Effect of next-to-nearest neighbor hopping on electronic properties of graphene: Graphene and graphite multilayers - Suprunenko, Y.F.; Gorbar, E.V.; Sharapov, S.G.; Loktev, V.M. (ФІЗИКА НИЗЬКИХ ТЕМПЕРАТУР, 2008)
In the tight-binding approximation, we take into account the next-to-nearest neighbor hopping in graphene that leads to nonrelativistic-like corrections in its low energy spectrum. The electronic density ofstates in a magnetic field is found and the fan diagram is plotted, which interpolates between those for the relativistic and nonrelativistic limiting cases. It is shown that the Berry phase for the system under consideration coincides exactly with its value for the relativistic system.