Physics (Internal)

Topology and Quantum Geometry in Flat Electronic Bands

This event is part of the Biophysics Seminars. 12:30PM.

Abstract:

Interacting electrons populating spectrally flat bands are an interesting playground to obtain strongly correlated topological states in condensed matter physics. While the fractional quantum Hall effect of electrons in a strong magnetic field is the most prominent example of such a state, I will discuss a wider class of systems called fractional Chern insulators that became a focus of intense research recently. These exotic many-body states are the result of a subtle interplay of topology and energetics, arising from the noncommutative quantum geometry that electrons experience despite the spectral flatness of the band. I will show how algebraic properties of the electronic position and density operators are determined by the Berry curvature and the quantum metric of single-particle states and how these quantities influence, respectively, the topological response and the energetics of the many-body state.