Abstract
Semiconductor Rashba nanowires are quasi-one dimensional systems that have large spin-orbit (SO) coupling arising from a broken inversion symmetry due to an external electric field. There exist parametrized multiband models that can describe accurately this effect. However, simplified single band models are highly desirable to study geometries of recent experimental interest, since they may allow to incorporate the effects of the low dimensionality and the nanowire electrostatic environment at a reduced computational cost. Commonly used conduction band approximations, valid for bulk materials, greatly underestimate the SO coupling in Zinc-blende crystal structures and overestimate it for Wurtzite ones when applied to finite cross-section wires, where confinement effects turn out to play an important role. We demonstrate here that an effective equation for the linear Rashba SO coupling of the semiconductor conduction band can reproduce the behavior of more sophisticated eight-band k$\cdot$p model calculations. This is achieved by adjusting a single effective parameter that depends on the nanowire crystal structure and its chemical composition. We further compare our results to the Rashba coupling extracted from magnetoconductance measurements in several experiments on InAs and InSb nanowires, finding excellent agreement. This approach may be relevant in systems where Rashba coupling is known to play a major role, such as in spintronic devices or Majorana nanowires.
Highlights
The spin-orbit (SO) interaction is a relativistic effect that couples the electron’s spin and momentum in the presence of an electric field
We propose to use an expression for the SO coupling with the same functional form of Eq (5), which is the dominant term in the expansion, but where the parameter P is substituted by an improved one, that we call Pfit, chosen so as to reproduce the Rashba SO coupling extracted from the 8B model of zinc-blende or wurtzite nanowires
Multiband k · p effective models are successfully used to indirectly extract the SO coupling of semiconductors from their band structure, but they can be computationally demanding in low-dimensional heterostructures of current interest, subject to arbitrary electrostatic environments
Summary
The spin-orbit (SO) interaction is a relativistic effect that couples the electron’s spin and momentum in the presence of an electric field. This equation is derived from the so-called eight-band (8B) k · p model, described in detail in Appendixes A and B This equation takes into account the dependence of αR with (i) the electric field generated by a spatially dependent electrostatic potential φ(r), (ii) the electron energy E , and (iii) the crystal structure and atomic composition through three effective parameters. One of these is known as the Kane parameter P [1], which represents the effective coupling between valence and conduction bands of the semiconductor. This paper is complemented with several comprehensive Appendixes on the 8B k · p Kane model for zinc-blende and wurtzite crystals (A), the derivation of the conduction band approximation (B), numerical methods (C and D), the comparison of the SO coupling between different semiconductor compounds (E), the independence of Pfit with the electrostatic environment (F) and the reliability of the conduction band approximation for the effective mass (G)
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