Metal-insulator transition in infinitesimally weakly disordered flat bands

Abstract

© 2021 American Physical Society.We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices. The lattices are generated from diagonal Hamiltonians by a sequence of (d+1) local unitary transformations parametrized by angles θi. Without loss of generality, we consider the case of two flat bands separated by a finite gap, Δ. The perturbed states originating from the flat bands are described by an effective tight-binding network with finite on- and off-diagonal disorder strength which depends on the manifold angles θi. The original infinitesimal on-site disorder strength W is only affecting the overall scale of the effective Hamiltonian. Upon variation of the manifold angles for d=1 and d=2 we find that localization persists for any choice of local unitaries, and the localization length can be maximized for specific values of θi. Instead, in d=3 we identify a nonperturbative metal-insulator transition upon varying all bands' flat manifold angles.