Plateau transitions in fractional quantum Hall liquids

TL;DR

This paper investigates the transitions between different conductance plateaux in fractional quantum Hall liquids, analyzing edge-state interactions, selection rules, and calculating shot-noise spectra and tunneling current scaling.

Contribution

It introduces a new selection rule for conductance sequences and provides explicit calculations of shot-noise spectra and tunneling current behavior.

Findings

Selection rule for conductance sequence starting at G=m/(mp±1)

Explicit calculation of shot-noise spectrum

Analysis of scaling behavior of tunneling current

Abstract

Effects of backward scattering between fractional quantum Hall (FQH) edge modes are studied. Based on the edge-state picture for hierarchical FQH liquids, we discuss the possibility of the transitions between different plateaux of the tunneling conductance $G$. We find a selection rule for the sequence which begins with a conductance $G=m/(mp\pm 1)$ ($m$: integer, $p$: even integer) in units of $e^2/h$. The shot-noise spectrum as well as the scaling behavior of the tunneling current is calculated explicitly.