An explicit closed form determination of the inverse dielectric function for an N-sheet two-dimensional ͑2D͒ electron superlattice embedded in a nonlocal bulk host semiconductor plasma is presented here, as well as for an infinite superlattice. The coupled plasmon dispersion relation is analyzed for the model in which the 2D quantum wells constituting the superlattice have just one occupied subband and the bulk plasma of the host has hydrodynamic nonlocality. Nonlocal corrections are obtained for a hybrid superlattice plasmon in interaction with the host bulk plasmon. In addition, we find that this model predicts a new nonlocal low-frequency mode.
I. INVERSE DIELECTRIC FUNCTION FOR N-2D QUANTUM WELLS EMBEDDED IN A NONLOCAL BULK PLASMAThe dynamic plasmon response of a quantum well superlattice ͑SL͒ has been examined in a variety of circumstances, but little attention has been given to the interaction of the SL plasmons with nonlocal bulk plasmons of the host semiconductor in which the SL is lodged. A full understanding of this is important for a proper analysis of the role of dynamic, nonlocal screening in processes that involve electron excitations out of the discrete levels of the quantum wells, into the continuum of energy states for motion across the wells and above the barriers between them. Moreover, the interaction of SL plasmons and three-dimensional-like ͑3D͒ bulk plasmons ͑nonlocal͒ is also of interest at high densities, for which quantum well subbands are filled and electrons spill over into the extended state 3D bands. In this paper we address this problem for a superlattice with an arbitrary number ͑N͒ of thin quantum wells embedded in a bulk semiconductor containing a background plasma, and we also extend our considerations to an infinite periodic SL. Our treatment of the subject is focused on an analytic determination of an explicit closed-from result for the inverse dielectric function K(1,2) (1ϭr 1 ,t 1 ;2ϭr 2 ,t 2 ) of the compound system under consideration in the case when only one discrete subband level in each quantum well is populated and active, for a very thin quantum well. Due to the planar character of the quantum wells involved there is translational invariance in the lateral rϭ(x,y) plane, and it is useful to represent this in terms of a 2D spatial Fourier transform r 1 Ϫr 2 →q as well as a Fourier time transform to frequency representation, t 1 Ϫt 2 →. Thus we have K͑r 1 ,r 2 ;t 1 Ϫt 2 ͒→K͑ z 1 ,z 2 ,q, ͒→K͑ z 1 ,z 2 ͒, and we suppress q,. The frequency poles of K(z 1 ,z 2 ) define the joint collective modes of the compound system, and the residues at the poles provide the relative excitation amplitudes ͑oscillator strengths͒. In terms of the polarizability ␣ defined as ␣͑1,2͒ϭ͑1,2͒Ϫ␦ 4 ͑ 1Ϫ2 ͒→␣͑ z 1 ,z 2 ͒ ϭ͑z 1 ,z 2 ͒Ϫ␦͑ z 1 Ϫz 2 ͒, ͑1͒the random phase approximation ͑RPA͒ may be expressed as an integral equationK͑z 1 ,z 1 Ј͒ϭ␦͑z 1 Ϫz 1 Ј͒Ϫ ͵ dz 2 ␣͑z 1 ,z 2 ͒K͑ z 2 ,z 1 Ј͒. ͑2͒We model the continuum of electron states for motion across the quantum wells and above the barriers by an...