Topological quantum states have been proposed and investigated on two-dimensional flat surfaces or lattices with different geometries like the plane, cylinder and torus. Here, we study quantum anomalous Hall (QAH) or Chern insulator (CI) states on two-dimensional singular surfaces (such as conical and helicoid-like surfaces). Such singular geometries can be constructed based on the disk geometry and a defined unit sector with n-fold rotational symmetry. The singular geometry induces novel and intriguing features of CI/QAH states, such as in-gap and in-band core states, charge fractionalization, and multiple branches of edge excitations.
@article{arxiv.1711.10116,
title = {Chern Insulators on Singular Geometries},
author = {Ai-Lei He and Wei-Wei Luo and Yi-Fei Wang and Chang-De Gong},
journal= {arXiv preprint arXiv:1711.10116},
year = {2018}
}