Berry Phases and Curvatures in Electronic-Structure Theory

In the last fifteen years, Berry phases have been found to play an increasingly important role in electronic-structure theory. I will briefly review some of the important developments in which Berry phases have been involved, starting with the theory of polarization and the closely related theory of Wannier functions and their Wannier centers. I will briefly discuss the theory of insulators in finite electric fields, in which the field is taken to couple linearly to the Berry-phase polarization. I will conclude by discussing the role of Berry phases and Berry curvatures in systems in which time-reversal symmetry has been broken, and in particular, the theory of orbital magnetization and the anomalous Hall effect in ferromagnets. A few results of density-functional calculations will be presented to illustrate these methods.

David Vanderbilt, Rutgers University


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