Inverse Dielectric Function of a Lateral Quantum Wire Superlattice Parallel to the Interface of a Plasma-Like Semiconductor

The dynamic, nonlocal and spatially inhomogeneous polarizability and dielectric function are discussed in this paper for a Coulomb-coupled system of a periodic lateral superlattice array of one-dimensional quantum wire plasmas in the vicinity of a semi-infinite bulk plasma. The spacetime matrix inverse of the dielectric function, i.e: the dynamic, nonlocal, inhomogeneous screening function of this system, is determined analytically here in closed form solving a random phase approximation (RPA) type integral equation in position representation. We treat both cases wherein the lateral quantum wire superlattice is outside the semi-infinite plasma as well as inside. We also determine the exact coupled plasmon dispersion relation for the combined system for both the “outside” and “inside” cases: in this, we examine the band/gap structure of the spectrum due to periodicity of the quantum wire superlattice in the first Brillouin zone as a function of reciprocal lattice wavenumber p, and also as a function of wavevector qx along the wire direction of full translational invariance. Furthermore, we analyze the spectrum of the combined system as a function of the period of the superlattice, showing that the detailed variation of the band-structure spectrum and gaps reflects on the period of the superlattice, opening the possibility of using surface plasmon resonance as a mechanism for optical sensing of nanostructure geometry. We also determine the dependence of the spectrum on distance of the superlattice from the bounding surface of the semi-infinite plasma, for both “outside” and “inside” cases. In the “outside” case, we show that at large distances the surface plasmon decouples from the superlattice plasmon band, while for short distances the two are fully coupled. For the “inside” case, they are similarly fully coupled for short distances, but for large distances, the surface plasmon decouples while the wire-superlattice plasmon band couples to the bulk plasmon deep in the semi-infinite medium.