Fractional disclination charge in two-dimensional Cn-symmetric topological crystalline insulators

Tianhe Li, Penghao Zhu, Wladimir A. Benalcazar, and Taylor L. Hughes
Phys. Rev. B 101, 115115 – Published 9 March 2020

Abstract

Robust fractional charge localized at disclination defects has recently been found as a topological response in C6-symmetric 2D topological crystalline insulators (TCIs). In this article, we thoroughly investigate the fractional charge on disclinations in Cn-symmetric TCIs, with or without time-reversal symmetry, and including spinless and spin-12 cases. We compute the fractional disclination charges from the Wannier representations in real space and use band representation theory to construct topological indices of the fractional disclination charge for all 2D TCIs that admit a (generalized) Wannier representation. We find the disclination charge is fractionalized in units of en for Cn-symmetric TCIs, and for spin-12 TCIs, with additional time-reversal symmetry, the disclination charge is fractionalized in units of 2en. We furthermore prove that with electron-electron interactions that preserve the Cn symmetry and many-body bulk gap, though we can deform a TCI into another which is topologically distinct in the free fermion case, the fractional disclination charge determined by our topological indices will not change in this process. Moreover, we use an algebraic technique to generalize the indices for TCIs with nonzero Chern numbers, where a Wannier representation is not applicable. With the inclusion of the Chern number, our generalized fractional disclination indices apply for all Cn-symmetric TCIs. Finally, we briefly discuss the connection between the Chern number dependence of our generalized indices and the Wen-Zee term.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
4 More
  • Received 17 July 2019
  • Accepted 24 February 2020
  • Corrected 4 December 2020

DOI:https://doi.org/10.1103/PhysRevB.101.115115

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Corrections

4 December 2020

Correction: A Grant Number in the Acknowledgment section contained an error and has been fixed.

Authors & Affiliations

Tianhe Li1,*, Penghao Zhu1,*, Wladimir A. Benalcazar2, and Taylor L. Hughes1

  • 1Department of Physics, Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 2Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16801, USA

  • *These authors contributed equally to this work.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 101, Iss. 11 — 15 March 2020

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×