LUTTINGER LIQUIDS AND COMPOSITE FERMIONS IN NANOSTRUCTURES - WHAT IS THE NATURE OF THE EDGE STATES IN THE FRACTIONAL QUANTUM HALL REGIME

We study the Aharonov-Bohm conductance oscillations of a constriction with an antidot in the fractional quantum Hall regime using a recently proposed composite-fermion Fermi liquid theory, and also using Wen's chiral Luttinger liquid theory extended to include mesoscopic effects. The predictions of the composite-fermion Fermi liquid theory are very similar to standard Fermi liquid theory and are consistent with recen t experiments. In our chiral Luttinger liquid theory, which is valid i n an experimentally realizable 'strong-antidot-coupling' regime for bu lk filling factors g = 1/q (q odd), the finite size of the antidot int roduces a new temperature scale T-0 = (h) over bar upsilon/pi k(B)L, w here upsilon is the Fermi velocity and L is the circumference of the a ntidot edge state. Chiral Luttinger liquid theory predicts the low-tem perature (T much less than T-0) Aharonov-Bohm amplitude to vanish with temperature as T-2q-2, in striking contrast to Fermi liquid theory (q = 1). Near T approximate to T-0, there is a pronounced maximum in the amplitude, also in contrast to a Fermi liquid. At high temperatures ( T much greater than T-0), however, we predict a new crossover to a T(2 q-1)e(-qT/T0) temperature dependence, which is qualitatively similar t o Fermi liquid behavior. We show how measurements in the strong-antido t-coupling regime, where transmission through the device is weak, shou ld be able to distinguish between Fermi liquid and chiral Luttinger li quid behavior both at low and high temperatures and in the linear and nonlinear response regimes. Finally, we predict new mesoscopic edge-cu rrent oscillations, which are similar to persistent current oscillatio ns in a mesoscopic ring, except that they are not reduced in amplitude by disorder. In the fractional regime, these 'chiral persistent curre nts' have a universal non-Fermi-liquid temperature dependence, and may be another ideal system to observe a chiral Luttinger liquid. (C) 199 7 Academic Press Limited