Flat Band Induced Metal-Insulator Transitions for Weak Magnetic Flux and Spin-Orbit Disorder
arXiv:2211.09410 · doi:10.1103/PhysRevB.107.174202
Abstract
We consider manifolds of tunable all-band flat (ABF) lattices in dimensions d = 1, 2, parametrized by a manifold angle parameter θ. 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 sub-exponential localization at flatband energies in d = 1, which differs from the usual Anderson localization. We also find diverging localisation 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 θ.
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