Quasiparticles on a normal sphere in a superconducting continuum

Abstract In N/S point contacts with “high energy” quasiparticle injection allowing for phonon production, a non-equilibrium situation is produced which may be described as a normal bubble within the superconducting half-space. This non-equilibrium state leads to a number of interesting features in the current—voltage characteristics such as hysteretic jumps and oscillations in the excess current. The latter have been interpreted as geometrical resonances due to interferences of bound quasiparticles in the normal bubble. As a first approach to this complex situation we investigate the quasiparticle spectrum of a normal sphere. The density of the bound states possesses a finite gap at an energy E G Δ , and subgap peaks due to a cut-off in each subband of the bound states spectrum. Finally, we calculate the total energy as a function of the normal sphere radius R . It contains periodic contributions, caused by the periodic entering of new bound state subbands which split off the continuum E > Δ and enter the gap regime E Δ . These periodic contributions are tentatively discussed in context with the above-mentioned experimentally observed oscillations in the excess current.