Quantum magnetotransport in two-dimensional Coulomb liquids

In this article we review recent progress in understanding of many-electron effects on the quantum magnetotransport in two-dimensional (2D) Coulomb liquids in which the interaction potential energy per electron can be approximately a hundred times larger than the mean kinetic energy. The conventional Fermi-liquid approach based on the introduction of weakly interacting excitations being not applicable, it is remarkable that a quantitative theoretical description of the equilibrium and transport properties of the 2D Coulomb liquid appears to be possible. An account of basic properties of the strongly interacting 2D electron system under magnetic field realized on a free surface of liquid helium is given. Due to the high magnetic field applied perpendicular to the system, the electron liquid constituted of strongly interacting electrons can be described as a collection of statistically independent electrons, each of them having the discrete Landau spectrum in a local reference frame moving ultra-fast with regard to the center-of-mass frame of the entire electron liquid. We found it surprising that the narrowing of Landau levels induced by Coulomb forces in local frames is accompanied by a strong Coulomb broadening of the electron dynamical structure factor (DSF) in the laboratory reference frame. We discuss in detail the magnetotransport theories in two-dimensions, especially the force-balance equation method and the memory function formalism which allow to reduce the electron transport problem to the description of the equilibrium electron DSF. We show that the whole body of the DC magnetoconductivity and cyclotron resonance absorption data measured and reported within the last two decades (even previously conflicting with theory) can be very well described by means of a simple model for the electron DSF entering the imaginary part of the memory function or the effective collision frequency of the electrons.