Andreev bound states for cake shape superconducting-normal systems

Details Andreev bound states for cake shape superconducting-normal systems Andreev bound states for cake shape superconducting-normal systems

2004-05-18

arxiv.org/abs/cond-mat/0405404v1

Journal of Physics: Condensed Matter 16, 6737-6746 (2004)

Physics

Condensed Matter

Superconductivity

12 pages, 5 figures

Scientific paper

10.1088/0953-8984/16/37/009

The energy spectrum of cake shape normal - superconducting systems is calculated by solving the Bogoliubov-de Gennes equation. We take into account the mismatch in the effective masses and Fermi energies of the normal and superconducting regions as well as the potential barrier at the interface. In the case of a perfect interface and without mismatch, the energy levels are treated by semi-classics. Analytical expressions for the density of states and its integral, the step function, are derived and compared with that obtained from exact numerics. We find a very good agreement between the two calculations. It is shown that the spectrum possesses an energy gap and the density of states is singular at the edge of the gap. The effect of the mismatch and the potential barrier on the gap is also investigated.

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