QUANTUM LIMIT MAGNETOCONDUCTIVITY IN THE DILUTE IMPURITY REGIME
QUANTUM LIMIT MAGNETOCONDUCTIVITY IN THE DILUTE IMPURITY REGIME
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Date
1980-03
Authors
ELEGBA, SHAMSI-DEEN BABATUNDE
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Abstract
Shamsi-Deen Babatunde Elegba for the degree of Doctor of Philosophy
in the Department of Physics to be taken March 1980
Title: Quantum Limit Magnetoconductivity in the Dilute Impurity RegimeSemiclassical calculation shows that in the limit of high magnetic
fields, the Hall conductivity is independent of any scattering mechanism
(for closed orbits of the carriers). That this result is not true
quantum mechanically for impurity scattering was recently shown by
Nozieres and collaborators. However, these workers used an oversimplified
model for the impurity scattering and their calculation contains
some logical inconsistencies.
In the present work, a system containing a low concentration of
impurities with short-ranged potentials in the presence of a very strong
magnetic field is investigated. Here, fairly realistic potential models,
such as the Thomas-Fermi potential are considered. These potential
models are approximated in a systematic fashion to obtain a potential
model for which there is an exact expression for the single-site t-matrix.
The single-site t-matrix is then inserted into a general expression for
the static magnetoconductivity tensor. The potential models used are all non-local and their non-locality alters the velocity operator which
in turn changes the transport properties of the system. This aspect of
the theory is very important and is correctly taken care of in this
work.
A generalization of the Nozieres result is obtained for the Hall
conductivity oxy plus a correction term which is very important in the
case of strong potential scattering. Thus the Hall conductivity obtained
in this work can differ greatly from the usual semiclassical expression
for strong scattering. The result obtained for oxx in the present
work is, however, similar to Nozieres' except that the inconsistency in
the potential model leads to a different numerical result.
Description
A DISSERTATION
Presented to the Department of Physics
and the Graduate School of the University of Oregon
in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Keywords
QUANTUM LIMIT,, MAGNETOCONDUCTIVITY,, DILUTE IMPURITY REGIME,