Topology andPTsymmetry in a non-Hermitian Su-Schrieffer-Heeger chain with periodic hopping modulation

We study the effect of periodic hopping modulation in a Su-Schrieffer-Heeger (SSH) chain with an additional onsite staggered imaginary potential (of strengthγ). Such dissipative, non-Hermitian (NH) extension amply modifies the features of the topological trivial phase (TTP) and the topological nontrivial phase (TNP) of the SSH chain, more so with the periodic hopping distribution. Generally a weak NH potential can respect the parity-time (PT) symmetry keeping the energy eigenvalues real, while a strong potential breaksPTconservation leading to imaginary edge state and complex bulk state energies in the system. We find that the non-zero energy in-gap states, that appear due to periodic hopping modulations even in theγ = 0 limit, take purely real or purely imaginary eigenvalues depending on the strength of bothγand Δ (dimerization parameter). The localization of topological edge states (in-gap states) at the boundaries are investigated that reveals extended nature not only near topological transitions (further away from|Δ/t|=1) but also near the unmodulated limit ofΔ=0. Moreover, localization of the bulk states is observed at the maximally dimerized limit of|Δ/t|=1, which increases further withγ. These dissipative features can offer additional tunability in modulating the gain-loss contrast in optical systems or in designing various quantum information processing and storage devices.