Chiral Luttinger Liquid Theory Research Articles

Tunneling spectroscopy of localized states near the quantum Hall edge

In the paper we dscuss experimental results of M. Grayson et al. on tunneling $I$-$V$ characteristics of the quantum Hall edge. We suggest a two step tunneling mechanism involving localized electron states near the edge, which might account for discrepancy between the experimental data and the predictions of the chiral Luttinger liquid theory of the quantum Hall edge.

Aharonov-Bohm effect in the chiral Luttinger liquid

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. A renormalization group analysis reveals the existence of a two-parameter universal scaling function G(X,Y) that describes the Aharonov-Bohm 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.

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 recent experiments. In our chiral Luttinger liquid theory, which is valid in an experimentally realizable ‘strong-antidot-coupling’ regime for bulk filling factorsg= 1/q(qodd), the finite size of the antidot introduces a new temperature scaleT0≡hv/ΠkBL, wherevis the Fermi velocity andLis the circumference of the antidot edge state. Chiral Luttinger liquid theory predicts the low-temperature (T<T0) Aharonov–Bohm amplitude to vanish with temperature asT2q–2, in striking contrast to Fermi liquid theory (q=1). NearT≈T0, there is a pronounced maximum in the amplitude, also in contrast to a Fermi liquid. At high temperatures (T>T0), however, we predict a new crossover to aT2q–1e–qT/T0temperature dependence, which is qualitatively similar to Fermi liquid behavior. We show how measurements in the strong-antidot-coupling regime, where transmission through the device is weak, should be able to distinguish between Fermi liquid and chiral Luttinger liquid behavior both at low and high temperatures and in the linear and nonlinear response regimes. Finally, we predict new mesoscopic edge-current oscillations, which are similar to persistent current oscillations in a mesoscopic ring, except that they are not reduced in amplitude by disorder. In the fractional 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.

Bosonization theory for tunneling spectra in smooth edges of quantum Hall systems

We calculate the spectral function of a smooth edge of a quantum Hall system in the lowest Landau level by means of a bosonization technique. We obtain a general relationship between the one electron spectral function and the dynamical structure factor. The resulting I-V characteristics exhibit, at low voltage and temperature, power law scaling, generally different from the one predicted by the chiral Luttinger liquid theory, and in good agreement with recent experimental results.

Mesoscopic Effects in the Fractional Quantum Hall Regime: Chiral Luttinger Liquid versus Fermi Liquid.

We study tunneling through an edge state formed around an antidot in the fractional quantum Hall regime using Wen's chiral Luttinger liquid theory extended to include mesoscopic effects. We identify a new regime where the Aharonov-Bohm oscillation amplitude exhibits a distinctive crossover from Luttinger liquid power-law behavior to Fermi-liquid-like behavior as the temperature is increased. Near the crossover temperature the amplitude has a pronounced maximum. This non-monotonic behavior and novel high-temperature nonlinear phenomena that we also predict provide new ways to distinguish experimentally between Luttinger and Fermi liquids.

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.