  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.
