Efficient hydrogen evolution reaction due to topological polarization

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