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

Abstract

We study a model consisting of a central PT -symmetric trimer with non-Hermitian strength parameter γ coupled to two semi-infinite Su-Schrieffer-Heeger (SSH) leads in order to demonstrate two qualitatively distinct types of PT -symmetry breaking. Within a subset of the parameter space corresponding to the topologically non-trivial phase of the SSH chains, we show that a gap opens within the broken PT regime of the discrete eigenvalue spectrum. For relatively smaller values of γ, the eigenvalues are embedded in the two SSH bands and hence become destabilized primarily due to the resonance interaction with the continuum. We refer to this as reservoir-assisted PT -symmetry breaking. As the value of γ is increased, the eigenvalues exit the two continuum 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. The second-order exceptional points (EP2s) associated with the PT -symmetry breaking thresholds form several two-dimensional exceptional surfaces in the parameter space of the model. For certain parameter values two of these surfaces intersect, forming a curve of fourth-order exceptional points (EP4s) along which the gap closes. Meanwhile, a second, qualitatively different scenario occurs in which the gap instead closes simultaneously along an extended domain of γ values.