Quantum spin Hall insulator interacting with quantum light: Inhomogeneous Dicke model

Time-periodic perturbations due to classical electromagnetic fields are useful to engineer the topological properties of matter using the Floquet theory. Here, we investigate the effect of quantized electromagnetic fields by focusing on the quantized light-matter interaction on the edge state of a quantum spin Hall insulator. We show that this interaction can be studied using an inhomogeneous Dicke model and that the corresponding Hamiltonian is integrable. A Dicke-type superradiant phase transition occurs at arbitrary weak coupling and the electronic spectrum acquires a finite gap. In addition, when the total number of excitations are fixed, a photocurrent is generated along the edge, pseudoquantized as ln in the low-frequency limit and decaying as 1/ for high frequencies with being the photon frequency.