Interacting Topological Crystalline Insulators

  • Hiroki IsobeEmail author
Part of the Springer Theses book series (Springer Theses)


We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and theorized in antiperovskite materials \(A_3BX\) with \(A=\) (Sr, La, Ca), \(B=\) (Sn, Pb) and \(X=\) (O, N, C). They host multivalley Dirac fermion surface states. Without interactions, such TCIs are classified by the mirror Chern number both for two and three dimensions. We find that electron interactions reduce the integer classification of noninteracting TCIs to a finite group \(\mathbb {Z}_4\) in two dimensions and \(\mathbb {Z}_8\) in three dimensions. The classification of the two-dimensional case is obtained by analyzing the one-dimensional edge modes using the bosonization method. For the classification of the three-dimensional case, the argument exploits the nonlocal nature of mirror symmetry and an explicit construction of surface states shows a reduction of the classification. Our construction builds on interacting edge states of \(U(1)\times Z_2\) symmetry-protected topological phases of fermions in two dimensions, which we classify. It reveals a deep connection between 3D topological phases protected by spatial symmetries and 2D topological phases protected by internal symmetries.


Topological crystalline insulator Symmetry-protected topological phase Mirror symmetry Bosonization 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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