Topological systems have exciting properties that may lead to new physics. The Chern numbers of a material platform are usually written in terms of the Berry curvature which depends on the normal modes of the system. From a computational point of view the calculation of the Chern number can be a rather formidable problem. Here, we use a gauge invariant Green’s function method (Phys. Rev. B, 99, 125155, 2019) to determine the topological invariants. We apply the method to a lossy photonic crystal formed by a hexagonal array of ferrite cylinders embedded in air with radius r=0.35a [Fig.1a]. The Chern numbers are calculated from first principles, i.e., without a tight-binding approximation.

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