Interference, Coulomb blockade, and the identification of non-abelian quantum Hall states

We examine the relation between different electronic transport phenomena in a Fabry-Perot interferometer in the fractional quantum Hall regime. In particular, we study the way these phenomena reflect the statistics of quantum Hall quasi-particles. For two series of states we examine, one abelian and one non-abelian, we show that the information that may be obtained from measurements of the lowest order interference pattern in an open Fabry-Perot interferometer is identical to the one that may be obtained from the temperature dependence of Coulomb blockade peaks in a closed interferometer. We argue that despite the similarity between the experimental signatures of the two series of states, interference and Coulomb blockade measurements are likely to be able to distinguish between abelian and non-abelian states, due to the sensitivity of the abelian states to local perturbations, to which the non-abelian states are insensitive.Comment: 10 pages. Published versio

Signatures of neutral quantum Hall modes in transport through low-density constrictions

Constrictions in fractional quantum Hall (FQH) systems not only facilitate backscattering between counter-propagating edge modes, but also may reduce the constriction filling fraction $\nu_c$ with respect to the bulk filling fraction $\nu_b$. If both $\nu_b$ and $\nu_c$ correspond to incompressible FQH states, at least part of the constriction region is surrounded by composite edges, whose low energy dynamics is characterized by a charge mode and one or several neutral modes. In the incoherent regime, decay of neutral modes describes the equilibration of composite FQH edges, while in the limit of coherent transport, the presence of neutral modes gives rise to universal conductance fluctuations. In addition, neutral modes renormalize the strength of scattering across the constriction, and thus can determine the relative strength of forward and backwards scattering.Comment: corrected description of the results of Ref. [10], Ref. [17] adde

The Physical Significance of Singularities in the Chern--Simons Fermi Liquid Description of a Partially Filled Landau Level

We analyze the linear response of a half filled Landau level to long wavelength and low frequency driving forces, using Fermi liquid theory for composite fermions. This response is determined by the composite fermions quasi--particle effective mass, $m^*$, and quasi--particle Landau interaction function $f(\theta-\theta')$. Analyzing infra--red divergences of perturbation theory, we get an exact expression for $m^*$, and conjecture the form of the $f(\theta-\theta')$. We then conclude that in the limit of infinite cyclotron frequency, and small ${\bf q},\omega$, the composite fermion excitation spectrum is continuous for $0<\omega<\gamma \frac{e^2}{\epsilon h}q$, with $\gamma$ an unknown number. For fractional quantum Hall states near a half filled Landau level, we derive an exact expression for the energy gap.Comment: 4 pages, RevTeX. This paper, being short and non-technical, could serve as a useful starting point for reading our manuscript cond-mat/9502032. The present paper does, however, include results not published in the forme

Are Microwave Induced Zero Resistance States Necessarily Static?

We study the effect of inhomogeneities in Hall conductivity on the nature of the Zero Resistance States seen in the microwave irradiated two-dimensional electron systems in weak perpendicular magnetic fields, and we show that time-dependent domain patterns may emerge in some situations. For an annular Corbino geometry, with an equilibrium charge density that varies linearly with radius, we find a time-periodic non-equilibrium solution, which might be detected by a charge sensor, such as an SET. For a model on a torus, in addition to static domain patterns seen at high and low values of the equilibrium charge inhomogeneity, we find that, in the intermediate regime, a variety of nonstationary states can also exist. We catalog the possibilities we have seen in our simulations. Within a particular phenomenological model, we show that linearizing the nonlinear charge continuity equation about a particularly simple domain wall configuration and analyzing the eigenmodes allows us to estimate the periods of the solutions to the full nonlinear equation.Comment: Submitted to PR

Screening of electrostatic potential in a composite fermion system

Screening of the electric field of a test charge by monolayer and double-layer composite fermion systems is considered. It is shown that the electric field of the test charge is partly screened at distances much large then the magnetic length. The value of screening as a function of the distance depends considerably on the filling factor. The effect of variation of the value of screening in the double-layer system upon a transition to a state described by the Halperin wave function is determined.Comment: 5 pages, 2 eps figures include

Exact Groundstates of Rotating Bose Gases close to a Feshbach Resonance

We study the groundstates of rotating Bose gases when interactions are affected by a nearby Feshbach resonance. We show that exact groundstates at high angular momentum can be found analytically for a general and realistic model for the resonant interactions. We identify parameter regimes where the exact groundstates are exotic fractional quantum Hall states, the excitations of which obey non-abelian exchange statistics.Comment: 4 page

Transport equations for a two-dimensional electron gas with spin-orbit interaction

The transport equations for a two-dimensional electron gas with spin-orbit interaction are presented. The distribution function is a 2x2-matrix in the spin space. Particle and energy conservation laws determine the expressions for the electric current and the energy flow. The derived transport equations are applied to the spin-splitting of a wave packed and to the calculation of the structure factor and the dynamic conductivity.Comment: 6 pages, 1 figure, revised versio