Exporting superconductivity across the gap: Proximity effect for semiconductor valence-band states due to contact with a simple-metal superconductor

The proximity effect refers to the phenomenon whereby superconducting properties are induced in a normal conductor that is in contact with an intrinsically superconducting material. In particular, the combination of nano-structured semiconductors with bulk superconductors is of interest because these systems can host unconventional electronic excitations such as Majorana fermions when the semiconductors charge carriers are subject to a large spin-orbit coupling. The latter requirement generally favors the use of hole-doped semiconductors. On the other hand, basic symmetry considerations imply that states from typical simple-metal superconductors will predominantly couple to a semiconductors conduction-band states and, therefore, in the first instance generate a proximity effect for band electrons rather than holes. In this article, we show how the superconducting correlations in the conduction band are transferred also to hole states in the valence band by virtue of inter-band coupling. A general theory of the superconducting proximity effect for bulk and low-dimensional hole systems is presented. The interplay of inter-band coupling and quantum confinement is found to result in unusual wave-vector dependencies of the induced superconducting gap parameters. One particularly appealing consequence is the density tunability of the proximity effect in hole quantum wells and nanowires, which creates new possibilities for manipulating the transition to nontrivial topological phases in these systems.

Suppression of Coulomb exchange energy in quasi-two-dimensional hole systems

We have calculated the exchange-energy contribution to the total energy of quasi-two-dimensional hole systems realized by a hard-wall quantum-well confinement of valence-band states in typical semiconductors. The magnitude of the exchange energy turns out to be suppressed from the value expected for analogous conduction-band systems whenever the mixing between heavy-hole and light-hole components is strong. Our results are obtained using a very general formalism for calculating the exchange energy of many-particle systems where single-particle states are spinors. We have applied this formalism to obtain analytical results for spin-3/2 hole systems in limiting cases.

Carrier-density-controlled anisotropic spin susceptibility of two-dimensional hole systems

We have studied quantum-well-confined holes based on the Luttinger-model description for the valence band of typical semiconductor materials. Even when only the lowest quasi-two-dimensional (quasi-2D) subband is populated, the static spin susceptibility turns out to be very different from the universal isotropic Lindhard-function lineshape obtained for 2D conduction-electron systems. The strongly anisotropic and peculiarly density-dependent spin-related response of 2D holes at long wavelengths should make it possible to switch between easy-axis and easy-plane magnetization in dilute magnetic quantum wells. An effective g factor for 2D hole systems is proposed.