Multifold Fermions and Fermi Arcs Boosted Catalysis in Nanoporous Electride 12CaO·7Al2 O3

Abstract

Topological materials have been recently regarded as ideal catalysts for heterogeneous reactions due to their surface metallic states and high carrier mobility. However, the underlying relationship between their catalytic performance and topological states is under debate. It has been discovered that the electride 12CaO·7Al₂ O₃ (C12A7:4e^- ) hosts multifold fermions and Fermi arcs on the (001) surface near the Fermi level due to the interstitial electrons. Through the comparison of catalytic performance under different doping and strain conditions, based on the hydrogen evolution process, it has been demonstrated that the excellent catalytic performance indeed originates from topological properties. A linear relationship between the length of Fermi arcs, and Gibbs free energy (ΔG_H* ) has been found, which not only provides the direct evidence to link the enhanced catalytic performance and surface Fermi arc states, but also fully clarifies the fundamental mechanism in topological catalysis.

Keywords: multifold fermions; topological electrides; topological quantum catalysts.

Figure 1

a) Crystal structure of electride C12A7:4e⁻. The cage structure is shown in the lower corner. b) The ELF of electride C12A7:4e⁻ with the isosurface values set as 0.65. The lower corner of (b) shows the confined electrons inside the cage. c) Bulk and (001) surface Brillouin zone of electride C12A7:4e⁻ with high symmetry points indicated. d) Band structure and PDOSs of electride C12A7:4e⁻. The band crossings at the H and P points are denoted as P₁ and P₂. “Inter.” denotes the interstitial electrons. e) The PED in the energy region of ±0.02 eV around P₁ and P₂. The isosurface value is chosen as 0.005 Bohr⁻³.

Figure 2

a) The (001) surface states of electride C12A7:4e⁻. b,c) show the (001) surface slice undercut 1 and cut 2 (the energy of cut 1 and cut 2 are taken exactly at SDP and FDP), respectively. In (a), (b), (c), the Fermi arcs are indicated by the white arrows. In (c), the illustrations on the right panel are the partially enlarged view of the states in the black (i) and green (ii) boxes.

Figure 3

a) The electronic band structures along k‐paths Г‐H‐P under different strains (namely without strain (i), and 0.5% strain along [111], [100], [110] directions (ii‐iv), respectively) for electride C12A7:4e⁻. These crossing points show six‐, four‐(Dirac), two‐fold (Weyl) and topological insulator, respectively. b) The surface states (i‐iv) corresponding to six‐, Dirac, Weyl fermions and topological insulator, where the red lines represent the Fermi arcs (six‐, Dirac‐, Weyl‐fermions) and Dirac cone (Topological insulator) surface states. c) The quantitative relationship between band degeneracy of different fermions and DOSs near the Fermi level on the (001) surface.

Figure 4

a) Schematic of the mechanism for the inhibited hydrogen poisoning (IHP) process on the (001) surface of C12A7:4e⁻: the long Fermi arcs induced by the SDP and FDP excitations activate the surface for IHP reaction. b) The electron depletion (the left panel) and accumulation (the right panel) during H adsorption on C12A7:4e⁻ surface. The isosurface values are set to 0.0025 e Å⁻³. c) The free energy diagram for hydrogen evolution at a potential U = 0 relative to the standard hydrogen electrode at pH = 0. The data for NbP, TaAs and NbAs are taken from ref.[11] d) Volcano plot for IHP of C12A7:4e⁻ in comparison with typical catalysts. The data are taken from refs.[11, 13, 38, 39] e) The quantitative relationship between band degeneracy of different fermions (six‐, Dirac‐, Weyl‐fermions, and topological insulator) and ΔG _H* on the (001) surface. f) shows the (001) surface states at the specific path of C12A7:4e⁻ without (i) and with (ii) the hydrogen adsorption, respectively.

Figure 5

a) The positions of SDP (blue line) and FDP (red line) in C12A7:4e⁻ with different charge states. The insets in (a) provide the ELF maps for C12A7:4e⁻/:2e⁻/:0e⁻, where the isosurface values are 0.65. b) The ΔG_H* of the (001) surface in C12A7:4e⁻ with different charge states. The insets in (b) show the corresponding (001) surface states for C12A7:4e⁻/:2e⁻/:0e⁻. c) The energy position of SDP and FDP corresponding to the Fermi level under hydrostatic distortions from −6% to +6%, where negative and positive values denote lattice compression and lattice expansion, respectively. The insets in (c) provide the ELF maps of electride C12A7:4e⁻ under −6%, 0%, and +6% lattice distortions, where the isosurface values are 0.65. d) The change of ΔG_H* on the (001) surface of C12A7:4e⁻ under different lattice distortions. e) The change of ΔG _H* on different positions of SDF by hole‐doping and strain. f) The linear relationship between Fermi arc length (L) of different surfaces and the corresponding surface DOSs (the left panel) and the catalytic ΔG _H* (the right panel).