Photonic design of the Haldane model and its non-Hermitian extension

Abstract

In this report, we present a topological phase transition induced by on-site gain and loss in a photonic Chern insulator based on a non-Hermitian extension of Haldane model. By arranging the gyromagnetic rods in a honeycomb lattice, the gain and loss parameter is tuned to achieve a non-Hermiticity-induced phase transition with Hermitian-like features. Prior to the introduction to this photonic crystal, the concepts of band topology and photonics will first be drawn together, followed by general consequences of non-Hermitian parameters in photonic crystals. As a state-of-the-art model of Hermitian honeycomb lattices, the Haldane model will then be reviewed in order to demonstrate the competition between parity symmetry breaking and time-reversal symmetry breaking, inducing topological phase transitions in Hermitian regime. The gain and loss parameter is eventually applied on the Haldane model and the corresponding photonic crystals, which in turn introduces a new degree of freedom of symmetry breaking to realize topological phase transitions. Bulk and edge dispersion will be illustrated in both Hermitian and non-Hermitian cases, highlighting bulk-edge correspondence and robustness of chiral edge states that are uncommon in non-Hermitian systems. Our results not only lead to the possibility to non-Hermitian control over band topology in Chern insulators, but also pave the way to novel applications in active topological photonic devices supported by its robustness against manufacturing errors.