Flat band induced metal-insulator transitions for weak magnetic flux and spin-orbit disorder

We consider manifolds of tunable all-bands-flat (ABF) lattices in dimensions $d=1,2$, parameterized by a manifold angle parameter $\ensuremath{\theta}$. We study localization properties of eigenstates in the presence of weak magnetic flux disorder and weak spin-orbit disorder. We demonstrate that weakly disordered ABF lattices are described by effective scale-free models, where the disorder strength is scaled out. For weak magnetic flux disorder, we observe subexponential localization at flatband energies in $d=1$, which differs from the usual Anderson localization. We also find diverging localization length at flatband energies for weak flux values in $d=2$; however, the character of the eigenstates at these energies is less clear. For weak spin-orbit coupling disorder in $d=2$ we identify a tunable metal-insulator transition with mobility edges. We also consider the case of mixed spin-orbit and diagonal disorder and obtain the metal-insulator transition driven by the manifold parameter $\ensuremath{\theta}$.