Angular Momentum Distribution Function of the Laughlin Droplet

We have evaluated the angular-momentum distribution functions for finite numbers of electrons in Laughlin states. For very small numbers of electrons the angular-momentum state occupation numbers have been evaluated exactly while for larger numbers of electrons they have been obtained from Monte-Carlo estimates of the one-particle density matrix. An exact relationship, valid for any number of electrons, has been derived for the ratio of the occupation numbers of the two outermost orbitals of the Laughlin droplet and is used to test the accuracy of the MC calculations. We compare the occupation numbers near the outer edges of the droplets with predictions based on the chiral Luttinger liquid picture of Laughlin state edges and discuss the surprisingly large oscillations in occupation numbers which occur for angular momenta far from the edge.Comment: 11 pages of RevTeX, 2 figures available on request. IUCM93-00

Edge and Bulk of the Fractional Quantum Hall Liquids

An effective Chern-Simons theory for the Abelian quantum Hall states with edges is proposed to study the edge and bulk properties in a unified fashion. We impose a condition that the currents do not flow outside the sample. With this boundary condition, the action remains gauge invariant and the edge modes are naturally derived. We find that the integer coupling matrix $K$ should satisfy the condition $\sum_I(K^{-1})_{IJ} = \nu/m$ ($\nu$: filling of Landau levels, $m$: the number of gauge fields ) for the quantum Hall liquids. Then the Hall conductance is always quantized irrespective of the detailed dynamics or the randomness at the edge.Comment: 13 pages, REVTEX, one figure appended as a postscript fil

Resonant Tunneling Between Quantum Hall Edge States

Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the Laughlin parent states, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for $\nu = 1/3$ which confirm this picture and provide a parameter-free prediction for the line shape.Comment: 14 pages , revtex , IUCM93-00

The effect of inter-edge Coulomb interactions on the transport between quantum Hall edge states

In a recent experiment, Milliken {\em et al.} demonstrated possible evidence for a Luttinger liquid through measurements of the tunneling conductance between edge states in the $\nu=1/3$ quantum Hall plateau. However, at low temperatures, a discrepancy exists between the theoretical predictions based on Luttinger liquid theory and experiment. We consider the possibility that this is due to long-range Coulomb interactions which become dominant at low temperatures. Using renormalization group methods, we calculate the cross-over behaviour from Luttinger liquid to the Coulomb interaction dominated regime. The cross-over behaviour thus obtained seems to resolve one of the discrepancies, yielding good agreement with experiment.Comment: 4 pages, RevTex, 2 postscript figures, tex file and figures have been uuencode

Collective edge modes in fractional quantum Hall systems

Over the past few years one of us (Murthy) in collaboration with R. Shankar has developed an extended Hamiltonian formalism capable of describing the ground state and low energy excitations in the fractional quantum Hall regime. The Hamiltonian, expressed in terms of Composite Fermion operators, incorporates all the nonperturbative features of the fractional Hall regime, so that conventional many-body approximations such as Hartree-Fock and time-dependent Hartree-Fock are applicable. We apply this formalism to develop a microscopic theory of the collective edge modes in fractional quantum Hall regime. We present the results for edge mode dispersions at principal filling factors $\nu=1/3,1/5$ and $\nu=2/5$ for systems with unreconstructed edges. The primary advantage of the method is that one works in the thermodynamic limit right from the beginning, thus avoiding the finite-size effects which ultimately limit exact diagonalization studies.Comment: 12 pages, 9 figures, See cond-mat/0303359 for related result

Quantized Thermal Transport in the Fractional Quantum Hall Effect

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated inter-channel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance, $K_H$, is shown to provide a new and universal characterization of the FQHE state, and reveals non-trivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances {\it violates} the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be {\it negative}. We argue that thermal transport may provide a unique way to detect the presence of the elusive upstream propagating modes, predicted for fractions such as $\nu=2/3$ and $\nu=3/5$.Comment: 6 pages REVTeX, 2 postscript figures (uuencoded and compressed

Current and charge distributions of the fractional quantum Hall liquids with edges

An effective Chern-Simons theory for the quantum Hall states with edges is studied by treating the edge and bulk properties in a unified fashion. An exact steady-state solution is obtained for a half-plane geometry using the Wiener-Hopf method. For a Hall bar with finite width, it is proved that the charge and current distributions do not have a diverging singularity. It is shown that there exists only a single mode even for the hierarchical states, and the mode is not localized exponentially near the edges. Thus this result differs from the edge picture in which electrons are treated as strictly one dimensional chiral Luttinger liquids.Comment: 21 pages, REV TeX fil

Exact perturbative solution of the Kondo problem

We explicitly evaluate the infinite series of integrals that appears in the "Anderson-Yuval" reformulation of the anisotropic Kondo problem in terms of a one-dimensional Coulomb gas. We do this by developing a general approach relating the anisotropic Kondo problem of arbitrary spin with the boundary sine-Gordon model, which describes impurity tunneling in a Luttinger liquid and in the fractional quantum Hall effect. The Kondo solution then follows from the exact perturbative solution of the latter model in terms of Jack polynomials.Comment: 4 pages in revtex two-colum

Impurity scattering and transport of fractional Quantum Hall edge state

We study the effects of impurity scattering on the low energy edge state dynamic s for a broad class of quantum Hall fluids at filling factor $\nu =n/(np+1)$, for integer $n$ and even integer $p$. When $p$ is positive all $n$ of the edge modes are expected to move in the same direction, whereas for negative $p$ one mode moves in a direction opposite to the other $n-1$ modes. Using a chiral-Luttinger model to describe the edge channels, we show that for an ideal edge when $p$ is negative, a non-quantized and non-universal Hall conductance is predicted. The non-quantized conductance is associated with an absence of equilibration between the $n$ edge channels. To explain the robust experimental Hall quantization, it is thus necessary to incorporate impurity scattering into the model, to allow for edge equilibration. A perturbative analysis reveals that edge impurity scattering is relevant and will modify the low energy edge dynamics. We describe a non-perturbative solution for the random $n-$channel edge, which reveals the existence of a new disorder-dominated phase, characterized by a stable zero temperature renormalization group fixed point. The phase consists of a single propagating charge mode, which gives a quantized Hall conductance, and $n-1$ neutral modes. The neutral modes all propagate at the same speed, and manifest an exact SU(n) symmetry. At finite temperatures the SU(n) symmetry is broken and the neutral modes decay with a finite rate which varies as $T^2$ at low temperatures. Various experimental predictions and implications which follow from the exact solution are described in detail, focusing on tunneling experiments through point contacts.Comment: 19 pages (two column), 5 post script figures appended, 3.0 REVTE

Edge reconstruction in the fractional quantum Hall regime

The interplay of electron-electron interaction and confining potential can lead to the reconstruction of fractional quantum Hall edges. We have performed exact diagonalization studies on microscopic models of fractional quantum Hall liquids, in finite size systems with disk geometry, and found numerical evidence of edge reconstruction under rather general conditions. In the present work we have taken into account effects like layer thickness and Landau level mixing, which are found to be of quantitative importance in edge physics. Due to edge reconstruction, additional nonchiral edge modes arise for both incompressible and compressible states. These additional modes couple to electromagnetic fields and thus can be detected in microwave conductivity measurements. They are also expected to affect the exponent of electron Green's function, which has been measured in tunneling experiments. We have studied in this work the electric dipole spectral function that is directly related to the microwave conductivity measurement. Our results are consistent with the enhanced microwave conductivity observed in experiments performed on samples with an array of antidots at low temperatures, and its suppression at higher temperatures. We also discuss the effects of the edge reconstruction on the single electron spectral function at the edge.Comment: 19 pages, 12 figure