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Aharonov-Bohm effect in the chiral Luttinger liquid

1997; American Physical Society; Volume: 56; Issue: 15 Linguagem: Inglês

10.1103/physrevb.56.9692

1095-3795

Michael R. Geller, Daniel Loss,

Physics of Superconductivity and Magnetism

Edge states of the quantum Hall fluid provide an almost unparalled opportunity to study mesoscopic effects in a highly correlated electron system. In this paper we develop a bosonization formalism for the finite-size edge state, as described by chiral Luttinger liquid theory, and use it to study the Aharonov-Bohm effect. 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 antidot edge state introduces a temperature scale ${T}_{0}\ensuremath{\equiv}\ensuremath{\Elzxh}v/\ensuremath{\pi}{k}_{B}L,$ where $v$ is the edge-state Fermi velocity. A renormalization group analysis reveals the existence of a two-parameter universal scaling function $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}(X,Y)$ that describes the Aharonov-Bohm conductance resonances. We also show that the strong renormalization of the tunneling amplitudes that couple the antidot to the incident edge states, together with the nature of the Aharonov-Bohm interference process in a chiral system, prevent the occurrence of perfect resonances as the magnetic field is varied, even at zero temperature. In an experimentally realizable strong-antidot-coupling regime, where the source-to-drain transmission is weak, and at bulk filling factor $g=1/q$ with $q$ an odd integer, we predict the low-temperature $(T\ensuremath{\ll}{T}_{0})$ Aharonov-Bohm amplitude to vanish with temperature as ${T}^{2q\ensuremath{-}2},$ in striking contrast to a Fermi liquid $(q=1).$ Near ${T}_{0},$ there is a pronounced maximum in the amplitude, also in contrast to a Fermi liquid. At high temperatures $(T\ensuremath{\gg}{T}_{0}),$ however, we predict a crossover to a ${T}^{2q\ensuremath{-}1}{e}^{\ensuremath{-}{qT/T}_{0}}$ temperature dependence, which is qualitatively similar to chiral Fermi liquid behavior. Careful measurements in the strong-antidot-coupling regime above ${T}_{0}$ should be able to distinguish between a Fermi liquid and our predicted nearly Fermi liquid scaling. In addition, we predict an interesting high-temperature nonlinear response 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, which are similar to the persistent current oscillations in a mesoscopic ring, except that they are not reduced in amplitude by weak disorder. In the fractional quantum Hall effects regime, these ``chiral persistent currents'' have a universal non-Fermi-liquid temperature dependence and may be another ideal system to observe a chiral Luttinger liquid.