Two-dimensional magnetoplasma/Bernstein modes coupled with bulk and surface optical phonons

Abstract

We analyze the interaction of two-dimensional (2D) magnetoplasmons, including 2D Bernstein modes, with bulk and surface optical phonons. The system studied is a 2D sheet of nonlocal electron magnetoplasma embedded in a semi-infinite semiconductor medium with optical phonons. We examine the longitudinal collective mode spectrum as a function of distance ${z}_{0}$ of the 2D sheet from the bounding surface of the semiconductor. In particular, the 2D magnetoplasma/Bernstein modes couple preferentially to the bulk LO-phonon deep in the medium ${(z}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}),$ whereas in the vicinity of the surface ${(z}_{0}\ensuremath{\rightarrow}0)$ they couple preferentially to the surface phonon. This study is carried out by explicitly inverting the spatially inhomogeneous dielectric function of the combined system of a planar quantum-well plasma and a semi-infinite semiconductor in a position representation. The resulting closed-form inverse dielectric function ${K(z}_{1}{,z}_{2})$ yields the oscillator strengths of the various modes as its position-dependent residues at the frequency poles defining the modes.