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.