Igor V. Lerner

Strongly correlated fermions and bosons in low-dimensional disordered systems

Preface. Part One: Zero-Dimensional Systems. The Kondo Screening Cloud I. Affleck. Quantum Interferometry with Electrons: Outstanding Challenges Y. Gefen. Photon Assisted Tunneling in Quantum Dots W.G. van der Wiel, et al. Part Two: One-Dimensional Systems. Bosonisation as the Hubbard-Stratonovich Transformation I.V. Yurkevich. Quasi One-dimensional Organic Conductors: Dimensional Crossover and Some Puzzles S. Biermann, et al. Proximity Induced and Intrinsic Superconductivity in Carbon Nanotubes M. Kociak, et al. Part Three: Two-Dimensional Systems. Quantum In-Plane Magnetoresistance in 2D Electron Systems J.S. Meyer, et al. Disordered Wigner crystals T. Giamarchi. Magneto-optics of Composite Fermions and Skyrmions I.V. Kukushkin. Metal-Insulator Transition in Dilute 2D Electron and Hole Gases A.K. Savchenko. Spectral Decomposition of Geodesic Flows on Constant Curvature Surfaces M. Muzykantskii, S. Roberts. Part Four: Systems of Any Dimensionality. Phase Coherence Phenomena in Disordered Superconductors A. Lamacraft, B.D. Simons. Keldysh and Doi-Peliti Techniques for out-of-Equilibrium Systems A. Kamenev. Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions I.V. Lerner. Exact Functionals, Effective Actions and (Dynamical) Mean-Field Theories: Some Remarks A. Georges. Index.

Universal spectral correlations at the mobility edge

We demonstrate the level statistics in the vicinity of the Anderson transition in dg2 dimensions to be universal and drastically different from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. The variance of the number of levels N in a given energy interval with 〈N〉\ensuremath{\gg}1 is proved to behave as 〈N

Anomalous dimensions of high gradient operators in the extended nonlinear σ model and distribution of mesoscopic fluctuations

{\mathrm{〉}}^{\ensuremath{\gamma}}

Applicability of scaling description to the distribution of mesoscopic fluctuations

where \ensuremath{\gamma}=1-(\ensuremath{\nu}d

Quantum transport thermometry for electrons in graphene

{)}^{\mathrm{\ensuremath{-}}1}

Jumps in current-voltage characteristics in disordered films.

and \ensuremath{\nu} is the correlation length exponent. The inequality \ensuremath{\gamma}1, shown to be required by an exact sum rule, results from nontrivial cancellations (due to the causality and scaling requirements) in calculating the two-level correlation function.

Spectral rigidity and eigenfunction correlations at the Anderson transition

Abstract Some problems of the theory of quantum disordered conductors required using the extended nonlinear σ model which includes high gradient vertices. Here we present a derivation of such a model starting from the usual model of free electrons in a random potential. We perform a renormalization group analysis of the extended σ model and show the anomalous dimensions of the charges attached to the high gradient vertices to be proportional to n2−n. As a result, these vertices turn out to be relevant, in particular, for the asymptotics of distributions of mesoscopic fluctuations of the conductance and density of states.

Random walks in media with constrained disorder

Abstract The distribution function for the mesoscopic conductance fluctuations is discussed from the viewpoint of applicability of the one-parameter scaling. It is shown that the distribution becomes nonuniversal and the scaling description fails in d =2 dimensions and in the critical region in d > 2 dimensions. It is argued that on approaching the region of strong localization ( d =2) or Anderson transition ( d > 2) a crossover should exist from a close-to-gaussian distribution with logarithmically normal tails to a completely logarithmically normal distribution.

Mesoscopic conductance fluctuations in graphene

We propose a method of measuring the electron temperature T_{e} in mesoscopic conductors and demonstrate experimentally its applicability to micron-size graphene devices in the linear-response regime (T_{e} approximately T, the bath temperature). The method can be especially useful in case of overheating, T_{e}>T. It is based on analysis of the correlation function of mesoscopic conductance fluctuations. Although the fluctuation amplitude strongly depends on the details of electron scattering in graphene, we show that T_{e} extracted from the correlation function is insensitive to these details.

NONPERTURBATIVE RESULTS FOR LEVEL CORRELATIONS FROM THE REPLICA NONLINEAR SIGMA MODEL

We argue that giant jumps of current at finite voltages observed in disordered films of InO, TiN, and YSi manifest a bistability caused by the overheating of electrons. One of the stable states is overheated and thus low resistive, while the other, high-resistive state is heated much less by the same voltage. The bistability occurs provided that cooling of electrons is inefficient and the temperature dependence of the equilibrium resistance R(T) is steep enough. We use experimental R(T) and assume phonon mechanism of the cooling taking into account its strong suppression by disorder. Our description of the details of the I-V characteristics does not involve adjustable parameters and turns out to be in quantitative agreement with the experiments. We propose experiments for more direct checks of this physical picture.