Thermodynamic Green's-function theory of quantum magnetic field effects in the dynamic, nonlocal longitudinal dielectric-response properties of a bounded solid-state plasma.

Abstract

The analysis of dynamic nonlocal longitudinal dielectric response properties of a slab of quantum plasma in a magnetic field H (perpendicular to the plane slab faces) is carried out here with use of a thermodynamic Green's-function formulation of the random-phase approximation (RPA). The magnetic field Green's function for the slab incorporates magnetic field effects in terms of a closed-form integral representation, and the boundary condition of specular reflection is imposed in two alternative ways, in terms of (1) a partial eigenfunction expansion, and (2) an image series of infinite-space Green's functions. The RPA integral equation is solved for the direct slab dielectric function subject to Landau quantization, with results expressed in terms of the density perturbation response function scrR=\ensuremath{\delta}\ensuremath{\rho}/\ensuremath{\delta}V which depends on both z and z' because of the lack of translational invariance perpendicular to the slab faces (parallel to H=Hz^). Correspondingly, scrR depends on two conjugate wave-vector transform variables ${q}_{z}$ and ${q}_{z}^{\mathcal{'}}$ which are interpreted as indices for rows and columns of scrR regarded as a matrix. The magnetic field dependencies and nonlocality of both the diagonal and nondiagonal elements of scrR are thoroughly examined here. Applications of this work to the Landau quantized nonlocal slab surface-plasmon dispersion relation are discussed.