Quantum Transport in Two-Channel Fractional Quantum Hall Edges

TL;DR

This paper investigates how backward scattering affects tunneling conductance in fractional quantum Hall edges, revealing different behaviors depending on edge channel directions and tunneling quasiparticles versus electrons.

Contribution

It provides a universal scaling dimension for tunneling conductance in same-direction edges and analyzes the crossover between quasiparticle and electron tunneling pictures.

Findings

Universal scaling dimension for same-direction edges

Different conductance behaviors for quasiparticle and electron tunneling

Phase diagram with distinct temperature dependencies for opposite-direction edges

Abstract

We study the effect of backward scatterings in the tunneling at a point contact between the edges of a second level hierarchical fractional quantum Hall states. A universal scaling dimension of the tunneling conductance is obtained only when both of the edge channels propagate in the same direction. It is shown that the quasiparticle tunneling picture and the electron tunneling picture give different scaling behaviors of the conductances, which indicates the existence of a crossover between the two pictures. When the direction of two edge-channels are opposite, e.g. in the case of MacDonald's edge construction for the $\nu=2/3$ state, the phase diagram is divided into two domains giving different temperature dependence of the conductance.