Credit: A. H. Castro Neto et al. [2]

Figure 1: Electronic dispersion of graphene. The conduction band and the valence band touch each other at six discrete points. These points are called $K$ points. The six points can be divided into two in-equivalent sets of three points each. The points within each set are all equivalent because they can reach each other by reciprocal lattice vectors. The two in-equivalent points are called $K$ and $K′$ and form the valley isospin degree of freedom in graphene. The name valley isospin stems from the similarity of the vicinity of these points with a valley. The zoom shows that the dispersion relation close to the $K$ points looks like the energy spectrum of massless Dirac particles.