Symmetry Protected Quantization and Bulk-Edge Correspondence of Massless Dirac Fermions: Application to Fermionic Shastry-Sutherland Model

The fermionic Shastry-Sutherland model has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Weyl fermion. Berry phases defined by the one-dimensional momentum as a parameter are quantized into 0 or pi due to the inversion symmetry combined with the time reversal, or existence of the glide plane, which also protects the massless Dirac cones with continuous parameters. This is the symmetry protected Z2 quantization. We have further demonstrated the Z2 Berry phases generically determine the existence of edge states in various phases and with different types of the boundaries as the bulk-edge correspondence of the massless Dirac fermion systems.