* Corresponding author. Tel.: #1-201-2165651; fax: #1- 201-2165638. E-mail address: nhoring@stevens-tech.edu (N.J.M. Horing). Physica B 299 (2001) 165 } 172 Coupling of 2D plasmons to nonlocal bulk plasmons Norman J.M. Horing*, Godfrey Gumbs, Tae-ik Park Department of Physics, Stevens Institute of Technology, Hoboken, NJ 07030, USA Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, NY 10021, USA Received 5 June 2000; received in revised form 25 August 2000 Abstract An explicit closed-form position-space expression for the highly inhomogeneous inverse dielectric response function of a quantum well (QW) of "nite 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 (z, z; q  , ), given in position representation for the z-direction across the well, depends on the in-plane wave vector q  and frequency  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 (z, z; q  , ) 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.  2001 Elsevier Science B.V. All rights reserved. PACS: 73.20.Mf; 71.35.Lk; 73.50.Mx; 78.66.!w Keywords: 2D plasmons; 3D plasmons; Nonlocality; Mode-coupling 1. Introduction Recently, interest in the electron transport and optical properties of a single quantum well (QW) has intensi"ed due to several new developments arising from newly found properties in materials such as GaN as well as magnetic "eld e!ects in double QWs. The role played by con"ned electron motion across the well (z-direction) is usually taken into account when dealing with semiconductor QWs. However, the continuum of extended states with energy eigenvalues above the well is generally neglected. The question of how the QW plasmons [1,2] interact with the bulk collective excitations of the continuum [3,4], when both QW subband states and extended continuum states are occupied, is a nontrivial problem which was recently con- sidered by one of us (NH) [5]. The coupling of these collective excitations corresponds to the frequency poles of the inverse dielectric function (r, r; ) of the joint, combined system, which describes the dynamic, nonlocal and inhomogeneous screening of an externally applied potential by the sea of interacting electrons in both classes of states for z-motion. We analyze  in the random-phase 0921-4526/01/$ - see front matter  2001 Elsevier Science B.V. All rights reserved. PII:S0921-4526(00)00585-8