Exceptional points in topological edge spectrum of PT symmetric domain walls

TL;DR

This paper explores non-Hermitian PT symmetric interfaces supporting dissipationless edge states with exceptional points, revealing their topological properties and potential for experimental realization in photonics.

Contribution

It demonstrates the existence of PT symmetric edge states with exceptional points and their topological invariance, connecting non-Hermitian systems to Hermitian topological phases.

Findings

Edge states support dissipationless propagation due to PT symmetry.

Exceptional points enable spectral overlap with bulk states without hybridization.

Nonreciprocal edge states are found at PT-Haldane phase interfaces.

Abstract

We demonstrate that the non-Hermitian parity-time (PT) symmetric interfaces formed between amplifying and lossy crystals support dissipationless edge states. These PT edge states exhibit gapless spectra in the complex band structure interconnecting complex-valued bulk bands as long as exceptional points (EPs) of edge states exist. As a result, regimes exist where the edge states can spectrally overlap with the bulk continuum without hybridization, and leakage into the bulk states is suppressed due to the PT symmetry. Two exemplary PT symmetric systems, based on valley and quantum hall topological phases, are investigated, and the connection with the corresponding Hermitian systems is established. We find that the edge states smoothly transit to the valley edge states found in Hermitian systems if the magnitude of gain/loss vanishes. The topological nature of the PT edge states can be established within the non-Hermitian Haldane model, where the topological invariance is found to be unaffected by gain or loss. Nonreciprocal PT edge states are discovered at the interfaces between PT-Haldane phases, indicating the interplay between the gain/loss and the magnetic flux. The proposed systems are experimentally feasible to realize in photonics. This has been verified by our rigorous full-wave simulations of edge states in PT-symmetric silicon-based photonic graphene.