WFU Physics Colloquium

Electric polarization and orbital magnetization turn out to be surprisingly difficult concepts to define precisely in a quantum-mechanical context, despite the fact that they are central to any elementary treatment of electrostatics and magnetostatics. I will review the theory that has emerged to describe the polarization and magnetization in 1993 and 2005, respectively. The basic approach is to decompose the continuous charge distribution into localized packets, known as Wannier functions, whose contributions are well defined. Alternatively, the theory can be cast in terms of so-called "Berry phases" and "Berry curvatures". Surprisingly, in the case of the orbital magnetization, a proper theory requires inclusion of a subtle surface term that is actually determined by bulk properties.