Next Nearest Neighbors Effects on Berry Curvature of Graphene

In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors was obtained by tight-binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave function the Berry connection and Berry curvature of our system are calculated. Our results are exactly consistent with previous methods and also the Berry curvature throughout the Brillouin zone get zero.