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Comprehensive Microscopic Theory for Coupling of Longitudinal--Transverse Fields and Individual--Collective Excitations

A plasmon is a collective excitation of electrons due to the Coulomb interaction. Both plasmons and single-particle excitations (SPEs) are eigenstates of bulk metallic systems and they are orthogonal to each other. However, in non-translationally symmetric systems such as nanostructures, plasmons and SPEs coherently interact. It has been well discussed that the plasmons and SPEs, respectively, can couple with transverse (T) electric field in such systems, and also that they are coupled with each other via longitudinal (L) field. However, there has been a missing link in the previous studies: the coherent coupling between the plasmons and SPEs mediated by the T field. Herein, we develop a theoretical framework to describe the self-consistent relationship between plasmons and SPEs through both the L and T fields. The excitations are described in terms of the charge and current densities in a constitutive equation with a nonlocal susceptibility, where the densities include the L and T components. The electromagnetic fields originating from the densities are described in terms of the Green's function in the Maxwell equations. The T field is generated from both densities, whereas the L component is attributed to the charge density only. We introduce a four-vector representation incorporating the vector and scalar potentials in the Coulomb gauge, in which the T and L fields are separated explicitly. The eigenvalues of the matrix for the self-consistent equations appear as the poles of the system excitations. The developed formulation enables to approach unknown mechanisms for enhancement of the coherent coupling between plasmons and the hot carriers generated by radiative fields.