Here, σ σ x and σ σ y are two of the three Pauli matrices. The factor τ τ = + / − − indicates whether the Hamiltonian describes is centred on the K or K ′ valley at the corner of hexagonal Brillouin zone. For graphene, the Dirac velocity is about ℏ ℏ v D ≈ ≈ 5.8 eV Å . An energy gap in the dispersion of graphene can be obtained from a low-energy Hamiltonian of the form