The ac response of a 2-D electron gas on liquid helium in a magnetic field

The low frequency ac response of a 2-D electron gas on liquid helium in a magnetic field is analysed in terms of _xx and _xy , the components of the magnetoresistivity tensor. The electrons are screened by parallel electrodes and the system forms a 2-D transmission line. The 2-D wave equation is solved numerically for a bounded electron sheet in a rectangular geometry which is excited by one of the electrodes. For 1, where is a relaxation time, heavily damped voltage waves propagate along the transmission line. In a field these waves propagate along the edges of the electron sheet with characteristic decay lengths or 2-D skin depths, parallel and perpendicular to the edges, which depend on _xx and _xy . The effects of these skin depths on measurements of the magnetoresistance and ac Hall effect are demonstrated. The relationship to the dc Hall effect and to edge magnetoplasmons is shown. The effects of incomplete screening, density inhomogeneities and edge capacitance are also discussed.