Flat Band Induced Metal-Insulator Transitions for Weak Magnetic Flux and Spin-Orbit Disorder

TL;DR

This paper investigates how weak magnetic flux and spin-orbit disorder affect localization and metal-insulator transitions in all-band flat lattices across one and two dimensions, revealing unique localization behaviors and a tunable transition.

Contribution

It introduces a scale-free model for disordered flat band lattices and uncovers novel localization phenomena and a tunable metal-insulator transition driven by lattice parameters.

Findings

Sub-exponential localization at flatband energies in 1D with weak flux.

Diverging localization length at flatband energies in 2D with weak flux.

Tunable metal-insulator transition with mobility edges in 2D with spin-orbit disorder.

Abstract

We consider manifolds of tunable all-band flat (ABF) lattices in dimensions d = 1, 2, parametrized by a manifold angle parameter {\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 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 {\theta}.