Spin-orbit coupling in semiconductor nanowires: Physical limits for Majorana states

Proximity induced superconductivity in semiconductor nanowires with spin-orbit coupling (SOC) provides a promising realization of Majorana fermions [1,2]. While SOC is typically included within only the first conduction band, such simplified models lack a more detailed understanding of Majorana fermions and their implementation. We perform systematic and comprehensive numerical investigations of SOC in zinc-blende and wurtzite semiconductor cylindrical nanowires. We employ the k.p method, with input parameters fitted to first-principles calculations, to determine realistic values of the Rashba and Dresselhaus spin-orbit fields in nanowires of varying diameters. Specifically, we use a state of the art 14 band k.p formalism together with the envelope function approach [1] to obtain the electronic band structure for various compounds, and analyze the effect of the quantum confinement on the effective masses and spin-orbit splitting of the subbands. We also make specific suggestions towards the optimal orientation and geometry, evaluating the prospects of the nanowires as platforms to observe Majorana states. [1] J. Alicea, Rep. Prog. Phys. 75, 076501 (2012). [2] A. Yu. Kitaev, Phys-Usp. 44, 131 (2001). [3] P. E. Faria Junior and G. M. Sipahi, J. Appl. Phys. 10, 103716 (2012).