Efficient hydrogen evolution reaction due to topological polarization

Ming-Chun Jiang, Guang-Yu Guo, Motoaki Hirayama, Tonghua Yu, Takuya Nomoto, and Ryotaro Arita

Phys. Rev. B 106, 165120 – Published 21 October 2022

Abstract

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 $π$ in the whole (111) projected Brillouin zone, which causes quantized electric polarization charges 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 bonds, the H states are localized in the energy spectrum, and the change in the Gibbs free energy ( $Δ G$ ) 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 $Δ G$ 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.

Received 13 July 2022
Accepted 3 October 2022

DOI:https://doi.org/10.1103/PhysRevB.106.165120

Physics Subject Headings (PhySH)

Electric polarization Electrocatalysis Hydrogen energy Surface states

Topological materials

First-principles calculations Wannier function methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ming-Chun Jiang ^1,2,*, Guang-Yu Guo^1,3, Motoaki Hirayama^2,4,†, Tonghua Yu ⁵, Takuya Nomoto ⁶, and Ryotaro Arita ^5,6

¹Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei 10617, Taiwan
²RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako 351-0198, Japan
³Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
⁴Quantum Phase Electronics Center, University of Tokyo, Tokyo 113-8656, Japan
⁵Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
⁶Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Meguro-ku, Tokyo, 153-8904, Japan

^*ming-chun.jiang@riken.jp
^†hirayama@ap.t.u-tokyo.ac.jp

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Issue

Vol. 106, Iss. 16 — 15 October 2022

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Images

Figure 1
Crystal structure, adsorption sites, and Brillouin zone of the $A_{3} B$ family. (a) The lattice structure of $A_{3} B$ in an orthorhombic supercell. The black vectors show the reduction to a hexagonal supercell. The blue box indicates the primitive cell with the cyan $a b$ facet being the (111) plane of the primitive cell. The red and green bonds form the tetrahedral and octahedral sites, which correspond to the hcp- and fcc-adsorption sites for hydrogen. (b) Stable hydrogen adsorption sites on the (111) surface. (c) Brillouin zone of primitive cell and its projection along the [111] direction. Crystal structures are generated via vesta [32].
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Figure 2
Electronic structure of ${Pt}_{3} Sn$ bulk and (111) slab in the absence of the spin-orbit coupling. (a) Electronic band structure and density of states of bulk ${Pt}_{3} Sn$ , with the high-symmetry $k$ points shown in Fig. 1. The calculated Zak phase on the (111) projected Brillouin zone of the (b) pink and (c) blue gap. The green region indicates the $π$ Zak phase. (d) Real bulk wave function of the eigenstate at the time-reversal invariant $M$ point pointed in black in (a). Yellow and blue represent the positive and negative components, respectively. The red slice in the middle indicates the (111) plane. (e), (f) Projected electronic band structure and density of states for the (111) surface of a 10-layer slab of ${Pt}_{3} Sn$ in the (e) tight-binding Hamiltonian and (f) the GGA. The color bar indicates the weights of the topological surface state. The Fermi level is set to 0 regarding all band structures. (g), (h) Real wave functions of topological surface state at the $\bar{M}$ point as circled in blue in (f). Yellow and blue represent the positive and negative components, respectively.
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Figure 3
Electron localized functions for (a) ${Pt}_{3} Sn$ (111) fcc adsorption and (b) ${Ni}_{3} Si$ (111) top adsorption.
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Figure 4
Bonding between ${Pt}_{3} Sn$ (111) and H atom. (a) Band structure of 10-layer ${Pt}_{3} Sn$ (111) fcc adsorption highlighted with states projected onto the H atom. (b) Band structure of 10-layer ${Pt}_{3} Sn$ (111) with a $H_{2}$ molecule sufficiently away from the substrate. The energy level of the $H_{2}$ molecule is highlighted in brown. (c) Schematic of covalent bonding and an intermediate between the covalent and ionic bonding. (d) Density of states of the H atom for 10-layer ${Pt}_{3} Sn$ (111) fcc, hcp, and top adsorptions. The cumulative sum of the density of states is shown in the lower panel.
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Figure 5
Surface electronic structures of ${Pt}_{3} Sn$ (111) with H adsorption onto the (a) fcc site, (b) hcp site, and (c) top site.
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Figure 6
Schematic plot of interaction between H atom with (a) the topological surface states and (b) the bulk states of the $A_{3} B$ family.
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