  Materials carrying topological surface states (TSS) provide a fascinating
platform for the hydrogen evolution reaction (HER). Based on systematic
first-principles calculations for $A_3 B$ ($A$ = Ni, Pd, Pt; $B$ = Si, Ge, Sn),
we propose that topological electric polarization characterized by the Zak
phase can be crucial to designing efficient catalysts for the HER. For $A_3 B$,
we show that the Zak phase takes a nontrivial value of $\pi$ in the whole (111)
projected Brillouin zone, which causes quantized electric polarization charge
at the surface. There, depending on the adsorption sites, the hydrogen (H) atom
hybridizes with the TSS rather than with the bulk states. When the
hybridization has an intermediate character between the covalent and ionic
bond, the H states are localized in the energy spectrum, and the change in the
Gibbs free energy ($\Delta G$) due to the H adsorption becomes small. Namely,
the interaction between the H states and the substrate becomes considerably
weak, which is a highly favorable situation for the HER. Notably, we show that
$\Delta G$ for Pt$_3$Sn and Pd$_3$Sn are just -0.066 and -0.092 eV,
respectively, which are almost half of the value of Pt.
