Inhomogeneous structure of the nonlocal dynamic dielectric response of a quantum-well bound state and a three-dimensional band of extended states

Abstract

An explicit position-space inversion of the highly inhomogeneous dielectric function of a planar quantum well with a bound state embedded in a bulk medium having a three-dimensional (3D) band of extended states is carried out here in closed form. The resulting nonlocal dynamic inverse dielectric function ${K(z,z}^{\ensuremath{'}};\overline{q},\ensuremath{\omega})$ given in position representation for the z direction across the well depends upon lateral wave vector $\overline{q}$ and frequency $\ensuremath{\omega}$ as well as on positional variables ${z,z}^{\ensuremath{'}}.$ ${K(z,z}^{\ensuremath{'}};\overline{q},\ensuremath{\omega})$ is exact within the framework of the random-phase approximation with the assumption that the 3D band of extended states is approximately translationally invariant in the z direction. Spatial inhomogeneity arises from the lack of translational invariance in the z direction due to the presence of the planar quantum well. The frequency poles of ${K(z,z}^{\ensuremath{'}};\overline{q},\ensuremath{\omega})$ obtained here represent the coupling of nonlocal bulk plasmons with 2D intrasubband plasmons of the quantum well, and the residues at these poles provide the oscillator strengths of such coupled collective modes. The dispersion relation of the coupled modes is examined using the hydrodynamic model of 3D plasma nonlocality.