Silver chalcogenides (e.g., Ag2Te) with slightly altered stoichiometry exhibit an unusual magnetoresistance. It is large and linear in field for magnetic fields up to about 6 tesla and temperatures between 5 and 300 K. [See this 1997 Nature paper].
Several possible physical origins of the magnetoresistance have been proposed.
1. A PRL earlier this year proposes is the material is a topological insulator with gapless surface states described by a highly anisotropic Dirac cone.
2. In 1998 Abrikosov proposed the materials are gapless semiconductors with a linear spectrum, doped to a small carrier concentration, and that only one Landau level contributes to the conductivity.
3. Parish and Littlewood's proposal that the key physics is that of a strongly spatially inhomogeneous semiconductor which can be described by a random resistor network.
4. I also note that a band structure which produces a non-zero Berry curvature can produce a linear magnetoresistance, according to p. 1984 of this Rev. Mod. Phys. [However, I suspect this is a very small effect].
The challenge is to come up with experimental signatures which can distinguish between the four different theoretical proposals.