  The combination of magneto-transport and topological properties has brought
great attention to rare-earth mono-pnictides semimetals. For some of them, like
LaSb, it is unclear whether they show non-trivial topology or not based on
density functional theory calculations and angular resolved photoemission
spectroscopy measurements. Here, we use hybrid density functional theory to
demonstrate that LaSb is in fact a trivial topological semimetal, in agreement
with experiments, but on the verge of a transition to a topological phase. We
show that under compressive epitaxial strain, the La $d$ band crosses the Sb
$p$ band near the X$_3$ point in the Brillouin zone, stabilizing a
topologically non-trivial phase, opening unique opportunities to probe the
inter-relation between magneto-transport properties and the effects of band
topology by examining epitaxially strained and unstrained thin films of the
same material.
