Flatband Engineering of Mobility Edges

TL;DR

This paper demonstrates how to engineer and precisely tune mobility edges in flatband lattices using quasiperiodic modulations, enabling control over metal-insulator transitions in one-dimensional systems.

Contribution

It provides analytic expressions for mobility edges in flatband lattices with quasiperiodic modulations, allowing for fine control of their spectral properties.

Findings

Derived analytic expressions for mobility edges

Engineered cases with small energy separations and divergencies

Controlled metal-insulator transition points

Abstract

Properly modulated flatband lattices have a divergent density of states at the flatband energy. Quasiperiodic modulations are known to host a metal insulator transition already in one space dimension. Their embedding into flatband geometries consequently allows for a precise engineering and fine tuning of mobility edges. We obtain analytic expressions for singular mobility edges for two flatband lattice examples. In particular, we engineer cases with arbitrarily small energy separations of mobility edge, zeroes, and divergencies.