Interaction of electromagnetic field with electrons in a Wigner crystal

The interaction between electrons that form a quasi-two-dimensional crystal, as well as their interaction with a dielectric/metallic substrate (image potential), is well understood within the standard theory of Wigner crystals. Here we analyze the influence of the quantized electromagnetic field on the dynamics of Wigner electrons, i.e., on the dispersion relation of Wigner phonons. We have found that a significant influence can be expected from the surface polariton field when the energies of the surface polaritons and Wigner phonons coincide. Such polaritons can be expected in ionic crystals or doped semiconductors and we have proposed a geometry that can lead to the detection of a Wigner crystal by measuring the dispersion relation of surface polaritons.