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Many-body effects on the resistivity of a multiorbital system beyond Landau's Fermi-liquid theory

I review many-body effects on the resistivity of a multiorbital system beyond Landau's Fermi-liquid (FL) theory. Landau's FL theory succeeds in describing electronic properties of some correlated electron systems at low temperatures. However, the behaviors deviating from the temperature dependence in the FL, non-FL-like behaviors, emerge near a magnetic quantum-critical point. These indicate the importance of many-body effects beyond Landau's FL theory. Those effects in multiorbital systems have been little understood, although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multiorbital systems. To improve this situation, I formulate the resistivity of a multiorbital Hubbard model using the extended Éliashberg theory and adopt this method to the inplane resistivity of quasi-two-dimensional paramagnetic ruthenates in combination with the fluctuation-exchange approximation including the current vertex corrections arising from the self-energy and Maki-Thompson term. The results away from and near the antiferromagnetic quantum-critical point reproduce the temperature dependence observed in Sr$_{2}$RuO$_{4}$ and Sr$_{2}$Ru$_{0.075}$Ti$_{0.025}$O$_{4}$, respectively. I highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems.