Hidden symmetry and protection of Dirac points on the honeycomb lattice

Abstract

The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now, the origin of the Dirac points is unclear yet. Here, we discover a hidden symmetry on the honeycomb lattice and prove that the existence of Dirac points is exactly protected by such hidden symmetry. Furthermore, the moving and merging of the Dirac points and a quantum phase transition, which have been theoretically predicted and experimentally observed on the honeycomb lattice, can also be perfectly explained by the parameter dependent evolution of the hidden symmetry.

5 pages, 2 figures, +6 pages of supplementary information. Welcome any comments!

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• Interfacial waveforms in chiral lattices with gyroscopic spinners
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• Quantum Anomalous Hall Effect and Anderson Chern Insulating Regime in Noncollinear Antiferromagnetic 3Q State
• Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem
• Dynamical bulk-edge correspondence for nodal lines in parameter space
• Magnon Hall effect in antiferromagnetic lattices
• Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
• Robustness of flat bands on the perturbed Kagome and the perturbed Super-Kagome lattice
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice