General Formula for the Magnetoresistance on the Basis of the Fermi Liquid Theory

The general expression for the magnetoresistance due to the Lorentz force is derived by using the Fermi liquid transport theory based on the Kubo formula. The obtained gauge-invariant formula is exact for any strength of the interaction, as for the most singular terms with respect to inverse of the quasiparticle damping, $1/\gamma^\ast$. The virtue of the present formula is that it includes general conserving laws, which is highly required to avoid unphysical results. According to our formula, we can calculate the magnetoresistance systematically within the framework of the conserving approximation, by taking the vertex corrections into account. Especially, the obtained expression is significant for the analysis of strongly correlated systems because the current vertex corrections will play important roles there. In contrast, the conventional Boltzmann approximation is unsatisfactory for correlated systems in that the conservation laws are violated. Our formula coincides with the result of the relaxation time approximation if we drop all the vertex corrections in it. In conclusion, the expression obtained in this paper will be the useful method of deriving a reliable magnetoresistance in strongly correlated systems, such as high-Tc superconductors and heavy Fermion systems. In Appendix D, we reply to the comment by O. Narikiyo in his recent e-print on cond-mat . (Note that Appendix D exists only in the cond-mat version.)