arXiv subjects

I. V. Gornyi

Publications and source records attributed to I. V. Gornyi.

At least 73 records · Page 4Linked to original sources

arXiv2014

Conductivity of a generic helical liquid

A quantum spin Hall insulator is a two-dimensional state of matter consisting of an insulating bulk and one-dimensional helical edge states. While these edge states are topologically protected against elastic backscattering in the presence of disorder, interaction-induced inelastic terms may yield a finite conductivity. By using a kinetic equation approach, we find the backscattering rate $τ^{-1}$ and the semiclassical conductivity in the regimes of high ($ω\gg τ^{-1}$) and low ($ω\ll τ^{-1}$) frequency. By comparing the two limits, we find that the parametric dependence of conductivity is described by the Drude formula for the case of a disordered edge. On the other hand, in the clean case where the resistance originates from umklapp interactions, the conductivity takes a non-Drude form with a parametric suppression of scattering in the dc limit as compared to the ac case. This behavior is due to the peculiarity of umklapp scattering processes involving necessarily the state at the "Dirac point". In order to take into account Luttinger liquid effects, we complement the kinetic equation analysis by treating interactions exactly in bosonization and calculating conductivity using the Kubo formula. In this way, we obtain the frequency and temperature dependence of conductivity over a wide range of parameters. We find the temperature and frequency dependence of the transport scattering time in a disordered system as $τ\sim [\max{(ω,T)}]^{-2K-2}$, for $K>2/3$ and $τ\sim [\max{(ω,T)}]^{-8K+2}$ for $K <2/3$.

cond-mat.mes-hall↗

arXiv2014

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

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 conventional chiral metals. In particular, the average density of states diverges as $ρ\propto E^{-1} |\ln E|^{-3/2}$ and the correlation length $L_c \propto \sqrt{|\ln E|}$ in the limit $E \to 0$. 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.

cond-mat.mes-hall↗

arXiv2014

Tunneling into the localized phase near Anderson transitions with Coulomb interaction

We study the tunneling density of states (TDOS) of a disordered electronic system with Coulomb interaction on the insulating side of the Anderson localization transition. The average TDOS shows a critical behavior at high energies, with a crossover to a soft Coulomb gap $Δ$ at low energies. We demonstrate that the single-particle excitations experience a localization transition (which belongs to the noninteracting universality class) at an energy $E=\pm E_c$. The mobility edge $E_c$ scales with the distance $μ_c-μ$ from the interacting critical point according to $E_c\propto (μ_c-μ)^{νz}$, where $ν$ and $z$ are the localization-length and the dynamical critical exponents. Local TDOS shows strong fluctuations and long-range correlations which reflect the multifractality associated with interacting and noninteracting fixed points as well the localization of low-energy excitations.

cond-mat.mes-hall↗

arXiv2013

Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point

We explore the longitudinal conductivity of graphene at the Dirac point in a strong magnetic field with two types of short-range scatterers: adatoms that mix the valleys and "scalar" impurities that do not mix them. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample as a function of impurity coordinates; an averaging over impurity positions is then performed numerically. The conductivity $σ$ is equal to the ballistic value $4e^2/πh$ for each disorder realization provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point with $σ\simeq 4 \times 0.4 e^2/h$ at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is obtained also at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes: remarkably, all key manifestations of Anderson localization and criticality in two dimensions are observed numerically in a single setup.

cond-mat.mes-hall↗

arXiv2013

Giant magneto-drag in graphene at charge neutrality

We report experimental data and theoretical analysis of Coulomb drag between two closely positioned graphene monolayers in weak magnetic field. Close enough to the neutrality point, coexistence of electrons and holes in each layer leads to a dramatic increase of the drag resistivity. Away from charge neutrality, we observe non-zero Hall drag. The observed phenomena are explained by decoupling of electric and quasiparticle currents which are orthogonal at charge neutrality. The sign of magneto-drag depends on the energy relaxation rate and geometry of the sample.

cond-mat.mes-hall↗

arXiv2013

Interaction and disorder effects in 3D topological insulator thin films

A theory of combined interference and interaction effects on the diffusive transport properties of 3D topological insulator surface states is developed. We focus on a slab geometry (characteristic for most experiments) and show that interactions between the top and bottom surfaces are important at not too high temperatures. We treat the general case of different surfaces (different carrier densities, uncorrelated disorder, arbitrary dielectric environment, etc.). In order to access the low-energy behavior of the system we renormalize the interacting diffusive sigma model in the one loop approximation. It is shown that intersurface interaction is relevant in the renormalization group (RG) sense and the case of decoupled surfaces is therefore unstable. An analysis of the emerging RG flow yields a rather rich behavior. We discuss realistic experimental scenarios and predict a characteristic non-monotonic temperature dependence of the conductivity. In the infrared (low-temperature) limit, the systems flows into a metallic fixed point. At this point, even initially different surfaces have the same transport properties. Investigating topological effects, we present a local expression of the $\mathbb Z_2$ theta term in the sigma model by first deriving the Wess-Zumino-Witten theory for class DIII by means of non-abelian bosonization and then breaking the symmetry down to AII. This allows us to study a response of the system to an external electromagnetic field. Further, we discuss the difference between the system of Dirac fermions on the top and bottom surfaces of a topological insulator slab and its non-topological counterpart in a double-well structure with strong spin-orbit interaction.

cond-mat.mes-hall↗

arXiv2013

Multifractality at Anderson transitions with Coulomb interaction

We explore mesoscopic fluctuations and correlations of the local density of states (LDOS) near localization transition in a disordered interacting electronic system. It is shown that the LDOS multifractality survives in the presence of Coulomb interaction. We calculate the spectrum of multifractal dimensions in $2+ε$ spatial dimensions and show that it differs from that in the absence of interaction. The multifractal character of fluctuations and correlations of the LDOS can be studied experimentally by scanning tunneling microscopy of two-dimensional and three-dimensional disordered structures.

cond-mat.mes-hall↗

arXiv2013

Strong magnetoresistance of disordered graphene

We study theoretically magnetoresistance (MR) of graphene with different types of disorder. For short-range disorder, the key parameter determining magnetotransport properties---a product of the cyclotron frequency and scattering time---depends in graphene not only on magnetic field $H$ but also on the electron energy $\varepsilon$. As a result, a strong, square-root in $H$, MR arises already within the Drude-Boltzmann approach. The MR is particularly pronounced near the Dirac point. Furthermore, for the same reason, "quantum" (separated Landau levels) and "classical" (overlapping Landau levels) regimes may coexist in the same sample at fixed $H.$ We calculate the conductivity tensor within the self-consistent Born approximation for the case of relatively high temperature, when Shubnikov-de Haas oscillations are suppressed by thermal averaging. We predict a square-root MR both at very low and at very high $H:$ $[\varrho_{xx}(H)-\varrho_{xx}(0)]/\varrho_{xx}(0)\approx C \sqrt{H},$ where $C$ is a temperature-dependent factor, different in the low- and strong-field limits and containing both "quantum" and "classical" contributions. We also find a nonmonotonic dependence of the Hall coefficient both on magnetic field and on the electron concentration. In the case of screened charged impurities, we predict a strong temperature-independent MR near the Dirac point. Further, we discuss the competition between disorder- and collision-dominated mechanisms of the MR. In particular, we find that the square-root MR is always established for graphene with charged impurities in a generic gated setup at low temperature.

cond-mat.dis-nn↗

arXiv2012

Coulomb drag between ballistic quantum wires

We develop a kinetic equation description of Coulomb drag between ballistic one-dimensional electron systems, which enables us to demonstrate that equilibration processes between right- and left-moving electrons are crucially important for establishing dc drag. In one-dimensional geometry, this type of equilibration requires either backscattering near the Fermi level or scattering with small momentum transfer near the bottom of the electron spectrum. Importantly, pairwise forward scattering in the vicinity of the Fermi surface alone is not sufficient to produce a nonzero dc drag resistivity $ρ_{\rm D}$, in contrast to a number of works that have studied Coulomb drag due to this mechanism of scattering before. We show that slow equilibration between two subsystems of electrons of opposite chirality, "bottlenecked" by inelastic collisions involving cold electrons near the bottom of the conduction band, leads to a strong suppression of Coulomb drag, which results in an activation dependence of $ρ_{\rm D}$ on temperature---instead of the conventional power law. We demonstrate the emergence of a drag regime in which $ρ_{\rm D}$ does not depend on the strength of interwire interactions, while depending strongly on the strength of interactions inside the wires.

cond-mat.str-el↗

arXiv2012

Conductivity of suspended graphene at the Dirac point

We study transport properties of clean suspended graphene at the Dirac point. In the absence of the electron-electron interaction, the main contribution to resistivity comes from interaction with flexural (out-of-plane deformation) phonons. We find that the phonon-limited conductivity scales with the temperature as $T^{-η}, $ where $η$ is the critical exponent (equal to $\approx 0.7$ according to numerical studies) describing renormalization of the flexural phonon correlation functions due to anharmonic coupling with the in-plane phonons. The electron-electron interaction induces an additional scattering mechanism and also affects the electron-phonon scattering by screening the deformation potential. We demonstrate that the combined effect of both interactions results in a conductivity that can be expressed as a dimensionless function of two temperature-dependent dimensionless constants, $G[T]$ and $G_e[T]$ which characterize the strength of electron-phonon and electron-electron interaction, respectively. We also discuss the behavior of conductivity away from the Dirac point as well as the role of the impurity potential and compare our predictions with available experimental data.

cond-mat.mes-hall↗

arXiv2012

Symmetries and weak (anti)localization of Dirac fermions in HgTe quantum wells

We perform a symmetry analysis of a 2D electron system in HgTe/HgCdTe quantum wells in the situation when the chemical potential is outside of the gap, so that the bulk of the quantum well is conducting. In order to investigate quantum transport properties of the system, we explore symmetries of the low-energy Hamiltonian which is expressed in terms of two flavors of Dirac fermions, and physically important symmetry-breaking mechanisms. This allows us to predict emerging patterns of symmetry breaking that control the weak localization and antilocalization showing up in transverse-field magnetoresistance.

cond-mat.mes-hall↗

arXiv2012

Coulomb drag in graphene near the Dirac point

We study Coulomb drag in double-layer graphene near the Dirac point. A particular emphasis is put on the case of clean graphene, with transport properties dominated by the electron-electron interaction. Using the quantum kinetic equation framework, we show that the drag becomes $T$-independent in the clean limit, $Tτ\to \infty$, where $T$ is temperature and $1/τ$ impurity scattering rate. For stronger disorder (or lower temperature), $Tτ\ll 1/α^2$, where $α$ is the interaction strength, the kinetic equation agrees with the leading-order ($α^2$) perturbative result. At still lower temperatures, $Tτ\ll 1$ (diffusive regime) this contribution gets suppressed, while the next-order ($α^3$) contribution becomes important; it yields a peak centered at the Dirac point with a magnitude that grows with lowering $Tτ$.

cond-mat.mes-hall↗

arXiv2012

Coulomb drag in graphene: perturbation theory

We study the effect of Coulomb drag between two closely positioned graphene monolayers. In the limit of weak electron-electron interaction and small inter-layer spacing ($μ_{1(2)}, T\ll v/d$) the drag is described by a universal function of the chemical potentials of the layers $μ_{1(2)}$ measured in the units of temperature $T$. When both layers are tuned close to the Dirac point, then the drag coefficient is proportional to the product of the chemical potentials $ρ_D\proptoμ_1μ_2$. In the opposite limit of low temperature the drag is inversely proportional to both chemical potentials $ρ_D\propto T^2/(μ_1μ_2)$. In the mixed case where the chemical potentials of the two layers belong to the opposite limits $μ_1\ll T\llμ_2$ we find $ρ_D\propto μ_1/μ_2$. For stronger interaction and larger values of $d$ the drag coefficient acquires logarithmic corrections and can no longer be described by a power law. Further logarithmic corrections are due to the energy dependence of the impurity scattering time in graphene (for $μ_{1(2)}\gg T$ these are small and may be neglected). In the case of strongly doped (or gated) graphene $μ_{1(2)}\gg v/d\gg T$ the drag coefficient acquires additional dependence on the inter-layer spacing and we recover the usual Fermi-liquid result if the screening length is smaller than $d$.

cond-mat.mes-hall↗

arXiv2011

Enhancement of superconductivity by Anderson localization

Influence of disorder on the temperature of superconducting transition (T_c) is studied within the sigma-model renormalization group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and assumed to be short-range. Two-dimensional systems in the weak localization and antilocalization regime, as well as systems near mobility edge are considered. It is shown that in all these regimes the Anderson localization leads to strong enhancement of T_c related to the multifractal character of wave functions.

cond-mat.mes-hall↗

arXiv2011

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

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 Al$_x$Ga$_{1-x}$As/GaAs/Al$_x$Ga$_{1-x}$As heterostructures.

cond-mat.mes-hall↗

arXiv2010

Tunneling into a Luttinger liquid revisited

We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond the lowest order of perturbation in the tunneling amplitude. We find that the conventional fixed point has a finite basin of attraction only in the point contact model, but a finite size of the contact makes it generically unstable to the tunneling-induced break up of the liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the tunneling conductance may show a nonmonotonic behavior with temperature or bias voltage.

cond-mat.str-el↗

arXiv2010

Coulomb interaction in graphene: Relaxation rates and transport

We analyze the inelastic electron-electron scattering in undoped graphene within the Keldysh diagrammatic approach. We demonstrate that finite temperature strongly affects the screening properties of graphene, which, in turn, influences the inelastic scattering rates as compared to the zero-temperature case. Focussing on the clean regime, we calculate the quantum scattering rate which is relevant for dephasing of interference processes. We identify an hierarchy of regimes arising due to the interplay of a plasmon enhancement of the scattering and finite-temperature screening of the interaction. We further address the energy relaxation and transport scattering rates in graphene. We find a non-monotonic energy dependence of the inelastic relaxation rates in clean graphene which is attributed to the resonant excitation of plasmons. Finally, we discuss the temperature dependence of the conductivity at the Dirac point in the presence of both interaction and disorder. Our results complement the kinetic-equation and hydrodynamic approaches for the collision-limited conductivity of clean graphene and can be generalized to the treatment of physics of inelastic processes in strongly non-equilibrium setups.

cond-mat.str-el↗

arXiv2010

Color-dependent conductance of graphene with adatoms

We study ballistic transport properties of graphene with a low concentration of vacancies or adatoms. The conductance of graphene doped to the Dirac point is found to depend on the relative distribution of impurities among different sites of the honeycomb lattice labeled in general by six colors. The conductivity is shown to be sensitive to the crystal orientation if adatom sites have a preferred color. Our theory is confirmed by numerical simulations using recursive Green's functions with no adjustable parameters.

cond-mat.mes-hall↗