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Ballistic electron motion in a random magnetic field

K. B. Efetov·V. R. Kogan
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Abstract

Using a new scheme of the derivation of the non-linear $σ$-model we consider the electron motion in a random magnetic field (RMF) in two dimensions. The derivation is based on writing quasiclassical equations and representing their solutions in terms of a functional integral over supermatrices $Q$ with the constraint $Q^2=1$. Contrary to the standard scheme, neither singling out slow modes nor saddle-point approximation are used. The $σ$-model obtained is applicable at the length scale down to the electron wavelength. We show that this model differs from the model with a random potential (RP).However, after averaging over fluctuations in the Lyapunov region the standard $σ$-model is obtained leading to the conventional localization behavior.

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K. B. Efetov, V. R. Kogan. 2003-10-14. Ballistic electron motion in a random magnetic field. https://doi.org/10.1103/physrevb.68.245313

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