# Weiss Oscillations in the Galilean-Invariant Dirac Composite Fermion Theory for Even-Denominator Filling Fractions of the Lowest Landau Level

## TL;DR

This paper investigates the impact of the dipole correction term in the Galilean-invariant Dirac composite fermion theory on quantum oscillations at even-denominator filling fractions, finding it insufficient to match experimental results and suggesting gauge fluctuations may be relevant.

## Contribution

It analyzes the effect of the dipole term in the Dirac composite fermion theory and highlights the need to consider gauge field fluctuations for accurate predictions.

## Key findings

- Dipole term does not resolve the discrepancy with experimental oscillation minima.
- Quantum oscillations at half- and quarter-filled levels are qualitatively similar.
- Gauge field fluctuations may be crucial for accurate theoretical modeling.

## Abstract

Standard field theoretic formulations of composite fermion theories for the anomalous metals that form at or near even-denominator filling fractions of the lowest Landau level do not possess Galilei invariance. To restore Galilei symmetry, these theories must be supplemented by "correction" terms. We study the effect of the leading "correction" term, known as the dipole term, in the Dirac composite fermion theory (a theory that consists of a Dirac fermion coupled to an Abelian Chern-Simons gauge field) on quantum oscillations in the electrical resistivity due to a periodic scalar potential about even-denominator filling fractions. We find the dipole term to be insufficient to resolve the systematic discrepancy, discovered in [Kamburov et. al., Phys. Rev. Lett. 113, 196801 (2014)], between the locations of the oscillation minima predicted by Dirac composite fermion theory without Galilei invariance and those observed in experiment. Further, in contrast to [Hossain et al., Phys. Rev. B 100, 041112 (2019)], we find the quantum oscillations about the half-filled and quarter-filled lowest Landau level to have qualitatively similar behavior. This analysis uses a mean-field approximation, in which gauge field fluctuations are neglected. Based on this and previous analyses, we speculate the discrepancy with experiment may be an indirect signature of the effect of gauge field fluctuations in composite fermion theory.