Single pair of charge-two high-fold fermions with type-II van Hove singularities on the surface of ultralight chiral crystals

Abstract

The realization of single-pair chiral fermions in Weyl systems remains challenging in topology physics, especially for the systems with higher chiral charges $C$. In this work, based on the symmetry analysis, low-energy effective model, and first-principles calculations, we identify the single-pair high-fold fermions in chiral cubic lattices. We first derive the minimal lattice model that exhibits a single pair of Weyl points with the opposite chiral charges of $C$ = $\pm{2}$. Furthermore, we show the ultralight chiral crystal P4$_3$32-type LiC$_2$ and its mirror enantiomer as high-quality candidate materials, which exhibit large energy windows to surmount the interruption of irrelevant bands. Since two enantiomers are connected by the mirror symmetry, we observe the opposite chiral charges $C$ and the reversal of the Fermi arc velocities, showing the correspondence of chirality in the momentum space and the real space. In addition, we also reveal type-II van Hove singularities on the helicoid surfaces, which may induce chirality-locked charge density waves on the crystal surface. Our work not only provides a promising platform for controlling the sign of topological charge through the structural chirality but also facilitates the exploration of electronic correlations on the surface of ultralight chiral crystals.