Effect of Anomalous Field Penetration on Capacitance

Abstract

The capacitance of an ideal capacitator, in which a thin metallic slab occupies a part of the space between the plates, is calculated with the use of the extended Thomas-Fermi method with particular emphasis on the nonlocal effect. It is assumed that the electrons in the interior of the slab suffer either specular or diffuse scattering at the slab boundaries. In the diffuse case, the two-sided Wiener-Hopf method developed by Baraff is applied. The field penetration into the slab yields an observable capacitance change. The quantum oscillations in the capacitance are also studied to show that, exactly as in the case of the Gantmakher-Kaner oscillations, the characteristics of the oscillations are determined by the geometrical structures of the Fermi surface, and that an external magnetic field gives rise to the amplitude modulation of the oscillations, which is observable under most favorable conditions.