Classical theory of the Hall-effect in an inhomogeneous magnetic field

Abstract

Inspired by recent experiments by Geim et al. we discuss the classical theory of the Hall effect of a 2 dimensional electron gas in an inhomogeneous magnetic field. The field modulation is in the form of flux tubes created by a superconductor overlayer. We find that an approach, where the vortices are treated as individual scatterers contributing to the collision term in the Boltzman equation will not work --- it leads to a vanishing Hall constant at $T=0$. If the field is treated as a smooth contribution to the driving term in the Boltzman equation, the classical Hall constant emerges, in agreement with experiments when the Fermi wavelength is short in comparison with all other lengths in the problem.