Low-frequency conductivity of a nondegenerate two-dimensional electron liquid in strong magnetic fields

We study the conductivity of a nondegenerate two-dimensional electron liquid in a quantizing magnetic field for frequencies well below the cyclotron frequency. The conductivity is formed by electron transitions in which the energy of a photon goes to the interaction energy of the many-electron system, whereas the involved momentum is transferred to the quenched disorder. The conductivity peak is non-Lorentzian. Its shape depends on the relation between the correlation length $r_{\mathrm{c}}$ of the disorder potential and the typical amplitude ${\delta }_{\mathrm{f}}$ of vibrations of the electrons about their quasiequilibrium positions in the liquid. The width of the peak is determined by the reciprocal time it takes to move an electron over $r_{\mathrm{c}}$ (or the magnetic length l for $r_{\mathrm{c}}<l).\mathrm{}$ In turn, this time is determined by vibrational or diffusive motion, depending on the ratio $r_c/{\delta }_{\mathrm{f}}.$ We analyze the tail of the conductivity peak for a short-range disorder. It is formed by multiple collisions with the disorder potential. We also analyze scattering by rare negatively charged traps, and show that the conductivity spectrum in this case depends on both short- and long-time electron dynamics.