Weiss oscillations in Galilean-invariant Dirac composite fermion theory for even-denominator filling fractions of the lowest Landau level

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 Galilean invariance. To restore Galilean 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 Galilean invariance and those observed in experiment. Further, in contrast to Hossain et al., [Phys. Rev. B 100, 041112(R) (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 that the discrepancy with experiment may be an indirect signature of the effect of gauge field fluctuations in composite fermion theory.