Charge carrier holes and Majorana fermions

摘要

Understanding Luttinger holes in low dimensions is crucial for numerous spin-dependent phenomena and nanotechnology. In particular, hole quantum wires that are proximity coupled to a superconductor is a promising system for the observation of Majorana fermions. Earlier treatments of confined Luttinger holes ignored a mutual transformation of heavy and light holes at the heteroboundaries. We derive the effective hole Hamiltonian in the ground state. The mutual transformation of holes is crucial for Zeeman and spin-orbit coupling, and results in several spin-orbit terms linear in momentum in hole quantum wires. We discuss the criterion for realizing Majorana modes in charge carrier hole systems. GaAs or InSb hole wires shall exhibit stronger topological superconducting pairing, and provide additional opportunities for its control compared to InSb electron systems.