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De-Haas van-Alphen effect in the quantum limit
In this work we apply the finite temperature formulation of quantum
statistical mechanics to an analysis of the de Haas-van Alphen effect
in the quantum limit. A new expression is derived for the differential
magnetic susceptibility which clearly shows the individual contributions
of zero-temperature and non-zero temperature terms.
Interactions have been included in a linearized approximation
and contact is made with more heuristic approaches.
Approximations in the form of algebraic expressions are made to
the temperature correction terms and these are compared to the exact
result for the various values of the parameters. The results, which
are valid at very low temperatures, may be regarded as the quantum
limit analog of the usual DHVA algebraic result.
Finally, the self-energy is calculated in Landau level states
using a Yukawa potential in the Born approximation. Suggestions are
made for a possible extension to a self-consistent Born approximation
which would retain full quantum number information as well as
incorporate range effects in a realistic fashion