Figure 1: The energy vs momentum of the states on the surface of a 3D topological insulator forms a Dirac cone. The red curve is a slice through this cone, measured with photoemission from the surface of the topological insulator ${\text{Bi}}_2{\text{Se}}_3$. (Inset) Schematic of the full Dirac cone and the circulation of the spin states (yellow arrows) associated with each momentum state. The spin circulation pattern leads to a Berry’s phase of $\pi$.