Tilen Čadež (IBS Korea): Metal-insulator transitions for weakly disordered flatbands

After an introduction of flat band systems, I will present our recent work, where we study all band flat (ABF) non-interacting systems in the presence of (infinitesimally) weak disorders. Our construction of ABF systems in the continuous manifold of local unitary transformation (LUT) angles enables a systematic study. We consider both on-site potential and time reversal symmetry breaking hopping disorders. By constructing the scale free and single scale models we explain the effects of weak disorders in ABF systems. We demonstrate that in the case of d = 1, two band ABF systems, the eigenstates are localized. In the case of d = 2 ABF lattices at infinitesimal disorder with time reversal breaking fraction δ, there is a Metal Insulator transition, driven either by the time reversal breaking fraction δ and/or the LUT manifold angles.