Who: Raffaele Resta, Istituto Officina dei Materiali, CNR, Trieste, Italy
Place: Donostia International Physics Center
Date: Friday, 23 November 2018, 12:00
I will start explaining what ?geometrical? means in quantum mechanics; then I will specialize to either band insulators or band metals, i.e. noninteracting electrons in a periodic potential. Therein all physical properties, geometrical observables included, are expressed as either Brillouin-zone integrals (in insulators) or Fermi-volume integrals (in metals) of the appropriate function of k. The known geometrical observables come in two very different classes: (i) observables whose bulk value is only defined modulo 2? (in dimensionless units), meaningful in insulators only, and (ii) observables exempt from such ambiguity, meaningful in both insulators and metals. Such a striking qualitative difference can be traced back to fundamental features of modern differential geometry. I will then focus on class (ii) only, whose most popular entries are anomalous Hall conductivity and orbital magnetization; these observables also enjoy a dual expression in r space, where they display a local nature.
 A. Marrazzo and R. Resta, Irrelevance of the boundary on the magnetization of metals, Phys. Rev. Lett. 116, 137201 (2016).
 A. Marrazzo and R. Resta, Locality of the anomalous Hall conductivity, Phys. Rev. B 95, 121114(R) (2017).
Host: Geza Giedke