Gauge field fluctuations and Weiss oscillations about the half-filled Landau level*

Numerical [Phys. Rev. Lett. 84, 4685 (2000)], [Science 352, 6282 (2016)] and experimental [Phys. Rev. Lett. 113, 196801 (2014)] observations indicate that a particle-hole (PH) symmetry is realized by two-dimensional electrons that half-fill a Landau level. Prior work [Phys. Rev. B 95,23 (2017)] studied the implications of weakly broken PH symmetry on Weiss oscillations, a type of magnetoresistance oscillation, about half-filling using the Dirac composite fermion theory proposed by Son [Phys. Rev. X 5, 031027 (2015)]. Here, we extend this prior work by including the effects of fluctuations of the emergent gauge field that couples to the Dirac composite fermion. We compare our results to experiment and other composite fermions theories such as [Phys. Rev. B 47, 7312 (1993)] and [Phys. Rev. B 92,16 (2015)].