Andreev bound states for cake shape superconducting-normal systems
Absztrakt:
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.