Density Functional Theory Study of the Spin-Orbit Insulating Phase in SnTe Cubic Nanowires: Implications for Topological Electronics

We investigate the electronic, structural, and topological properties of the SnTe and PbTe cubic nanowires using ab initio calculations. Using standard and linear-scale density functional theory, we go from the ultrathin limit up to the nanowire thicknesses observed experimentally. Finite-size effects in the ultrathin limit produce an electric quadrupole and associated structural distortions; these distortions increase the band gap, but they get reduced with the size of the nanowires and become less and less relevant. Ultrathin SnTe cubic nanowires are trivial band gap insulators; we demonstrate that by increasing the thickness, there is an electronic transition to a spin-orbit insulating phase due to trivial surface states in the regime of thin nanowires. These trivial surface states with a spin-orbit gap of a few meV appear at the same k-point of the topological surface states. Going to the limit of thick nanowires, we should observe the transition to the topological crystalline insulator phase with the presence of two massive surface Dirac fermions hybridized with the persistent trivial surface states. Therefore, we have the copresence of massive Dirac surface states and trivial surface states close to the Fermi level in the same region of the k-space. According to our estimation, the cubic SnTe nanowires are trivial insulators below the critical thickness t(c1) = 10 nm, and they become spin-orbit insulators between t(c1) = 10 nm and t(c2) = 17 nm, while they transit to the topological phase above the critical thickness of t(c2) = 17 nm. These critical thickness values are in the range of typical experimental thicknesses, making the thickness a relevant parameter for the synthesis of topological cubic nanowires. Pb1-xSnxTe nanowires would have both these critical thicknesses t(c1) and t(c2) at larger values depending on the doping concentration. We discuss the limitations of density functional theory in the context of topological nanowires and the consequences of our results on topological electronics.