Dynamic dielectric response of a quantum wire superlattice in interaction with a nonlocal host medium

We study nonlocality effects of a bulk plasmalike dielectric medium on the plasmon spectrum of a one-dimensional (1D) quantum wire superlattice in interaction with the 3D nonlocal host bulk plasma, by carrying out a closed-form analytic determination of the inverse dielectric function κ for the joint nanostructure system within the random phase approximation (RPA), in which we treat nonlocality of the 1D superlattice in the RPA and that of the bulk medium in the hydrodynamic model. By examining the frequency poles of κ (i.e., the dispersions relations), we show analytically that coupled plasmon modes of the interacting 1D superlattice-3D nonlocal host are damped in high frequencies (damping is pronounced near resonance region) and that nonlocality of the host medium introduces nonlocal low frequency (real) modes into the spectrum, which have cutoff frequencies for finite wave vector values. In order to describe the impact of nonlocality effects more clearly, we also examine the spectrum numerically.