I have written several posts (e.g, this post) about the outstanding question of the origin of the longitudinal interlayer magnetoresistance is some layered metals. They have the strange property that the magnetoresistance is largest (smallest) when the current is parallel (perpendicular) to the magnetic field direction. This is the opposite angular dependence to that expected if the Lorentz force (F=qvxB) causes the magnetoresistance, as it does in most metals.
Tony Wright brought to my attention a recent preprint
Longitudinal interlayer magnetoresistance in quasi-2D metals
P. D. Grigoriev
He finds a magnetoresistance which has the desired properties. Basically, the magnetoresistance arises because electron scattering rate becomes dependent on the magnetic field. He considers the Landau level structure and calculates the self-energy according to the self-consistent Born approximation for scattering from point-like impurities.
Considering the relative magnitude of the different energy scales
t_perp (interlayer hopping integral), hbar omega_c (Landau level spacing), Gamma (Landau level width due to impurities), Fermi energy
is key to the analysis.
As the magnetic field increases there is crossover from a linear dependence on the magnitude of the magnetic field perpendicular to the layers to a square root dependence.
An outstanding question is whether this mechanism can also describe the unusual temperature dependence, including the violation of Kohler's rule, that is usually associated with this magnetoresistance.