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

The low-frequency a-c response of a 2-D electron gas on liquid helium in a magnetic field is analyzed in terms of ρxx and ρxy, 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 ωτ << 1, where τ 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 ρxx and ρxy. The effects of these skin depths on measurements of the magnetoresistance and a-c 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