Geometric Bloch oscillations and transverse displacement in flat band systems

We investigate transport phenomena and dynamical effects in flat bands where the band dispersion plays no role. We show that wave packets in geometrically nontrivial flat bands can display dynamics when inhomogeneous electric fields are present. This dynamics is revealed both for the wave-packet 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 wave-packet position and for the wave-packet variance, whereas in the two-dimensional case we observe a transverse displacement of the wave packet 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.