AHARONOV-BOHM EFFECT IN THE CHIRAL LUTTINGER LIQUID

Edge states of the quantum Hall fluid provide an almost unparalled opp ortunity to study mesoscopic effects in a highly correlated electron s ystem. In this paper we develop a bosonization formalism for the finit e-size edge state, as described by chiral Luttinger liquid theory, and use it to study the Aharonov-Bohm affect, The problem we address may be realized experimentally by measuring the tunneling current between two edge states through a third edge state formed around an antidot in the fractional quantum Hall effect regime. The finite size L of the a ntidot edge state introduces a temperature scale T-0=(h) over bar v/pi k(B)L, where v is the edge-state Fermi velocity. A renormalization gr oup analysis reveals the existence of a two-parameter universal scalin g function (G) over tilde(X,Y) that describes the Aharonov-Bohm conduc tance resonances. We also show that the strong renormalization of the tunneling amplitudes that couple the antidot to the incident edge stat es, together with the nature of the Aharonov-Bohm interference process in a chiral system, prevent the occurrence of perfect resonances as t he magnetic field is varied, even at zero temperature. In an experimen tally realizable strong-antidot-coupling regime, where the source-to-d rain transmission is weak, and at bulk filling factor g=1/q with q an odd integer, we predict the low-temperature (T much less than T-0) Aha ronov-Bohm amplitude to vanish with temperature as T2q-2, in striking contrast to a Fermi liquid (q=1). Near T-0, there is a pronounced maxi mum in the amplitude, also in contrast to a Fermi liquid. At high temp eratures (T much greater than T-0), however, we predict a crossover to a T(2q-1)e(-qT/T0) temperature dependence, which is qualitatively sim ilar to chiral Fermi liquid behavior. Careful measurements in the stro ng-antidot-coupling regime above T-0 should be able to distinguish bet ween a Fermi liquid and our predicted nearly Fermi liquid scaling. In addition, we predict an interesting high-temperature nonlinear respons e regime, where the voltage satisfies V>T>T-0, which may also be used to distinguish between chiral Fermi liquid and chiral Luttinger liquid behavior. Finally, we predict mesoscopic edge-current oscillations, w hich are similar to the persistent current oscillations in a mesoscopi c ring, except that they are not reduced in amplitude by weak disorder . In the fractional quantum Hall effects regime, these ''chiral persis tent currents'' have a universal non-Fermi-liquid temperature dependen ce and may be another ideal system to observe a chiral Luttinger liqui d.