Quantization Scheme of Surface Plasmon Polaritons in Two-Dimensional Helical Liquids

The collective modes of two-dimensional helical electron gases interacting with light have been studied in an extended random phase approximation. An inverse operator transformation that interprets electron oscillations and photons with quasi particles is developed. Because photons are initially included in the model, one can directly derive and compare the static and radiation (or vector) fields for the excited collective modes. Unlike the traditional quantization scheme that the electron oscillation's contribution is totally hidden in the dielectric function, we can directly investigate their roles when the collective modes interact with other particles. As an example, we find an additional term which plays an important role at small distance arising from electron exchanging effect when the collective modes couple to emitters.