Theory of Shubnikov--De Haas Oscillations Around the $ν=1/2$ Filling Factor of the Landau Level: Effect of Gauge Field Fluctuations

Abstract

We present a theory of magnetooscillations around the $ν=1/2$ Landau level filling factor based on a model with a fluctuating Chern--Simons field. The quasiclassical treatment of the problem is appropriate and leads to an unconventional $\exp\left[-(π/ω_cτ^*_{1/2})^4\right]$ behavior of the amplitude of oscillations. This result is in good qualitative agreement with available experimental data.