Depth-dependent static shielding of an impurity by a quantum plasma in a magnetic field

Abstract

The static shielding of a charged impurity embedded in a quantum plasma is studied with the use of linear-response theory. The required response function is calculated in the random-phase approximation with a uniform magnetic field applied in a direction perpendicular to the surface. The surface is assumed to be an infinite potential barrier. When quantum-interference effects between incident and reflected electrons scattered off the surface are ignored, an analog of the Debye-Thomas-Fermi shielding law for a semi-infinite plasma is derived when all electrons with the same spin are in the lowest Landau level. In the quantum strong-field limit, the induced electron number density is calculated numerically. The results, which exhibit Friedel-Kohn oscillations, are analyzed when the depth of the impurity below the surface is varied. It is suggested that these effects might be studied experimentally by conversion electron M\"ossbauer spectroscopy in appropriate materials.