Coulomb effects on the quantum cyclotron resonance from a two-dimensional electron liquid with extremely narrow Landau levels

We report results of experimental and theoretical studies of cyclotron resonance (CR) absorption from a strongly interacting nondegenerate two-dimensional electron liquid with extremely narrow Landau levels realized on the free surface of liquid helium. We found that the main many-electron effect on the quantum CR originates from the ultrafast fluctuational motion of electron orbit centers, causing inelastic scattering in the moving frames. This effect is described by means of the memory function formalism, employing a many-electron approximation for the electron dynamic structure factor (DSF). Remarkably, the Coulombic effect leads to a narrowing of Landau levels and at the same time produces a strong broadening of the electron DSF and the relaxation kernel of the dynamic conductivity. This explains the observed transformation of the CR line shape and the successive narrowing and broadening of the CR linewidth with the increase of the electron density. It is shown that the Coulomb narrowing and broadening of the CR data respond differently to a change of the resonant frequency in accordance with the concept proposed.