kinetic equation taking into account dissipation due to Coulomb interaction and find the viscosity of Dirac fermions in graphene for arbitrary densities. The viscous terms have a dramatic effect on transport coefficients in clean samples at high temperatures. Within linear response, we show that viscosity manifests itself in the nonlocal conductivity as well as dispersion of hydrodynamic plasmons. Beyond linear response, we apply the derived nonlinear hydrodynamics to the problem of hot spot relaxation in graphene.

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Hydrodynamics in graphene: Linear-response transport

Physical Review B, 2015

We develop a hydrodynamic description of transport properties in graphene-based systems which we ... more We develop a hydrodynamic description of transport properties in graphene-based systems which we derive from the quantum kinetic equation. In the interaction-dominated regime, the collinear scattering singularity in the collision integral leads to fast unidirectional thermalization and allows us to describe the system in terms of three macroscopic currents carrying electric charge, energy, and quasiparticle imbalance. Within this "three-mode" approximation we evaluate transport coefficients in monolayer graphene as well as in double-layer graphene-based structures. The resulting classical magnetoresistance is strongly sensitive to the interplay between the sample geometry and leading relaxation processes. In small, mesoscopic samples the macroscopic currents are inhomogeneous which leads to linear magnetoresistance in classically strong fields. Applying our theory to doublelayer graphene-based systems, we provide microscopic foundation for phenomenological description of giant magnetodrag at charge neutrality and find magnetodrag and Hall drag in doped graphene.

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Magnetoresistance in Two-Component Systems

by Igor Gornyi and A. Dmitriev

Physical Review Letters, 2015

Two-component systems with equal concentrations of electrons and holes exhibit non-saturating, li... more Two-component systems with equal concentrations of electrons and holes exhibit non-saturating, linear magnetoresistance in classically strong magnetic fields. The effect is predicted to occur in finite-size samples at charge neutrality in both disorder-and interaction-dominated regimes. The phenomenon originates in the excess quasiparticle density developing near the edges of the sample due to the compensated Hall effect. The size of the boundary region is of the order of the electronhole recombination length that is inversely proportional to the magnetic field. In narrow samples and at strong enough magnetic fields, the boundary region dominates over the bulk leading to linear magnetoresistance. Our results are relevant for semimetals and narrow-band semiconductors including most of the topological insulators.

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Density of states in a two-dimensional chiral metal with vacancies

Physical review letters, Jan 31, 2014

We study quantum interference effects in a two-dimensional chiral metal (bipartite lattice) with ... more We study quantum interference effects in a two-dimensional chiral metal (bipartite lattice) with vacancies. We demonstrate that randomly distributed vacancies constitute a peculiar type of chiral disorder leading to strong modifications of critical properties at zero energy as compared to those of conventional chiral metals. In particular, the average density of states diverges as ρ∝E(-1)|lnE|(-3/2) and the correlation length L(c)∝√[|lnE|] in the limit E→0. When the average density of vacancies is different in the two sublattices, a finite concentration of zero modes emerges and a gap in the quasiclassical density of states opens around zero energy. Interference effects smear this gap, resulting in exponentially small tails at low energies.

Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface

The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions is a... more The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions is analyzed. We discuss possible experimental measurements of the half-integer Hall conductance gxy of topological insulator surface states and explain how to reconcile Laughlin's flux insertion argument with half-integer gxy. Using a vortex state representation of Landau Level wavefunctions, we calculate current density beyond linear response, which is in particular relevant to the topological image monopole effect. As a major result, the field theory describing the localization physics of the quantum Hall effect of a single species of Dirac fermions is derived. In this connection, the issue of (absent) parity anomaly is revisited. The renormalization group (RG) flow and the resulting phase diagram are extensively discussed. Starting values of the RG flow are given by the semiclassical conductivity tensor which is obtained from the Boltzmann transport theory of the anomalous Hall effect.

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Magnetoresistance induced by rare strong scatterers in a high-mobility two-dimensional electron gas

We observe a strong negative magnetoresistance at non-quantizing magnetic fields in a high mobili... more We observe a strong negative magnetoresistance at non-quantizing magnetic fields in a high mobility two-dimensional electron gas (2DEG) realized in a GaAs/Al0.25 Ga0.75 As quantum well. The negative magnetoresistance consists of a peak around zero magnetic field and a huge magnetoresistance at larger fields. The peak is attributed to the interplay of smooth disorder and rare strong scatterers. The density of the strong scatterers nS is determined from the curvature of the peak.

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Analysis of negative magnetoresistance: Statistics of closed paths. I. Theory

Statistics of closed paths in two-dimensional (2D) systems, which just determines the interferenc... more Statistics of closed paths in two-dimensional (2D) systems, which just determines the interference quantum correction to conductivity and anomalous magnetoconductance, has been studied by computer simulation of a particle motion over the plane with randomly distributed scatterers. Both ballistic and diffusion regimes have been considered. The results of simulation have been analyzed in the framework of diffusion approximation. They are used for calculation of the magnetic field dependence of magnetoconductance in the model 2D system. It is shown that the anomalous magnetoconductance can be in principle described by the well known expression, obtained in the diffusion approximation, but with the prefactor less than unity and phase breaking length which differs from true value.

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From Quantum Disorder to Quantum Chaos

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble... more We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic σ-model approach. We analyze conditions of applicability of the σ-model, emphasizing the role played by the single-particle mean free path and the Lyapunov exponent due to the random potential. In particular, we present a resolution of the puzzle of repetitions of periodic orbits counted differently by the σ-model and by the trace formula.

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Loschmidt echo and Lyapunov exponent in a quantum disordered system

Physical Review E, 2003

We investigate the sensitivity of a disordered system with diffractive scatterers to a weak exter... more We investigate the sensitivity of a disordered system with diffractive scatterers to a weak external perturbation. Specifically, we calculate the fidelity M (t) (also called the Loschmidt echo) characterizing a return probability after a propagation for a time t followed by a backward propagation governed by a slightly perturbed Hamiltonian. For short-range scatterers we perform a diagrammatic calculation showing that the fidelity decays first exponentially according to the golden rule, and then follows a power law governed by the diffusive dynamics. For long-range disorder (when the diffractive scattering is of small-angle character) an intermediate regime emerges where the diagrammatics is not applicable. Using the path integral technique, we derive a kinetic equation and show that M (t) decays exponentially with a rate governed by the classical Lyapunov exponent.

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Joint Scientific Session of the Physical Sciences Division of the Russian Academy of Sciences and the Joint Physical Society of the Russian Federation "Strongly correlated electrons in two-dimensional systems" (26 October 2005)

Physics-uspekhi, 2006

A joint scientific session of the Physical Science Division of the Russian Academy of Sciences an... more A joint scientific session of the Physical Science Division of the Russian Academy of Sciences and the Joint Physical Society of the Russian Federation was held on 26 October 2006 at the conference room of the Lebedev Physics Institute, RAS. The following reports were presented at the session.(1) Pudalov V M (Lebedev Physics Institute, RAS) "Metal ± insulator transitions and

Dephasing in presence of a magnetic field

International Journal of Nanoscience, Vol 6, Nos 3 and 4, 2007

ABSTRACT Effect of the magnetic field on the rate of phase breaking is studied. It is shown that ... more ABSTRACT Effect of the magnetic field on the rate of phase breaking is studied. It is shown that the magnetic field resulting in the decrease of phase relaxation rate makes the negative magnetoresistance due to suppression of the electron interference to be smoother in shape and lower in magnitude than that found with constant -value. Nevertheless our analysis shows that experimental magnetoconductance curves can be well fitted by the Hikami–Larkin–Nagaoka expression.1 The fitting procedure gives the value of τ/τϕ, where τ is the quasi-momentum relaxation time, which is close to the value of τ/τϕ(B = 0) with an accuracy of 25% or better when the temperature varies within the range from 0.4 to 10 K. The value of the prefactor α found from this procedure lies within the interval 0.9–1.2.

Relaxation processes in a disordered Luttinger liquid

by Igor Gornyi and Dmitry Bagrets

Semiconductors, 2008

The Luttinger liquid model, which describes interacting electrons in a single-channel quantum wir... more The Luttinger liquid model, which describes interacting electrons in a single-channel quantum wire, is completely integrable in the absence of disorder and as such does not exhibit any relaxation to equilibrium. We consider relaxation processes induced by inelastic electron-electron interactions in a disordered Luttinger liquid, focusing on the equilibration rate and its essential differences from the electron-electron scattering rate as well as the rate of phase relaxation. In the first part of the paper, we review the basic concepts in the disordered Luttinger liquid at equilibrium. These include the elastic renormalization, dephasing, and interference-induced localization. In the second part, we formulate a conceptually important framework for systematically studying the nonequilibrium properties of the strongly correlated (non-Fermi) Luttinger liquid. We derive a coupled set of kinetic equations for the fermionic and bosonic distribution functions that describe the evolution of the nonequilibrium Luttinger liquid. Remarkably, the energy equilibration rate in the conducting disordered quantum wire (at sufficiently high temperature, when the localization effects are suppressed by dephasing) is shown to be of the order of the rate of elastic scattering off disorder, independent of the interaction constant and temperature.

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Metallic proximity effect in ballistic graphene with resonant scatterers

Semiconductor Science and Technology, 2010

We study the effect of resonant scatterers on the local density of states in a rectangular graphe... more We study the effect of resonant scatterers on the local density of states in a rectangular graphene setup with metallic leads. We find that the density of states in a vicinity of the Dirac point acquires a strong position dependence due to both metallic proximity effect and impurity scattering. This effect may prevent uniform gating of weakly-doped samples. We also demonstrate that even a single-atom impurity may essentially alter electronic states at lowdoping on distances of the order of the sample size from the impurity.

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