C_n -symmetric quasi-periodic Chern insulators

Abstract

Chern insulators have been recently extended to quasicrystal systems, namely the quasi-periodic Chern insulators (QCIs). Here we study the topological properties and topological response of QCIs on two-dimensional singular surfaces. Such singular QCIs with arbitrary n−fold rotational symmetry (i.e. Cn-symmetric QCIs) can be constructed by “cutting and gluing” unit sectors on the Dürer’s pentagonal tiling. Chiral edge states and real-space Chern number can well characterize the topological properties of Cn-symmetric QCIs. Intriguingly, we numerically identify the emergence of charge fractionalization in unit of e/10 around the singular center in Cn-symmetric QCIs though their bulk densities are inhomogeneous. In addition, we explore the phase transitions of these Cn-symmetric QCIs.