# 12.04.23: Talk by Johannes Mitscherling "Quantum geometry of multiband systems with and without flat bands"

Department of Physics, University of California, Berkeley, California 94720, USA

12.04.2023 at 10:00

Studying the geometry of Bloch wave function manifolds helps us identify and understand phenomena that are not solely captured by the energy dispersion. The Berry curvature and the related topology are well-known examples. Recently, geometric effects of the quantum metric, which defines a distance between wave functions, as well as other exotic geometric quantities have been identified and are still far less explored. Systems with flat bands are particularly promising candidates to show these new effects since observables arising from the slope or curvature of the dispersion vanish. In this talk, I will explain both the formalism behind wave function geometry as well as its application to transport in multiband systems, where quantum geometry may serve as a natural description of interband contributions to transport. This relation enables us to draw a direct connection between abstract geometric objects and physical observables. As an example, we will explore the electrical dc conductivity of a generic noninteracting multiband model and identify a metric-related contribution to the conductivity, which has been noticed only recently. Applied to flat-band systems, the electrical dc conductivity for an isolated flat band is given by the integrated quantum metric, which in turn implies that a geometrically nontrivial flat band should conduct although the quasiparticle velocity vanishes. This result opens a new perspective on the challenging task of understanding transport in flat-band systems such as geometrically frustrated lattices.

Room A 450