Theory of Shubnikov–de Haas oscillations around the ν=1/2 filling factor of the Landau level: Effect of gauge-field fluctuations

We present a theory of magneto-oscillations 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[-(π/${\mathrm{\omega }}_{\mathit{c}}$ ${\mathrm{\tau }}_{1/2}^{\mathrm{*}}$ ${)}^4$] behavior of the amplitude of oscillations. This result is in good qualitative agreement with available experimental data, although the experimental value of ${\mathrm{\tau }}_{1/2}^{\mathrm{*}}$ exceeds considerably our theoretical estimate.