Ballistic electron motion in a random magnetic field

Details Ballistic electron motion in a random magnetic field Ballistic electron motion in a random magnetic field

2003-07-17

arxiv.org/abs/cond-mat/0307424v2

Phys. Rev. B 68, 245313 (2003)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, no figures, to be submitted in PRB v2: Section IV is removed

Scientific paper

10.1103/PhysRevB.68.245313

Using a new scheme of the derivation of the non-linear $\sigma$-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 $\sigma$-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 $\sigma$-model is obtained leading to the conventional localization behavior.

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