Resonant Tunneling between quantum Hall states at filling \nu = 1 and \nu = 1/3

TL;DR

This paper investigates resonant tunneling between a Fermi liquid and a fractional quantum Hall edge at filling factor 1/3, revealing a low-temperature perfect resonance with conductance e^2/2h linked to Luttinger liquid and Kondo physics.

Contribution

It provides a detailed analysis of the crossover from weak to strong coupling in resonant tunneling at fractional quantum Hall edges using renormalization group methods.

Findings

Achieves a perfect resonance with conductance e^2/2h at low temperatures.

Identifies the resonance as a realization of the g=1/2 Luttinger liquid and two-channel Kondo fixed point.

Discusses experimental regimes and implications for observed resonances in edge structures.

Abstract

We study the problem of resonant tunneling between a Fermi liquid and the edge of a $\nu=1/3$ fractional quantum Hall state. In the limit of weak coupling, the system is adequately described within the sequential tunneling approximation. At low temperatures, however, the system crosses over to a strong coupling phase, which we analyze using renormalization group techniques. We find that at low temperatures a "perfect" can be achieved by tuning two parameters. This resonance has a peak conductance $G = e^2/2h$ and is a realization of the weak backscattering limit of the $g=1/2$ Luttinger liquid, as well as the non Fermi liquid fixed point of the two channel Kondo problem. We discuss several regimes which may be experimentally accessible as well as the implications for resonances recently observed in cleaved edge overgrowth structures.