Geometrical observables of the electronic ground state
DIPC Seminars
- Speaker
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Raffaele Resta, Istituto Officina dei Materiali, CNR, Trieste, Italy
- When
-
2018/11/23
13:00 - Place
- Donostia International Physics Center
- Add to calendar
-
iCal
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 2Ï€ (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