Geometrical observables of the electronic ground state
DIPC Seminars
 Speaker

Raffaele Resta, Istituto Officina dei Materiali, CNR, Trieste, Italy
 When

2018/11/23
13:00  Place
 Donostia International Physics Center
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I will start explaining what â€œgeometricalâ€ 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
Brillouinzone integrals (in insulators) or Fermivolume 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