Figure 1: Model system and analytically calculated homogeneous bulk spectra.

(a) Schematics of the structure. (The presence of metal plates and dielectrics permits a general theoretical treatment but is not essential to the topological behaviours of 2D MP). (b) No magnetic field is present. The two circles connected by a dashed line represent the particle–hole symmetry of the dispersion curves. (c) A uniform magnetic field is applied along the positive z direction. Different branches carry different Chern numbers. The negative-frequency branch reflects the redundant degrees of freedom of the real-valued classical field and so is shaded. Here , where is a characteristic frequency defined to normalize the frequencies (see Methods: Theoretical model).