Coupling of 2D plasmons to nonlocal bulk plasmons

Abstract

An explicit closed-form position-space expression for the highly inhomogeneous inverse dielectric response function of a quantum well (QW) of finite width (with a single bound subband state) embedded in a bulk medium having a continuum of extended states is derived here analytically. The resulting position-dependent nonlocal dynamic inverse dielectric function ε −1(z,z′; q ||, ω) , given in position representation for the z-direction across the well, depends on the in-plane wave vector q || and frequency ω as well as on the positional variables z, z′. Spatial inhomogeneity arises from the lack of translational invariance in the z-direction due to the presence of the QW. The frequency poles of ε −1(z,z′; q ||, ω) obtained here represent the coupling of nonlocal bulk plasmons with two-dimensional (2D) intrasubband plasmons of the QW. The dispersion relation of the coupled modes is examined. The bulk particle–hole modes damp the collective excitations of the coupled 2D and bulk systems and we estimate the damping rate.