Flat-band engineering of mobility edges

Abstract

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