The band theory of crystalline solids provides the fundamental basis for understanding materials and phenomena. It is generally believed that for most physical applications the band dispersion alone carries sufficient information to give proper account of various thermodynamic and transport properties. Recently, this belief is challenged by the realization that the Berry phase of the electronic wave function can also have a profound effect on material properties and is responsible for a spectrum of quantum phenomena. In this talk, I will review the basic concept of the Berry phase in crystals, followed by its application in a number of interesting phenomena, such as the anomalous Hall effect and valley-dependent phenomena. Given its broad range of applications and essential role in understanding these phenomena, it is clear that the Berry phase should be included as a basic ingredient in the electron theory of materials.
Watch a video of the colloquium (sorry, the slides failed to be recorded).