Geometrical observables of the electronic ground state

DIPC Seminars

Raffaele Resta, Istituto Officina dei Materiali, CNR, Trieste, Italy
Donostia International Physics Center
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Geometrical observables of the electronic ground state 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 2π (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. References: [1] A. Marrazzo and R. Resta, Irrelevance of the boundary on the magnetization of metals, Phys. Rev. Lett. 116, 137201 (2016). [2] A. Marrazzo and R. Resta, Locality of the anomalous Hall conductivity, Phys. Rev. B 95, 121114(R) (2017). Host: Geza Giedke