Haldane Sashes in Quantum Hall Spectra

We show that the low-temperature sash features in the lowest Landau-level (LLL) tunneling density-of-states (TDOS) recently discovered by Dial and Ashoori are intimately related to the discrete Haldane-pseudopotential interaction energy scales that govern fractional quantum Hall physics. Our analysis is based on expressions for the tunneling density-of-states which become exact at filling factors close to $\nu=0$ and $\nu=1$, where the sash structure is most prominent. We comment on other aspects of LLL correlation physics that can be revealed by accurate temperature-dependent tunneling data.Comment: Added referenc

Asymptotically exact trial wave functions for yrast states of rotating Bose gases

We revisit the composite fermion (CF) construction of the lowest angular momentum yrast states of rotating Bose gases with weak short range interaction. For angular momenta at and below the single vortex, $L \leq N$, the overlaps between these trial wave functions and the corresponding exact solutions {\it increase} with increasing system size and appear to approach unity in the thermodynamic limit. In the special case $L=N$, this remarkable behaviour was previously observed numerically. Here we present methods to address this point analytically, and find strongly suggestive evidence in favour of similar behaviour for all $L \leq N$. While not constituting a fully conclusive proof of the converging overlaps, our results do demonstrate a striking similarity between the analytic structure of the exact ground state wave functions at $L \leq N$, and that of their CF counterparts. Results are given for two different projection methods commonly used in the CF approach

Edge State Tunneling in a Split Hall Bar Model

In this paper we introduce and study the correlation functions of a chiral one-dimensional electron model intended to qualitatively represent narrow Hall bars separated into left and right sections by a penetrable barrier. The model has two parameters representing respectively interactions between top and bottom edges of the Hall bar and interactions between the edges on opposite sides of the barrier. We show that the scaling dimensions of tunneling processes depend on the relative strengths of the interactions, with repulsive interactions across the Hall bar tending to make breaks in the barrier irrelevant. The model can be solved analytically and is characterized by a difference between the dynamics of even and odd Fourier components. We address its experimental relevance by comparing its predictions with those of a more geometrically realistic model that must be solved numerically.Comment: 13 pages, including 4 figures,final version as publishe

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

Interaction-Enhanced Coherence Between Two-Dimensional Dirac Layers

We estimate the strength of interaction-enhanced coherence between two graphene or topological insulator surface-state layers by solving imaginary-axis gap equations in the random phase approximation. Using a self-consistent treatment of dynamic screening of Coulomb interactions in the gapped phase, we show that the excitonic gap can reach values on the order of the Fermi energy at strong interactions. The gap is discontinuous as a function of interlayer separation and effective fine structure constant, revealing a first order phase transition between effectively incoherent and interlayer coherent phases. To achieve the regime of strong coherence the interlayer separation must be smaller than the Fermi wavelength, and the extrinsic screening of the medium embedding the Dirac layers must be negligible. In the case of a graphene double-layer we comment on the supportive role of the remote $\pi$-bands neglected in the two-band Dirac model.Comment: 14 pages, 9 figure

Space shuttle navigation analysis. Volume 1: GPS aided navigation

Analytical studies related to space shuttle navigation are presented. Studies related to the addition of NAVSTAR Global Positioning System user equipment to the shuttle avionics suite are presented. The GPS studies center about navigation accuracy covariance analyses for both developmental and operational phases of GPS, as well as for various orbiter mission phases

Numerical Tests of the Chiral Luttinger Liquid Theory for Fractional Hall Edges

We report on microscopic numerical studies which support the chiral Luttinger liquid theory of the fractional Hall edge proposed by Wen. Our calculations are based in part on newly proposed and accurate many-body trial wavefunctions for the low-energy edge excitations of fractional incompressible states.Comment: 12 pages + 1 figure, Revte

Chiral boundary conditions for Quantum Hall systems

A quantum mesoscopic billiard can be viewed as a bounded electronic system due to some external confining potential. Since, in general, we do not have access to the exact expression of this potential, it is usually replaced by a set of boundary conditions. We discuss, in addition to the standard Dirichlet choice, the other possibilities of boundary conditions which might correspond to more complicated physical situations including the effects of many body interactions or of a strong magnetic field. The latter case is examined more in details using a new kind of chiral boundary conditions for which it is shown that in the Quantum Hall regime, bulk and edge characteristics can be described in a unified way.Comment: 16 pages, LaTeX, 2 figures, to be published in the Proceedings of the Minerva workshop on Mesoscopics, Fractals and Neural Networks, Phil. Mag. (1997

Correlations in Two-Dimensional Vortex Liquids

We report on a high temperature perturbation expansion study of the superfluid-density spatial correlation function of a Ginzburg-Landau-model superconducting film in a magnetic field. We have derived a closed form which expresses the contribution to the correlation function from each graph of the perturbation theory in terms of the number of Euler paths around appropriate subgraphs. We have enumerated all graphs appearing out to 10-th order in the expansion and have evaluated their contributions to the correlation function. Low temperature correlation functions, obtained using Pad\'{e} approximants, are in good agreement with Monte Carlo simulation results and show that the vortex-liquid becomes strongly correlated at temperatures well above the vortex solidification temperature.Comment: 18 pages (RevTeX 3.0) and 4 figures, available upon request, IUCM93-01