Mobility edges in $\mathcal{P}\mathcal{T}$-symmetric cross-stitch flat band lattices

Abstract

We study the cross-stitch flat band lattice with a $\mathcal{P}\mathcal{T}$-symmetric on-site potential and uncover mobility edges with exact solutions. Furthermore, we study the relationship between the $\mathcal{P}\mathcal{T}$ symmetry broken point and the localization-delocalization transition point, and verify that mobility edges in this non-Hermitian model is available to signal the $\mathcal{P}\mathcal{T}$ symmetry breaking.

5 pages, 2 figures; Comments and suggestions are welcome