Cn -symmetric quasi-periodic Chern insulators

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 <?CDATA $n-$?> n − fold rotational symmetry (i.e. C n -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 C n -symmetric QCIs. Intriguingly, we numerically identify the emergence of charge fractionalization in unit of <?CDATA $e/10$?> e / 10 around the singular center in C n -symmetric QCIs though their bulk densities are inhomogeneous. In addition, we explore the phase transitions of these C n -symmetric QCIs.