Coherent quantum phenomena in a normal cylindrical conductor with a superconducting coating

Abstract

The thermodynamic properties of a mesoscopic-size, simply connected cylindrical normal metal in good metallic contact with superconducting banks are studied theoretically. It is commonly accepted that if the superconductor thickness is quite small (of the order of the coherence length), as is assumed to be the case here, a vector potential field, whose value can be varied, exists inside the normal layer. It is further assumed that the quasiparticles with energy E<Δ (2Δ is the superconducting gap) move ballistically through the normal metal and undergo Andreev scattering caused by the off-diagonal potential of the superconductor. An equation is obtained within the multidimensional quasiclassical method which permits us to determine the spectrum of the Andreev levels and to calculate the density of states of the system in question. It is shown that the Andreev levels shift as the trapped flux Φ changes inside the normal conductor. At a certain flux value they coincide with the Fermi level. A resonance spike in the density of states ν(E) appears in this case, since near E=0 there is strong degeneracy of the quasiparticle states in respect to the quantum number q characterizing their motion along the cylinder axis. As a result, a macroscopic number of q states contribute to the amplitude of the effect. As the flux is increased, the density of states v(E) behaves as a stepwise function of Φ. The distance between the steps is equal to the superconducting flux quantum hc/2e.