We have investigated Andreev-reflection processes occurring at a clean interface between a $p$-type semiconductor and a conventional superconductor. Our calculations are performed within a generalized Bogoliubov-de Gennes formalism where the details of the semiconductor band structure are described by a $6\times 6$ Kane model. It is found that Andreev reflection of light-hole and heavy-hole valence-band carriers is generally possible and that the two valence-band hole types can be converted into each other in the process. The normal-reflection and Andreev-reflection amplitudes depend strongly on the semiconductor’s carrier concentration and on the angle of injection. In the special case of perpendicular incidence, Andreev reflection of heavy holes does not occur. Moreover, we find conversionless Andreev reflection to be impossible above some critical angle, and another critical angle exists above which the conversion of a heavy hole into a light hole cannot occur.

• Received 11 July 2011

DOI:https://doi.org/10.1103/PhysRevB.84.104526