Chern Insulators on Singular Geometries

TL;DR

This paper explores how Chern insulator states behave on two-dimensional singular geometries, revealing unique features like core states, charge fractionalization, and multiple edge excitation branches, expanding understanding beyond flat surfaces.

Contribution

It introduces the study of Chern insulators on singular geometries like cones and helicoids, uncovering novel phenomena not observed in flat geometries.

Findings

Discovery of in-gap and in-band core states

Observation of charge fractionalization

Multiple branches of edge excitations

Abstract

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.