Spin-orbit coupling in InSb semiconductor nanowires: physical limits for majorana states

The search for Majorana fermions is a hot subject nowadays [1]. One of the possibilities for their realization is the use of semiconductor nanowires and p-type superconductors coupled together. Following this path, the first step is the determination of realistic band structures of these wires including spin-orbit effects. To consider the spin-orbit effects, its common to use models that take into account only the first conduction band. Although these reduced models have been successfully used to determine some physical properties, a more realistic description of the spin-orbit coupling between the bands is required to further investigate possible ways to realize the Majorana fermions. In this study we use a state of the art 14 band k.p formalism together with the envelope function approach [2] to determine the band structure of InAs semiconductor nanowires and analyze how the quantum confinement change the coupling between the bands. As a result we have extracted the effective masses and the spin-orbit splitting for a large range of nanowire radial sizes and for several conduction bands that can be used in effective models. [1] J. Alicea, Rep. Prog. Phys. 75, 076501 (2012). [2] P. E. Faria Junior and G. M. Sipahi, J. Appl. Phys. 10, 10, 103716 (2012).