Tunneling of quasiholes in the fractional quantum Hall regime

TL;DR

This paper investigates quasihole tunneling in fractional quantum Hall systems using numerical diagonalization, confirming quasihole stability and exploring tunneling mechanisms in finite systems with potential constrictions.

Contribution

It introduces a numerical approach to study quasihole tunneling and examines the effects of different potentials on quasihole dynamics in FQH systems.

Findings

Evidence for tunnel coupling between localized quasihole states.

Confirmation of fractional charge and stability of quasiholes.

Insights into quasihole injection and tunneling near constrictions.

Abstract

The elementary low energy excitations in the fractional quantum Hall (FQH) regime are known to be fractionally charged quasiparticles and quasiholes. This work focusses on quasiholes in a finite system of a few electrons treated by exact numerical diagonalization. Recent experimental [Chung et al., PRB 67, 201104 (2003)] and theoretical [Kane, Fisher, PRB 67, 045307 (2003)] work on quantum point contacts in the FQH regime showed strong evidence for single quasiparticle tunneling to be forbidden at low temperature. We want to gain insight into such constricted FQH systems by a numerical approach. Initially the basics of numerically treating a system in rectangular geometry and procedures to insert a quasihole excitation are presented. The excitations' stability and fractional charge is confirmed for different interactions. The question of quasihole tunneling is approached in two different systems: 1. A system posessing bound, localized states of a quasihole shows evidence for tunnel coupling between these states to exist. 2. Different potential forms to model a quantum point contact are investigated and the injection of a single quasihole near the constriction is surveyed in the system's time evolution.