In most metals the magnetoresistance [change in electrical resistance with external magnetic field B] depends quadratically on the B.
The past few years there have been a plethora of papers about linear magnetoresistance in topological insulators, iron pnictide superconductors, and Dirac semi-metals. I wrote a post which discusses the issue and also links to an earlier post that considers different theoretical explanations.
Many of these papers, particularly those in the baby Natures, want to link the linear magnetoresistance to the Dirac cone and possibly the Berry geometric phase associated with it.
However, there are some critical and constructive papers. For example,
Magnetotransport of proton-irradiated BaFe2As2 and BaFe1.985Co0.015As2 single crystals
D. A. Moseley, K. A. Yates, N. Peng, D. Mandrus, A. S. Sefat, W. R. Branford, and L. F. Cohen
By using proton-beam irradiation to change the defect scattering density, we find that the dependence of the magnitude of the linear magnetoresistance on scattering quite clearly contravenes this prediction [of Abrikosov's quantum model].There is a nice paper that gives a rather mundane explanation for the experiments.
Linear magnetoresistance in metals: Guiding center diffusion in a smooth random potential
Justin C. W. Song, Gil Refael, and Patrick A. Lee
We predict that guiding center (GC) diffusion yields a linear and nonsaturating (transverse) magnetoresistance in 3D metals. Our theory is semiclassical and applies in the regime where the transport time is much greater than the cyclotron period and for weak disorder potentials which are slowly varying on a length scale much greater than the cyclotron radius. Under these conditions, orbits with small momenta along magnetic field B are squeezed and dominate the transverse conductivity. When disorder potentials are stronger than the Debye frequency, linear magnetoresistance is predicted to survive up to room temperature and beyond. We argue that magnetoresistance from GC diffusion explains the recently observed giant linear magnetoresistance in 3D Dirac materials.In their calculations the Berry phase plays no role.