Chern Insulators on Singular Geometries

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.

5 pages, 5 figures

References in corpus (33)

• Experimental realisation of the topological Haldane model
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Topological orders and Edge excitations in FQH states
• Nearly-flat bands with nontrivial topology
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Spin Anisotropy and Quantum Hall Effect in the Kagome Lattice - Chiral Spin State based on a Ferromagnet-
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulator
• Electron fractionalization in two-dimensional graphenelike structures
• Fractional Quantum Hall States and Jack Polynomials
• Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
• Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
• Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
• Non-Abelian Quantum Hall Effect in Topological Flat Bands
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
• Pseudopotential Formalism for Fractional Chern Insulators
• Bound States of Conical Singularities in Graphene-Based Topological Insulators
• Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces
• Bulk-edge correspondence in fractional Chern insulators
• Corner states of topological fullerenes
• Edge excitations of bosonic fractional quantum Hall phases in optical lattices
• Fractional charge and inter-Landau level states at points of singular curvature
• Geometric Defects in Quantum Hall States
• Shot Noise Signatures of Charge Fractionalization in the $\nu =2$ Quantum Hall edge
• Nontrivial topological states on a Möbius band
• Edge Excitations in Fractional Chern Insulators
• Topological insulators on a Mobius Strip
• Lowest Landau level on a cone and zeta determinants
• Wave Functions for Fractional Chern Insulators on Disk Geometry
• Fractional quantum Hall states of bosons on cones

Cited by in corpus (5)

• Fractional disclination charge in two-dimensional $C_n-$symmetric topological crystalline insulators
• Quasicrystalline Chern Insulators
• Fractional Chern Insulators in Singular Geometries
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Gravitational Response of Topological Quantum States of Matter