  Based on the first-principles electronic structure calculations and the
symmetry analysis, we predict that the topological superconductivity may occur
on the surface of the LnPd$_{2}$Sn (Ln=Sc, Y, Lu) class of Heusler alloys. The
calculated electronic band structure and topological invariant demonstrate that
the LnPd$_{2}$Sn family is topologically nontrivial. The further slab
calculations show that the nontrivial topological surface states of
LnPd$_{2}$Sn exist within the bulk band gap and meanwhile they cross the Fermi
level. Considering that the LnPd$_{2}$Sn class of compounds were all found
experimentally to be superconducting at low temperature, the surface
topological superconductivity is likely to be generated via the proximity
effect. Thus the LnPd$_{2}$Sn class of compounds shall be a promising platform
for exploring novel topological superconductivity and handling Majorana zero
modes.
