k.p theory of freestanding narrow band gap semiconductor nanowires

Abstract

We report on a theoretical study of the electronic structures of freestanding nanowires made from narrow band gap semiconductors GaSb, InSb and InAs. The nanowires are described by the eight-band k.p Hamiltonians and the band structures are computed by means of the finite element method in a mixture basis consisting of linear triangular elements inside the nanowires and constrained Hermite triangular elements near the boundaries. The nanowires with two crystallographic orientations, namely the [001] and [111] orientations, and with different cross-sectional shapes are considered. For each orientation, the nanowires of the three narrow band gap semiconductors are found to show qualitatively similar characteristics in the band structures. However, the nanowires oriented along the two different crystallographic directions are found to show different characteristics in the valence bands. In particular, it is found that all the conduction bands show simple, good parabolic dispersions in both the [001]- and [111]-oriented nanowires, while the top valence bands show double-maximum structures in the [001]-oriented nanowires, but single-maximum structures in the [111]-oriented nanowires. The wave functions and spinor distributions of the band states in these nanowires are also calculated. It is found that significant mixtures of electron and hole states appear in the bands of these narrow band gap semiconductor nanowires. The wave functions exhibit very different distribution patterns in the nanowires oriented along the [001] direction and the nanowires oriented along the [111] direction. It is also shown that single-band effective mass theory could not reproduce all the band state wave functions presented in this work.Comment: 17 pages, 19 figure

Multiple topological transitions driven by the interplay of normal scattering and Andreev scattering

“…Here P = (p +τ z eA/c), m(r) is the spatially varying effective mass, U (r) is the confining potential,τ i (i = x, y, z) are the Pauli matrices acting in the electron -hole space, and the superconducting order parameter ∆(r) is nonzero only in the shell. For simplicity, we consider the hybrid nanowire of a circular cross-section [25] and use cylindrical coordinates r = (r, ϕ, z). Neglecting the order parameter inhomogeneity in the shell, we suggest a simplified model describing the magnetic flux dependence of the superconducting gap taking account of the entries of multiquanta vortices [26]:…”

Spin-orbit coupling effects in zinc-blende InSb and wurtzite InAs nanowires: Realistic calculations with multiband k·p method

“…It is worth mention that our band structure is in agreement with previously published results. 48,49,82,83 A.…”

Improved effective equation for the Rashba spin-orbit coupling in semiconductor nanowires

“…Instead, Rashba couplings that depend on the electrostatic environment and/or interfaces with other materials are less amenable to ab initio methods and tend to be described using effective models. In particular, multiband k • p theory has been successfully used to compute the energy bands of Rashba semiconductors including several conduction and hole bands [1,[32][33][34][35][36][37].…”