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

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