Symmetry-protected quantization and bulk-edge correspondence of massless Dirac fermions: Application to the fermionic Shastry-Sutherland model

Toshikaze Kariyado and Yasuhiro Hatsugai

Phys. Rev. B 88, 245126 – Published 20 December 2013

Abstract

Berry phases defined by the one-dimensional momentum as a parameter show $Z_{2}$ quantization due to the inversion symmetry combined with the time reversal, or existence of the reflection plane, which also protects the massless Dirac cones with continuous parameters. This is the symmetry protected $Z_{2}$ quantization. These ideas are applied in the fermionic Shastry-Sutherland model, which has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Weyl fermion. We also demonstrate that the $Z_{2}$ Berry phases determine the existence of edge states as the bulk-edge correspondence of the massless Dirac fermion systems.