  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. A Dicke-type superradiant phase transition occurs
at arbitrary weak coupling, the electronic spectrum acquires a finite gap and
the resulting ground state manifold is topological with Chern number $\pm 1$.
When the total number of excitations is conserved, a photocurrent is generated
along the edge, being pseudo-quantized as $\omega\ln(1/\omega)$ in the low
frequency limit, and decaying as $1/\omega$ for high frequencies with $\omega$
the photon frequency. The photon spectral function exhibits a clean Goldstone
mode, a Higgs like collective mode at the optical gap and the polariton
continuum.
