Tunneling in Fractional Quantum Hall line junctions

TL;DR

This paper analyzes tunneling currents between counterpropagating edge modes in fractional quantum Hall systems, revealing nonlinearities and interference effects influenced by interactions and barrier length.

Contribution

It provides a perturbative calculation of tunneling currents in extended regions for fractional quantum Hall edge states, including effects of strong interactions and finite barrier length.

Findings

Tunneling current exhibits nonlinear behavior due to Luttinger liquid properties.

Interference patterns arise from the finite length of the tunneling barrier.

Strong interactions lead to nonuniversal exponents even in integer quantum Hall edges.

Abstract

We study the tunneling current between two counterpropagating edge modes described by chiral Luttinger liquids when the tunneling takes place along an extended region. We compute this current perturbatively by using a tunnel Hamiltonian. Our results apply to the case of a pair of different two-dimensional electron gases in the fractional quantum Hall regime separated by a barrier, e. g. electron tunneling. We also discuss the case of strong interactions between the edges, leading to nonuniversal exponents even in the case of integer quantum Hall edges. In addition to the expected nonlinearities due to the Luttinger properties of the edges, there are additional interference patterns due to the finite length of the barrier.