Topological magnetic crystalline insulators and corepresentation theory

Rui-Xing Zhang and Chao-Xing Liu
Phys. Rev. B 91, 115317 – Published 26 March 2015

Abstract

Gapless surface states of time reversal invariant topological insulators are protected by the antiunitary nature of the time-reversal operation. Very recently, this idea was generalized to magnetic structures, in which time-reversal symmetry is explicitly broken, but there is still an antiunitary symmetry operation combining time-reversal symmetry and crystalline symmetry. These topological phases in magnetic structures are dubbed “topological magnetic crystalline insulators.” In this work, we present a general theory of topological magnetic crystalline insulators in different types of magnetic crystals based on the corepresentation theory of magnetic crystalline symmetry groups. We construct two concrete tight-binding models of topological magnetic crystalline insulators, the Ĉ4Θ̂ model and the τ̂Θ̂ model, in which topological surface states and topological invariants are calculated explicitly. Moreover, we check different types of antiunitary operators in magnetic systems and find that the systems with Ĉ4Θ̂,Ĉ6Θ̂, and τ̂Θ̂ symmetry are able to protect gapless surface states. Our work will pave the way to search for topological magnetic crystalline insulators in realistic magnetic materials.

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  • Received 22 February 2014
  • Revised 1 March 2015

DOI:https://doi.org/10.1103/PhysRevB.91.115317

©2015 American Physical Society

Authors & Affiliations

Rui-Xing Zhang and Chao-Xing Liu

  • Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA

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Issue

Vol. 91, Iss. 11 — 15 March 2015

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