Weiss oscillations and particle-hole symmetry at the half-filled Landau level

TL;DR

This paper investigates how weak particle-hole symmetry breaking affects magnetoresistance oscillations near half-filling in a 2D electron gas, using Dirac composite fermion theory, and finds that different theories predict similar oscillation behaviors.

Contribution

It demonstrates that Dirac and HLR composite fermion theories produce identical oscillation minima locations, suggesting they may describe the same physics at long wavelengths.

Findings

Oscillation minima are asymmetrically biased at fixed electron density.

Oscillations are symmetric when varying electron density at fixed magnetic field.

The Dirac and HLR theories predict identical minima locations within experimental resolution.

Abstract

Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal $\pm e^2/2h$ at half-filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half-filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field, the oscillations occur symmetrically as the electron density is varied about half-filling. We find an approximate "sum rule" obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long wavelength physics.