Quantum dynamics of plasmons in nanomaterials

Van Hieu Nguyen and Bich Ha Nguyen

Abstract

Newly emerging and being rapidly developed, plasmonics is a key prospective direction of research in nanoscience and nanotechnology. Numerous experimental works on a large variety of photonic processes in which the plasmons play substantial roles have been done, but there are only few theoretical works on these processes, and they are mainly phenomenological. In the present paper we propose an approach based on functional integral formalism, which would be able to be applied to the theoretical study of all physical processes with the participation of plasmons. After the presentation of the basics of functional integral technique, this technique is applied to the study of systems of interacting electrons in nanomaterials. The dynamical equation of plasmon is derived and quantum plasmonic field introduced. In the case of homogeneous and isotropic electron gas in three-dimensional space, this dynamical equation gives rise to the plasmon dispersion exactly coinciding with that derived from the conventional theories. However, the proposed calculation method, based on functional integral technique, can be effectively applied to the study of plasmons in nanostructures with complicated shapes, while the conventional theories are not able to be applied