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First principles calculation of topological invariants of non-Hermitian photonic crystals

Prudêncio, F. ; Silveirinha, M. G.

Communications Physics Vol. 3, Nº 1, pp. 1 - 9, December, 2020.

ISSN (print): 2399-3650
ISSN (online):

Scimago Journal Ranking: 2,38 (in 2020)

Digital Object Identifier: 10.1038/s42005-020-00482-3

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Topological photonic systems have recently emerged as an exciting new paradigm to guide light without back-reflections. The Chern topological numbers of a photonic platform are usually written in terms of the Berry curvature, which depends on the normal modes of the system. Here, we use a gauge invariant Green’s function method to determine from first principles the topological invariants of photonic crystals. The proposed formalism does not require the calculation of the photonic band-structure, and can be easily implemented using the operators obtained with a standard plane-wave expansion. Furthermore, it is shown that the theory can be readily applied to the classification of topological phases of non-Hermitian photonic crystals with lossy or gainy materials, e.g., parity-time symmetric photonic crystals.