Spin-orbit coupling effects and g-factors in zinc-blende InSb and wurtzite InAs nanowires using realistic multiband k · p method - Campos, Tiago de (2017)
Spin-dependent phenomena in semiconductor nanowires have recently gained a lot of attention, in special because these nanostructures can be a viable setup to study exotic states of matter like the Majorana fermions. One of the key ingredients to accommodate the Majorana zero modes is the spin-orbit coupling in the nanowires, which has been usually treated with two-band Hamiltonians. The spin-orbit coupling in semiconductors arise from two distinct sources being the bulk inversion asymmetry, when the unit cell does not present inversion symmetry, e.g. when the crystal unit cell is composed by two different atoms, and the structural inversion asymmetry, when the whole system does not have a mirror symmetry. To describe the system these effective models take as input, parameters that are dependent on the system configuration and measurement setups. Although these effective models have been successful in determine relevant physical properties, a more realistic description of the interacting energy bands is required, specially in quantum confined systems where the interplay between both sources of spin-orbit coupling can change the systems properties in non-trivial ways. For instance, in quantum wells there is an anisotropy of the g-factor due to the quantum confinement and structural inversion asymmetry. Furthermore, the in-plane g-factor also have an anisotropy which is due to the intrinsic spin-orbit coupling and it is not captured by these effective models. In this study, we use realistic multiband k · p Hamiltonians, including both spin-orbit coupling mechanisms, to determine the band structure of zincblende InSb and wurtzite InAs nanowires under a transverse electric field. We analyze the effects of the lateral quantum confinement for a hexagonal cross-section geometry and of the change in growth directions, extracting the relevant physical parameters for the first conduction subband. We found that the g-factors are heavily dependent on the quantum confinement and nanowire orientation, with in-plane/out-of-plane anisotropies up to 3%. We also found that for zinc-blende nanowires the extrinsic spin-orbit coupling is dominant over the intrinsic one whereas, for wurztize, the opposite behavior holds. In order to assess if the nanowires could host the aforementioned Majorana zero modes we investigate under which circumstances the topological phase transition occurs, using the Bogoliubov-de Gennes formalism to couple the nanowire with a superconductor, and we found that using realistic and experimental feasible parameters, indeed, the phase transition occurs. In conclusion, our systematic investigation of nanowires shows that the spin-orbit coupling energy can be fine tuned by the external electric field in experimentally achievable setups that ultimately could guide the search for the elusive Majorana modes. Moreover, our numerical approach is not restricted to a specific material or dimensionality and can be used to study others systems to provide useful insights into the electronic and spintronic fields.