  Superconductor proximitized one-dimensional semiconductor nanowires with
strong spin-orbit interaction (SOI) are at this time the most promising
candidates for the realization of topological quantum information processing.
In current experiments the SOI originates predominantly from extrinsic fields,
induced by finite size effects and applied gate voltages. The dependence of the
topological transition in these devices on microscopic details makes scaling to
a large number of devices difficult unless a material with dominant intrinsic
bulk SOI is used. Here we show that wires made of certain ordered alloys
InAs$_{1-x}$Sb$_x$ have spin-splittings up to 20 times larger than those
reached in pristine InSb wires. In particular, we show this for a stable
ordered CuPt-structure at $x = 0.5$, which has an inverted band ordering and
realizes a novel type of a topological semimetal with triple degeneracy points
in the bulk spectrum that produce topological surface Fermi arcs.
Experimentally achievable strains can drive this compound either into a
topological insulator phase, or restore the normal band ordering making the
CuPt-ordered InAs$_{0.5}$Sb$_{0.5}$ a semiconductor with a large intrinsic
linear in $k$ bulk spin splitting.
