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We consider the generic problem of a two-level quantum emitter near atwo-dimensional Chern insulator in the dipole approximation, and study how thefrequency-dependent response and electronic density of states of the insulatormodifies the transition rate of the emitter between the ground and excitedlevels. To this end, we obtain the full real-frequency behavior of theconductivity tensor by performing a tight-binding calculation based on theQi-Wu-Zhang model and using a Kubo formula, and derive the full electromagneticGreen tensor of the system, which breaks Onsager reciprocity. This enables usto find that for frequencies smaller than the maximum band gap, the system issensitive to time reversal symmetry-breaking, whereas for much largerfrequencies the system becomes insensitive, with implications for thediscrimination of the state of a circularly polarised dipole emitter. We alsostudy the impact of a van Hove singularity on the surface-induced correction tothe transition rate, finding that it can enhance its amplitude by a few ordersof magnitude compared to the case where the conductivity is set to its staticvalue. By considering configurations in which the dipole is circularlypolarised or parallel with the surface of the Chern insulator, we find that thesurface correction to the transition rate can exhibit a novel decay with sineintegral-like oscillations.

Spontaneous emission of a quantum emitter near a Chern insulator: interplay of time reversal symmetry breaking and van Hove singularity