arXiv subjects

P. M. Ostrovsky

Publications and source records attributed to P. M. Ostrovsky.

At least 55 records · Page 3Linked to original sources

arXiv2012

Hybridization of wave functions in one-dimensional localization

A quantum particle can be localized in a disordered potential, the effect known as Anderson localization. In such a system, correlations of wave functions at very close energies may be described, due to Mott, in terms of a hybridization of localized states. We revisit this hybridization description and show that it may be used to obtain quantitatively exact expressions for some asymptotic features of correlation functions, if the tails of the wave functions and the hybridization matrix elements are assumed to have log-normal distributions typical for localization effects. Specifically, we consider three types of one-dimensional systems: a strictly one-dimensional wire and two quasi-one-dimensional wires with unitary and orthogonal symmetries. In each of these models, we consider two types of correlation functions: the correlations of the density of states at close energies and the dynamic response function at low frequencies. For each of those correlation functions, within our method, we calculate three asymptotic features: the behavior at the logarithmically large "Mott length scale", the low-frequency limit at length scale between the localization length and the Mott length scale, and the leading correction in frequency to this limit. In the several cases, where exact results are available, our method reproduces them within the precision of the orders in frequency considered.

cond-mat.mes-hall↗

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↗

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

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

Effective spin-flip scattering in diffusive superconducting proximity systems with magnetic disorder

We revisit the problem of diffusive proximity systems involving superconductors and normal metals (or ferromagnets) with magnetic disorder. On the length scales much larger than its correlation length, the effect of sufficiently weak magnetic disorder may be incorporated as a local spin-flip term in the Usadel equations. We derive this spin-flip term in the general case of a three-dimensional disordered Zeeman-type field with an arbitrary correlation length. Three different regimes may be distinguished: pointlike impurities (the correlation length is shorter than the Fermi wavelength), medium-range disorder (the correlation length between the Fermi wavelength and the mean free path), and long-range disorder (the correlation length longer than the mean free path). We discuss the relations between these three regimes by using the three overlapping approaches: the Usadel equations, the non-linear sigma model, and the diagrammatic expansion. The expressions for the spin-flip rate agree with the existing results obtained in less general situations.

cond-mat.supr-con↗

arXiv2009

Correlations of the local density of states in quasi-one-dimensional wires

We report a calculation of the correlation function of the local density of states in a disordered quasi-one-dimensional wire in the unitary symmetry class at a small energy difference. Using an expression from the supersymmetric sigma-model, we obtain the full dependence of the two-point correlation function on the distance between the points. In the limit of zero energy difference, our calculation reproduces the statistics of a single localized wave function. At logarithmically large distances of the order of the Mott scale, we obtain a reentrant behavior similar to that in strictly one-dimensional chains.

cond-mat.dis-nn↗

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↗

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

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↗

arXiv2006

Electron transport in disordered graphene

We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder. We show that the transport properties of the system depend strongly on the character of disorder. Away from half filling, the concentration dependence of conductivity is linear in the case of strong scatterers, in line with recent experimental observations, and logarithmic for weak scatterers. At half filling the conductivity is of the order of e^2/h if the randomness preserves one of the chiral symmetries of the clean Hamiltonian; otherwise, the conductivity is strongly affected by localization effects.

cond-mat.mes-hall↗

arXiv2006

Proximity effect in the presence of Coulomb interaction and magnetic field

We consider a small metallic grain coupled to a superconductor by a tunnel contact. We study the interplay between proximity and charging effects in the presence of the external magnetic field. Employing the adiabatic approximation we develop a self-consistent theory valid for an arbitrary ratio of proximity and Coulomb strength. The magnetic field suppresses the proximity-induced minigap in an unusual way. We find the phase diagram of the grain in the charging energy - magnetic field plane. Two distinct states exist with different values and magnetic field dependences of the minigap. The first-order phase transition occurs between these two minigapped states. The transition to the gapless state may occur by the first- or second-order mechanism depending on the charging energy. We also calculate the tunneling density of states in the grain. The energy dependence of this quantity demonstrates two different gaps corresponding to the Coulomb and proximity effects. These gaps may be separated in sufficiently high magnetic field.

cond-mat.supr-con↗

arXiv2006

Local correlations of different eigenfunctions in a disordered wire

We calculate the correlator of the local density of states <ρ_{E}(r_1)ρ_{E+ω}(r_2)> in quasi-one-dimensional disordered wires in a magnetic field, assuming that |r_1-r_2| is much smaller than the localization length. This amounts to finding the zero mode of the transfer-matrix Hamiltonian for the supersymmetric sigma-model, which is done exactly by the mapping to the three-dimensional Coulomb problem. Both the regimes of level repulsion and level attraction are obtained, depending on |r_1-r_2|. We demonstrate that the correlations of different eigenfunctions in the quasi-one-dimensional and strictly one-dimensional cases are dissimilar.

cond-mat.mes-hall↗