Majorana fermions in charge carrier hole quantum wires*

In order to realize Majorana fermions in a hybrid semiconductor- superconductor structure, spin helical order is needed, which prevents “fermion doubling”. A natural proposal for Majarana fermion setting is to utilize charge carrier hole systems, which have strong spin orbit couplings that can result in a spin helix. In this work, we demonstrate that transformation of heavy holes into light holes and vice versa upon reflection from the heterostructure boundaries crucially affects Luttinger hole spectrum in low dimensions, and most importantly, spin-orbit interactions in the ground sub-band of a hole quantum wire. Spin orbit interactions are dominated by several terms linear in the hole momentum. We show that the criterion for realizing proximity-induced topologically non-trivial superconducting phase and zero Majorana modes in a hole wire is similar to that for electrons, but an extra constraint should be satisfied. Due to their stronger spin-orbit coupling, the hole systems can be promising settings to study Majorana fermions experimentally.