Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model*

We study a parity-time (PT)-symmetric trimer with non-Hermitian strength parameter γ coupled to two semi-infinite Su-Schrieffer-Heeger (SSH) leads. Two zero-energy modes occur, one of which is localized while the other is anti-localized, that have properties in common with SSH edge modes. We demonstrate two types of PT-symmetry breaking. Within the parameter space corresponding to the topologically non-trivial phase of the SSH chains, a gap opens within the broken PT regime of the discrete eigenvalue spectrum. For smaller values of γ, the eigenvalues are embedded in the two SSH bands, becoming destabilized primarily due to the resonance interaction with the continuum. We call this reservoir-assisted PT-symmetry breaking. As γ is increased, the eigenvalues exit the SSH bands and the discrete eigenstates become more strongly localized in the central trimer region. This approximate decoupling results in the discrete spectrum behaving more like the independent trimer, including both a region in which the PT-symmetry is restored (the gap) and a second region in which it is broken again. At the upper edge of the gap, two eigenstates coalesce with the localized zero-energy mode, resulting in a third-order exceptional point that can be detected in the survival probability dynamics.