Mobility edges generated by the non-Hermitian flatband lattice

Abstract

We study the cross-stitch flatband lattice subject to the quasiperiodic complex potential exp(ix). We first identify the exact expression of quadratic mobility edges through analytical calculation, then verify theoretical predictions by numerically calculating the inverse participation ratio. Further more, we study the relationship between the real-complex spectrum transition and the localization-delocalization transition, and demonstrate that mobility edges in this non-Hermitian model not only separate localized from extended states but also indicate the coexistence of complex and real spectrum.

Real eigenvalues determined by recursion of eigenstates

“…In fact, real eigenvalues in many complicated models [23][24][25] also originated from the recursion of eigenstates. However, due to the complexity of models, obtaining rigorous mathematical solutions is very difficult.…”