Moving and merging of Dirac points on a square lattice and hidden symmetry protection

Abstract

First, we study a square fermionic lattice that supports the existence of massless Dirac fermions, where the Dirac points are protected by a hidden symmetry. We also consider two modified models with a staggered potential and the diagonal hopping terms, respectively. In the modified model with a staggered potential, the Dirac points exist in some range of magnitude of the staggered potential, and move with the variation of the staggered potential. When the magnitude of the staggered potential reaches a critical value, the two Dirac points merge. In the modified model with the diagonal hopping terms, the Dirac points always exist and just move with the variation of amplitude of the diagonal hopping. We develop a mapping method to find hidden symmetries evolving with the parameters. In the two modified models, the Dirac points are protected by this kind of hidden symmetry, and their moving and merging process can be explained by the evolution of the hidden symmetry along with the variation of the corresponding parameter.

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• Symmetry protected topological phases characterized by isolated exceptional points
• Hybrid exceptional point created from type III Dirac point
• Unruh effect for interacting particles with ultracold atoms
• Hidden symmetry and protection of Dirac points on the honeycomb lattice
• Hidden antiunitary symmetry behind "accidental" degeneracy and its protection of degeneracy
• Weyl semimetals in optical lattices: moving and merging of Weyl points, and hidden symmetry at Weyl points
• Dynamical bulk-edge correspondence for nodal lines in parameter space
• Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem
• Larkin-Ovchinnikov state of superconducting Weyl metals: Fundamental differences between pairings restricted and extended in the $\text{k}$-space
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Dirac points merging and wandering in a model Chern insulator