arXiv subjects

I. V. Gornyi

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

At least 91 records · Page 5Linked to original sources

arXiv2010

Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions

We analyze the critical behavior of the dephasing rate induced by short-range electron-electron interaction near an Anderson transition of metal-insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in $2+ε$ dimensions) with numerical simulations on the Chalker-Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.

cond-mat.mes-hall↗

arXiv2010

Anderson Transitions: Criticality, Symmetries, and Topologies

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. We focus on the character of criticality as well as on underlying symmetries and topologies that are crucial for understanding phase diagrams and the critical behavior.

cond-mat.dis-nn↗

arXiv2010

Diffusion and criticality in undoped graphene with resonant scatterers

A general theory is developed to describe graphene with arbitrary number of isolated impurities. The theory provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the minimal conductivity of graphene with resonant scatterers. In the case of smooth resonant impurities conductivity grows logarithmically with increasing impurity concentration, in agreement with renormalization group analysis for the symmetry class DIII. For vacancies (or strong on-site potential impurities) the conductivity saturates at a constant value that depends on the vacancy distribution among two sublattices as expected for the symmetry class BDI.

cond-mat.mes-hall↗

arXiv2010

Full counting statistics in disordered graphene at Dirac point: From ballistics to diffusion

The full counting statistics of the charge transport through an undoped graphene sheet in the presence of smooth disorder is studied. At the Dirac point both in clean and diffusive limits, transport properties of a graphene sample are described by the universal Dorokhov distribution of transmission probabilities. In the crossover regime, deviations from universality occur which can be studied analytically both on ballistic and diffusive sides. In the ballistic regime, we use a diagrammatic technique with matrix Green functions. For a diffusive system, the sigma model is applied. Our results are in good agreement with recent numerical simulations of electron transport in disordered graphene.

cond-mat.mes-hall↗

arXiv2010

Aharonov-Bohm conductance through a single-channel quantum ring: Persistent-current blockade and zero-mode dephasing

We study the effect of electron-electron interaction on transport through a tunnel-coupled single-channel ring. We find that the conductance as a function of magnetic flux shows a series of interaction-induced resonances that survive thermal averaging. The period of the series is given by the interaction strength $α$. The physics behind this behavior is the blocking of the tunneling current by the circular current. The main mechanism of dephasing is due to circular-current fluctuations. The dephasing rate is proportional to the tunneling rate and does not depend on $α$.

cond-mat.str-el↗

arXiv2010

Charge transport in graphene with resonant scatterers

The full counting statistics for the charge transport through an undoped graphene sheet in the presence of strong potential impurities is studied. Treating the scattering off the impurity in the s-wave approximation, we calculate the impurity correction to the cumulant generating function. This correction is universal provided the impurity strength is tuned to a resonant value. In particular, the conductance of the sample acquires a correction of 16e^2/(pi^2 h) per resonant impurity.

cond-mat.mes-hall↗

arXiv2009

Metallic proximity effect in ballistic graphene with resonant scatterers

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 low-doping on distances of the order of the sample size from the impurity.

cond-mat.mes-hall↗

arXiv2009

Interaction-induced criticality in Z_2 topological insulators

Critical phenomena and quantum phase transitions are paradigmatic concepts in modern condensed matter physics. A central example in the field of mesoscopic physics is the localization-delocalization (metal-insulator) quantum phase transition driven by disorder -- the Anderson transition. Although the notion of localization has appeared half a century ago, this field is still full of surprising new developments. The most recent arenas where novel peculiar localization phenomena have been studied are graphene and topological insulators, i.e., bulk insulators with delocalized (topologically protected) states on their surface. Besides exciting physical properties, the topological protection renders such systems promising candidates for a variety of prospective electronic and spintronic devices. It is thus of crucial importance to understand properties of boundary metallic modes in the realistic systems when both disorder and interaction are present. Here we find a novel critical state which emerges in the bulk of two-dimensional quantum spin Hall (QSH) systems and on the surface of three-dimensional topological insulators with strong spin-orbit interaction due to the interplay of nontrivial Z_2 topology and the Coulomb repulsion. At low temperatures, this state possesses a universal value of electrical conductivity. In particular, we predict that the direct QSH phase transition occurs via this novel state. Remarkably, the interaction-induced critical state emerges on the surface of a three-dimensional topological insulator without any adjustable parameters. This ``self-organized quantum criticality'' is a novel concept in the field of interacting disordered systems.

cond-mat.mes-hall↗

arXiv2009

Nonequilibrium kinetics of a disordered Luttinger liquid

We develop a kinetic theory for strongly correlated disordered one-dimensional electron systems out of equilibrium, within the Luttinger liquid model. In the absence of inhomogeneities, the model exhibits no relaxation to equilibrium. We derive kinetic equations for electron and plasmon distribution functions in the presence of impurities and calculate the equilibration rate $γ_E$. Remarkably, for not too low temperature and bias voltage, $γ_E$ is given by the elastic backscattering rate, independent of the strength of electron-electron interaction, temperature, and bias.

cond-mat.str-el↗

arXiv2008

Ballistic transport in disordered graphene

An analytic theory of electron transport in disordered graphene in a ballistic geometry is developed. We consider a sample of a large width W and analyze the evolution of the conductance, the shot noise, and the full statistics of the charge transfer with increasing length L, both at the Dirac point and at a finite gate voltage. The transfer matrix approach combined with the disorder perturbation theory and the renormalization group is used. We also discuss the crossover to the diffusive regime and construct a ``phase diagram'' of various transport regimes in graphene.

cond-mat.mes-hall↗

arXiv2008

Quantum interference and spin-charge separation in a disordered Luttinger liquid

We study the influence of spin on the quantum interference of interacting electrons in a single-channel disordered quantum wire within the framework of the Luttinger liquid (LL) model. The nature of the electron interference in a spinful LL is particularly nontrivial because the elementary bosonic excitations that carry charge and spin propagate with different velocities. We extend the functional bosonization approach to treat the fermionic and bosonic degrees of freedom in a disordered spinful LL on an equal footing. We analyze the effect of spin-charge separation at finite temperature both on the spectral properties of single-particle fermionic excitations and on the conductivity of a disordered quantum wire. We demonstrate that the notion of weak localization, related to the interference of multiple-scattered electron waves and their decoherence due to electron-electron scattering, remains applicable to the spin-charge separated system. The relevant dephasing length, governed by the interplay of electron-electron interaction and spin-charge separation, is found to be parametrically shorter than in a spinless LL. We calculate both the quantum (weak localization) and classical (memory effect) corrections to the conductivity of a disordered spinful LL. The classical correction is shown to dominate in the limit of high temperature.

cond-mat.str-el↗

arXiv2008

Relaxation processes in a disordered Luttinger liquid

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.

cond-mat.mes-hall↗

arXiv2008

Effect of gauge-field interaction on fermion transport in 2D: Hartree conductivity correction and dephasing

We consider the quantum corrections to the conductivity of fermions interacting via a Chern-Simons gauge field, and concentrate on the Hartree-type contributions. The first-order Hartree approximation is only valid in the limit of weak coupling λto the gauge field, and results in an antilocalizing conductivity correction, \sim λ^2 g \ln^2 T (g is the conductance). In the case of strong coupling, an infinite summation of higher-order terms is necessary, including both the virtual (renormalization) and real (dephasing) processes. At intermediate temperatures 1/g^2τ<<T<<1/gτ(τis the transport time), the T-dependence of the conductivity is determined by the Hartree correction. At low temperatures T<<1/g^2τ, the Hartree correction assumes a logarithmic form with a coefficient of order unity. As a result, the negative exchange contribution becomes dominant, yielding localization in the limit of zero T. We further discuss dephasing at strong coupling and show that the dephasing rates are of the order of T, owing to the interplay of inelastic scattering and renormalization. On the other hand, the dephasing length is anomalously short, L_ϕ<<L_T. For the case of composite fermions with long-range Coulomb interaction, the Hartree correction has the usual T-dependence, and for realistic g is overcompensated by the negative exchange contribution due to the gauge-boson and scalar parts of the interaction. In this case, the dephasing length L_ϕis of the order of L_T for not too low T and exceeds L_T for T<1/gτ.

cond-mat.mes-hall↗

arXiv2007

Theory of Anomalous Quantum Hall Effects in Graphene

Recent successes in manufacturing of atomically thin graphite samples (graphene) have stimulated intense experimental and theoretical activity. The key feature of graphene is the massless Dirac type of low-energy electron excitations. This gives rise to a number of unusual physical properties of this system distinguishing it from conventional two-dimensional metals. One of the most remarkable properties of graphene is the anomalous quantum Hall effect. It is extremely sensitive to the structure of the system; in particular, it clearly distinguishes single- and double-layer samples. In spite of the impressive experimental progress, the theory of quantum Hall effect in graphene has not been established. This theory is a subject of the present paper. We demonstrate that the Landau level structure by itself is not sufficient to determine the form of the quantum Hall effect. The Hall quantization is due to Anderson localization which, in graphene, is very peculiar and depends strongly on the character of disorder. It is only a special symmetry of disorder that may give rise to anomalous quantum Hall effects in graphene. We analyze the symmetries of disordered single- and double-layer graphene in magnetic field and identify the conditions for anomalous Hall quantization.

cond-mat.mes-hall↗

arXiv2007

Magnetotransport of electrons in quantum Hall systems

Recent theoretical results on magnetotransport of electrons in a 2D system in the range of moderately strong transverse magnetic fields are reviewed. The phenomena discussed include: quasiclassical memory effects in systems with various types of disorder, transport in lateral superlattices, interaction-induced quantum magnetoresistance, quantum magnetooscillations in dc and ac transport, and oscillatory microwave photoconductivity.

cond-mat.dis-nn↗

arXiv2007

Conductivity of disordered graphene at half filling

We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder at half filling. We show that the transport properties of the system depend strongly on the symmetry of disorder. We find that the localization is ineffective if the randomness preserves one of the chiral symmetries of the clean Hamiltonian or does not mix valleys. We obtain the exact value of minimal conductivity $4e^2/πh$ in the case of chiral disorder. For long-range disorder (decoupled valleys), we derive the effective field theory. In the case of smooth random potential, it is a symplectic-class sigma model including a topological term with $θ= π$. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of $e^2/h$. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and the conductivity acquires the value characteristic for the quantum Hall transition.

cond-mat.mes-hall↗

arXiv2007

Quantum criticality and minimal conductivity in graphene with long-range disorder

We consider the conductivity $σ_{xx}$ of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class $σ$-model including a topological term with $θ=π$. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of $e^2/h$. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and $σ_{xx}$ acquires the value characteristic for the quantum Hall transition.

cond-mat.mes-hall↗

arXiv2007

Electron transport in disordered Luttinger liquid

We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. Two alternative approaches to the problem are developed, both combining fermionic and bosonic treatment of the underlying physics. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit. Our approach provides a framework for a systematic study of mesoscopic effects in strongly correlated electron systems.

cond-mat.dis-nn↗