Andreev bound states for cake shape superconducting-normal systems
arXiv:cond-mat/0405404 · doi:10.1088/0953-8984/16/37/009
Abstract
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.
12 pages, 5 figures
References in corpus (7)
- Three "universal" mesoscopic Josephson effects
- Proximity-induced sub-gaps in Andreev billiards
- Ring--Shaped Andreev Billiards in Quantizing Magnetic Fields
- Excitation spectra for Andreev billiards of Box and Disk geometries
- Theory of anomalous magnetic interference pattern in mesoscopic SNS Josephson junctions
- A logarithmic contribution to the density of states of rectangular Andreev billiards
- Andreev bound states for superconducting-ferromagnetic box