Quantum Corrections to the Screening Length and Anisotropy in Magnetic Field

Abstract

A. FORTINIThe self-consistent linearized Poisson equation leading to the screened potential of an ionized centre embedded in a free carrier plasma, is rewritten in a closed form taking into account the quantum character of the plasma. Complete resolution in the case of Boltzmann statistics clearly shows how quantum corrections cause a departure of the screening length from its usual semiclassical value. Quantum corrections are also responsible for the anisotropy of the screening in a static magnetic field. Calculations are worked out for the case of a strong quantizing field.Die selbstkonsistente linearisierte Poissongleichung, die zu dem abgeschirmten Potential eines ionisierten Zentrums, das in einem Plasma freier Trager eingebettet ist, fiihrt, wird in einer geschlossenen Form umformuliert unter Berucksichtigung des Quantencharakters des Plasmas. Eine vollstandige Losung fur den Fall der Boltzmannstatistik zeigt deutlich, wie die Quantenkorrekturen eine Abweichung der Abschirmlange von ihrem normalen halbklassischen Wert verursachen. Die Quantenkorrekturen sind auch verantwortlich fur die Anisotropie der Abschirmung im statischen Magnetfeld. Berechnungen werden fur den Fall eines starken quantisierenden Feldes durchgefiihrt.

Electrical Conductivity of Hot Electrons in Narrow‐Gap Semiconductors in the Extreme Quantum Limit at Low Temperatures

“…The inclusion of the quantum screening increases the scattering rate compared to the classical screening and this leads to a reduction in the hot electron conductivity for the quantum screening compared to the classical screening. The effective quantum screening length is found to be less than the Debye inverse screening length due to the quantum confinement effect [3]. This is ultimately responsible for the enhancement in the matrix element of the scattering potential leading to hgher scattering rate for the quantum screening length compared to classical screening.…”

Energy Loss Rate of Hot Electrons in n‐HgxCd1−xTe at High Temperatures in the Presence of a Quantizing Magnetic Field

“…It becomes a magnetic field dependent anisotropic parameter different from the classical Debye screening [4]. The effect of modified screening arising due to magnetic quantization is found to produce a different electric field dependence of the hot electron parameter compared to the classical screening.…”

Alloy scattering limited longitudinal resistivity inn-type Hg0.8Cd0.2Banerji1, Chakraborty2, Sarkar3 1997Phys. Rev. B1000View full textAdd to dashboardCite

“…The quantum effects incorporate important changes in the electron energy spectrum due to the magnetic field ͑Landau quantization͒ and this results in substantial magnetic-field quantum effects that modify the static shield-ing law. [7][8][9][10][11][12] The occurrence of such magnetic-field quantum effects generally results in spatial anisotropy of the shielding law. 9 Such quantum effects, which may be of importance even in the absence of the field, result from the noncommutation of the free-carrier Hamiltonian with the potential of the scattering centers.…”

“…[7][8][9][10][11][12] The occurrence of such magnetic-field quantum effects generally results in spatial anisotropy of the shielding law. 9 Such quantum effects, which may be of importance even in the absence of the field, result from the noncommutation of the free-carrier Hamiltonian with the potential of the scattering centers. The application of the magnetic field causes the electrons to redistribute themselves, resulting in a net increase in the screening length.…”