Su-Schrieffer-Heeger chain with one pair of [Formula: see text] -symmetric defects

The topologically nontrivial edge states induce [Formula: see text] transition in Su-Schrieffer-Heeger (SSH) chain with one pair of gain and loss at boundaries. In this study, we investigated a pair of [Formula: see text] -symmetric defects located inside the SSH chain, in particular, the defects locations are at the chain centre. The [Formula: see text] symmetry breaking of the bound states leads to the [Formula: see text] transition, the [Formula: see text] -symmetric phases and the localized states were studied. In the broken [Formula: see text] -symmetric phase, all energy levels break simultaneously in topologically trivial phase; however, two edge states in topologically nontrivial phase are free from the influence of the [Formula: see text] -symmetric defects. We discovered [Formula: see text] -symmetric bound states induced by the [Formula: see text] -symmetric local defects at the SSH chain centre. The [Formula: see text] -symmetric bound states significantly increase the [Formula: see text] transition threshold and coalesce to the topologically protected zero mode with vanishing probabilities on every other site of the left-half chain and the right-half chain, respectively.