Exact density of states for lowest Landau level in white noise potential superfield representation for interacting systems

Quantum Diffusion in the Lowest Landau Level of Disordered Graphene

Electronic transport in the lowest Landau level of disordered graphene sheets placed in a homogeneous perpendicular magnetic field is a long-standing and cumbersome problem which defies a conclusive solution for several years. Because the modeled system lacks an intrinsic small parameter, the theoretical picture is infested with singularities and anomalies. We propose an analytical approach to the conductivity based on the analysis of the diffusive processes, and we calculate the density of states, the diffusion coefficient and the static conductivity. The obtained results are not only interesting from the purely theoretical point of view but have a practical significance as well, especially for the development of the novel high-precision calibration devices.

Dimensional Crossover of the Integer Quantum Hall Plateau Transition and Disordered Topological Pumping

We study the quantum Hall plateau transition on rectangular tori. As the aspect ratio of the torus is increased, the two-dimensional critical behavior, characterized by a subthermodynamic number of topological states in a vanishing energy window around a critical energy, changes drastically. In the thin-torus limit, the entire spectrum is Anderson localized; however, an extensive number of states retain a Chern number C≠0. We resolve this apparent paradox by mapping the thin-torus quantum Hall system onto a disordered Thouless pump, where the Chern number corresponds to the winding number of an electron's path in real space during a pump cycle. We then characterize quantitatively the crossover between the one- and two-dimensional regimes for finite torus thickness, where the average Thouless conductance also shows anomalous scaling.

Delocalization and quantum chaos in atom-field systems

Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest nonintegrable atom-field system, the Dicke model. A close correlation between the classical Lyapunov exponents and the quantum Participation Ratio of coherent states on the eigenenergy basis is exhibited for different points in the phase space. It is also shown that the Participation Ratio scales linearly with the number of atoms in chaotic regions and with its square root in the regular ones.

Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system

We investigate the relation between the diagonal (σ(xx)) and off-diagonal (σ(xy)) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy by a constant value [Formula: see text] with τ the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width [Formula: see text]. Analytic formulae are obtained for both σ(xx) and σ(xy) within the framework of this simple approximation at low temperatures. By examining the leading terms in σ(xx) and σ(xy), we find a proportional relation between dσ(xy)/dB and Bσ(xx)(2). The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic field regime where spin splitting is negligibly small.

Shape of disorder-broadened Landau subbands in graphene

In this Letter, we calculate the density of states of graphene under a highly uniform magnetic field and white-noise random potential. We discover that the disorder-broadened zero-energy Landau band has a Gaussian shape and its width is proportional to the random potential variance and the square root of magnetic field. We also use the Wegner-type calculation to justify our simulation results.