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

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

W. Pan, W. Kang, M. P. Lilly, J. L. Reno, K. W. Baldwin, K. W. West, L. N. Pfeiffer, and D. C. Tsui

Phys. Rev. Lett. 124, 156801 – Published 15 April 2020

Abstract

We report on detailed experimental studies of a high-quality heterojunction insulated-gate field-effect transistor (HIGFET) to probe the particle-hole symmetry of the fractional quantum Hall effect (FQHE) states about half-filling in the lowest Landau level. The HIGFET is 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 $ν = 1 / 3, 2 / 5, 3 / 7 \dots$ and its particle-hole conjugate states at filling factors $1 − ν = 2 / 3, 3 / 5, 4 / 7 \dots$ have a very similar energy gap. Moreover, a reflection symmetry can be established in the magnetoconductivities between the $ν$ and $1 − ν$ states about half-filling. Our results demonstrate that the FQHE states in the lowest Landau level are manifestly particle-hole symmetric.

Received 19 March 2019
Revised 14 December 2019
Accepted 19 March 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.156801

Physics Subject Headings (PhySH)

Fractional quantum Hall effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

W. Pan^1,2,3, W. Kang⁴, M. P. Lilly³, J. L. Reno³, K. W. Baldwin⁵, K. W. West⁵, L. N. Pfeiffer⁵, and D. C. Tsui⁵

¹Materials Physics Department, Sandia National Laboratories, Livermore, California 94551, USA
²Quantum Phenomena Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
³Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
⁴Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
⁵Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA