Quantum transport in non-Hermitian impurity array

Abstract: We study the formation of band gap bound states induced by a non-Hermitian impurity embedded in a Hermitian system. We show that a pair of bound states emerges inside the band gap when a parity-time ($\mathcal{PT}$) imaginary potential is added in a strongly coupled bilayer lattices and the bound states become strongly localized when the system approaches to the exceptional point (EP). As a direct consequence of such $\mathcal{PT}$ impurity-induced bound states, an impurity array can be constructed and protected by energy gap. The effective Hamiltonian of the impurity array is non-Hermitian Su-Schrieffer-Heeger (SSH) type and hosts Dirac probability-preserving dynamics. We demonstrate the conclusion by numerical simulations for the quantum transport of wave packet in right-angle bends waveguide and $Y$-beam splitter. Our finding provides alternative way to fabricate quantum device by non-Hermitian impurity.