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

Abstract

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.

5 pages

References in corpus (9)

• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• The Zak phase and the existence of edge states in graphene
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Low-Energy Effective Hamiltonian and the Surface States of Ca_3PbO
• Coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice
• Degeneracy and Consistency Condition of Berry phases: Gap Closing under the Twist
• SU(3) Dirac electrons in the 1/5-depleted square-lattice Hubbard model at 1/4 filling
• Symmetry protected weak topological phases in a superlattice

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