Topology and PT Symmetry in a Non-Hermitian Su-Schrieffer-Heeger Chain with Periodic Hopping Modulation.

Abstract

We study the effect of periodic hopping modulation in a Su-Schrieffer-Heeger (SSH) chain with an additional onsite staggered imaginary potential (of strength γ). Such dissipative, non-Hermitian (NH) extension amply modifies the features of the topological trivial phase (TTP) and the topo- logical 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 breaks PT conservation 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 the γ = 0 limit, take purely real or purely imaginary eigenvalues depending on the strength of both γ and ∆ (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 |∆/t| = 1) but also near the unmodulated limit of ∆ = 0. Moreover, localization of the bulk states is observed at the max- imally dimerized limit of |∆/t| = 1, which increases further with γ. 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.