Conduction and Excitations of Low-Dimensional Electron Liquid

The problems of the conduction of one-dimensional electron liquid and of the collective excitations in a two-dimensional electron liquid confined to a narrow channel are studied theoretically. The conduction is studied within the framework of the scattering theory of electron transport. A renormalization group (RG) technique is developed to calculate the renormalization of the potential scattering due to the electron-electron interactions and to find the transmission coefficient of an electron at any energy. This technique enables us to generalize the well-known formula for the conductance of a one-dimensional channel (Landauer formula) onto the case of interacting electrons. For the first time, simple formulas that describe the conductance at any temperature are derived. In real spin- 1over2 systems, electron -electron backscattering is found to cause the low-temperature conductance to deviate from the results of the usual Luttinger liquid theory. Non-monotonic temperature dependence of the conductance and singularity in the differential conductance in the presence of a magnetic field are predicted. For the problem of collective excitations, the hydrodynamic equations of motion for an electron liquid subject to a magnetic field are solved exactly for the strip geometry. The complete spectra of the acoustic excitations in such a system are found for a magnetic field of arbitrary strength. The lifetime and oscillator strength of the modes are calculated, based on which the optimal experimental observability conditions for the acoustic modes are established.