  We investigate the light-matter interaction between the edge state of a 2D
topological insulator and quantum electromagnetic field. The interaction
originates from the Zeeman term between the spin of the edge electrons and the
magnetic field, and also through the Peierls substition. The continuous U(1)
symmetry of the system in the absence of the vector potential reduces into
discrete time reversal symmetry in the presence of the vector potential. Due to
light-matter interaction, a superradiant ground state emerges with
spontaneously broken time reversal symmetry, accompanied by a net photocurrent
along the edge, generated by the vector potential of the quantum light. The
spectral function of the photon field reveals polariton continuum excitations
above a threshold energy, corresponding to a Higgs mode and another low energy
collective mode due to the phase fluctuations of the ground state. This
collective mode is a zero energy Goldstone mode that arises from the broken
continuous U(1) symmetry in the absence of the vector potential, and acquires
finite a gap in the presence of the vector potential. The optical conductivity
of the edge electrons is calculated using the random phase approximation by
taking the fluctuation of the order parameter into account. It contains the
collective modes as a Drude peak with renormalized effective mass, which moves
to finite frequencies as the symmetry of the system is lowered by the inclusion
of the vector potential.
