Enhancement of detached topological edge modes in the presence of non-Hermitian on-site potentials.

This article presents the role of non-Hermitian on-site potentials over the detached edge modes which exists in the regions of non-Hermitian skin effect. We considered a non-Hermitian extension of Su-Schrieffer-Heeger model with competing nonreciprocal hopping with complex on-site potentials. The competing non-reciprocal hopping induce left and right non-Hermitian skin effect (LNHSE and RNHSE) in different parametric regimes and those regimes are identified using non-Bloch band theory. In these NHSE regions, even though all the bulk modes pile up at one end of the lattice (as dictated by the hopping profile), we can observe a detached edge mode which localize at the opposite side. This detached edge mode is found to be present in the weaker regions of NHSE (or in the boundary between LNHSE and RNHSE) and there arises question about the possible ways to strengthen these detached edge modes. This article shows that the introduction of loss and gain can strengthen these detached edge modes. Remarkably, significant widening of detached edge mode is observed soon after the introduction of loss and gain. Even though the detached edge mode can persist in both LNHSE and RNHSE regimes, the form of non-reciprocal hopping at the intercell and intracell level determines how readily these modes can coexist within the LNHSE or RNHSE regions.