Synopsis: What would Lorentz say?
According to the Lorentz force law, a magnetic field directed parallel to the motion of a charge will not exert a force on the charge. In some materials, however, the electrical resistance changes when a magnetic field is applied along the direction of a current, a counterintuitive result called “longitudinal magnetoresistance.”
If the resistance change is of order a few to a few tens of a percent, then one possible explanation for the effect is that the Fermi surface, and hence the electronic properties of the material, are anisotropic: As electrons move with the current, they fluctuate in the transverse direction, experiencing the Lorentz force from the field. Normally, these fluctuations should cancel each other out and make no net contribution to the resistance along the direction of the current, but if the material is anisotropic, this may not be the case.
Writing in Physical Review B, Hridis Pal and Dimitri Maslov of the University of Florida in Gainesville, US, have used the semiclassical Boltzmann equation to derive necessary and sufficient conditions on the anisotropy of the Fermi surface for longitudinal magnetoresistance to be present. Their results should be useful as a starting point for calculating this effect in specific materials and determining whether experimental results can be explained by electronic structure alone or if other mechanisms are at work. – Brad Rubin