Geometrical Resonances in the Tunneling Characteristics of Thick Superconducting Films

Abstract

In addition to the presence of an energy gap, the excitation spectrum of the BCS ground state differs from that of the corresponding normal state by virtue of a twofold energy-momentum degeneracy; two wave vectors satisfying k l (E) Δ (Fig. 1). One anticipates that additional elementary excitations (quasi-particles) can result from the coherent composition of these degenerate states. The propagation velocity of such composite excitations can be the same as that of single BCS excitations, both rapidly approaching v F with increasing E.In this limited sense, composite excitations (away from the gap) resemble normal-state excitations. Because of interference effects, however, composite excitations may transport very little momentum compared to ħ k F and therefore may have de Broglie wavelengths much longer than λ F =2π/k F ,In this sense there is a profound difference between such excitations and corresponding normal-state excitations, i.e., those which occur in the absence of a pairing interaction. In the superconductor, standing waves can be established across very thick films, effects having been observed with In films as thick as 30µ.These resonances influence the density-of-states function, thereby giving rise to structure in the Giaever tunneling current between a superconductive film S (Pb, In, or Sn) some microns thick and a much thinner superconductive Al film serving as analyzer. Systematic studies of geometrical tunneling resonances of this type yield experimental determinations of E(k) and v F , as well as information involving various boundary phenomena, presumably related to the proximity effect.