We demonstrate that the parity-time ($\mathcal{PT}$) symmetric interfaces formed between non-Hermitian amplifying (“gainy”) and lossy topological crystals exhibit $\mathcal{PT}$ phase transitions separating phases of lossless and decaying/amplifying topological edge transport. The spectrum of these interface states exhibits exceptional points (EPs) separating (i) a $\mathcal{PT}$ symmetric real-valued regime with an evenly distributed wave function in both gainy and lossy domains and (ii) a $\mathcal{PT}$ broken complex-valued regime, in which edge states asymmetrically localize in one of the domains. Despite its complex-valued character, the edge spectrum remains gapless and connects complex-valued bulk bands through the EPs. We find that the regimes exist when the real edge spectrum is embedded into the bulk continuum without mixing, indicating that the edge states are protected against leakage into the bulk by the $\mathcal{PT}$ symmetry. Two exemplary $\mathcal{PT}$ symmetric systems, exhibiting valley and Chern topological phases, respectively, are investigated and the connection with the corresponding Hermitian systems is established. Interestingly, despite the complex bulk spectrum of the Chern insulator, the bulk-interface correspondence principle still holds, as long as the topological gap remains open. The proposed systems are experimentally feasible in photonics, which is evidenced by our rigorous full-wave simulations of $\mathcal{PT}$ symmetric silicon-based photonic graphene.

• Received 13 January 2018
• Revised 5 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.165129