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 ${\theta }_i$. Without loss of generality, we consider the case of two flat bands separated by a finite gap, $\mathrm{\Delta }$. 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 ${\theta }_i$. 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 ${\theta }_i$. Instead, in $d=3$ we identify a nonperturbative metal-insulator transition upon varying all bands' flat manifold angles.

• Received 26 July 2021
• Revised 29 October 2021
• Accepted 2 November 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L180201