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Linear magnetoresistance induced by intra-scattering semiclassics of Bloch electrons

The weak field magnetoresistance has seen a revived interest due to the distinct role played by the momentum-space Berry curvature of Bloch electrons. While most previous studies in this regard focus on the inter-scattering motion of semiclassical Bloch electrons in electromagnetic fields, the intra-scattering effects of the semiclassical dynamics augmented by the Berry curvature, magnetic moment and shift vector on the magnetoresistance have been largely overlooked. Here we uncover that these intra-scattering effects, which are neglected in the field-independent relaxation time approximation to the Boltzmann collision integral, can be as important as the inter-scattering ones. Concrete calculations on the two dimensional gapped Dirac model show that the sign of the negative linear magnetoresistance given by the Berry curvature alone is reversed when one considers the magnetic moment and shift vector.