Geometric Bloch oscillations and transverse displacement in flat band systems

TL;DR

This paper explores how wavepackets in flat band systems exhibit unique dynamical behaviors, such as Bloch oscillations and transverse displacement, driven purely by geometric effects without band dispersion.

Contribution

It demonstrates that geometric properties induce observable dynamics in flat bands, extending semiclassical equations to non-Abelian cases and revealing new transport phenomena.

Findings

Bloch oscillations in 1D flat bands

Transverse displacement in 2D flat bands without Berry curvature

Dynamics driven solely by geometric effects

Abstract

We investigate transport phenomena and dynamical effects in flat bands where the band dispersion plays no role. We show that wavepackets in geometrically non-trivial flat bands can display dynamics when inhomogeneous electric fields are present. This dynamics is revealed both for the wavepacket trajectory and for its variance, for which we derive semiclassical equations extended to the non-Abelian case. Our findings are tested in flat band models in one- and two-dimensional lattices where the dynamics is solely determined by geometric effects, in the absence of band dispersion. In particular, in the one-dimensional case, we show the existence of Bloch oscillations for the wavepacket position and for the wavepacket variance, whereas in the two-dimensional case we observe a transverse displacement of the wavepacket in the absence of Berry curvature. This work paves the way for understanding quantum-geometry-induced dynamical effects in flat band materials and also opens the possibility for their observation with synthetic matter platforms.