Topological materials are recently regarded as the idea catalysts due to the protected surface metallic states and high carrier mobility, however the fundamental mechanism and the underlying relationship between the catalytic performance and topological states are in debate. Here, by means of symmetry analysis and first-principles calculations, we discover that the electride material of C12A7 hosts the multiple-fold fermions due to the interstitial-electrons, with the sixfold- and fourfold- degenerate points locating at high symmetric points near the Fermi energy, which are identified as the underlying reason of the enhanced catalytic ability in C12A7-based catalysts. The multiple-fold fermions exhibit much longer Fermi arcs on the (001) surface than traditional Weyl/Dirac fermions, the surface is thus highly chemical active and possesses a low Gibbs free energy for the hydrogen evolution reaction. The underlying relationship between catalytic performance and the topological surface state is explicitly verified by artificially hole doping, external strain and similar electride without the Fermi arcs, where the Gibbs free energies are significantly increased when the Fermi arcs is shifted to higher energy level. This work offers a guiding principle for understanding catalytic nature of electrides and the topological quantum catalysts.
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