Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level

TL;DR

This study experimentally confirms that fractional quantum Hall effect (FQHE) states in the lowest Landau level exhibit particle-hole symmetry, using a specially designed heterojunction device to compare states at conjugate filling factors.

Contribution

It provides direct experimental evidence of particle-hole symmetry in FQHE states at half-filling in the lowest Landau level, using variable density measurements in a high-quality heterojunction device.

Findings

FQHE states at nu=1/3, 2/5, 3/7 have similar energy gaps as their conjugates at 2/3, 3/5, 4/7.

Magnetoconductivities show reflection symmetry between nu and 1 - nu states.

Results demonstrate manifest particle-hole symmetry in the lowest Landau level FQHE states.

Abstract

We report on detailed experimental studies of a high-quality heterojunction insulated-gate field-effect transistor (HIGFET) to probe the particle-hole symmetry (PHS) of the FQHE states about half-filling in the lowest Landau level. The HIGFET was specially designed to vary the density of a two-dimensional electronic system under constant magnetic fields. We find in our constant magnetic field, variable density measurements that the sequence of FQHE states at filling factors nu = 1/3, 2/5, 3/7 ... and its particle-hole conjugate states at filling factors 1 - nu = 2/3, 3/5, 4/7 ... have a very similar energy gap. Moreover, a reflection symmetry can be established in the magnetoconductivities between the nu and 1 - nu states about half-filling. Our results demonstrate that the FQHE states in the lowest Landau level are manifestly particle-hole symmetric.