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–x
Sn
x
Te 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.