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).