Impurity and dispersion effects on the linear magnetoresistance in the quantum limit

Magnetoresistance, that is, the change of the resistance with the magnetic field, is usually a quadratic function of the field strength. A linear magnetoresistance usually reveals extraordinary properties of a system. In the quantum limit where only the lowest Landau band is occupied, a quantum linear magnetoresistance was believed to be the signature of the Weyl fermions with 3D linear dispersion. Here, we comparatively investigate the quantum-limit magnetoresistance of systems with different band dispersions as well as different types of impurities. We find that the magnetoresistance can also be linear for the quadratic energy dispersion. We show that both longitudinal and transverse magnetoresistance can be linear if long-range-Gaussian-type impurities dominate, but Coulomb-type impurities can only induce linear transverse magnetoresistance. Moreover, we find a negative longitudinal magnetoresistance in massless Dirac fermions, regardless of the impurity type, as a result of the combined effect of the linear dispersion and the scattering mechanism. Our findings well explain some of the linear magnetoresistance observed in the experiments and provide insights to the understanding of quantum-limit magnetoresistance.