Electron energy spectrum and the Berry phase in a graphite bilayer

We emphasize that there exist four Dirac-type points in the electron energy spectrum of a graphite bilayer near the point K of its Brillouin zone. One of the Dirac points is at the point K, and three Dirac points lie nearby. Each of these three points generates the Berry phase pi, while the Dirac point at K gives the phase -pi. It is these four points that determine the Berry phase in the bilayer. If an electron orbit surrounds all these points, the Berry phase is equal to 2 pi.