Microscopic theory on charge transports of a correlated multiorbital system

Current vertex correction (CVC), the back-flow-like correction to the current, comes from conservation laws, and the CVC due to electron correlation contains information about many-body effects. However, it has been little understood how the CVC due to electron correlation affects the charge transports of a correlated multiorbital system. To improve this situation, I studied the inplane resistivity, $\rho_{ab}$, and the Hall coefficient in the weak-field limit, $R_{\textrm{H}}$, in addition to the magnetic properties and the electronic structure, for a $t_{2g}$-orbital Hubbard model on a square lattice in a paramagnetic state away from or near an antiferromagnetic (AF) quantum-critical point (QCP) in the fluctuation-exchange (FLEX) approximation with the CVCs arising from the self-energy ($\Sigma$), the Maki-Thompson (MT) irreducible four-point vertex function, and the main terms of the Aslamasov-Larkin (AL) one. Then, I found three main results about the CVCs. First, the main terms of the AL CVC does not qualitatively change the results obtained in the FLEX approximation with the $\Sigma$ CVC and the MT CVC. Second, $\rho_{ab}$ and $R_{\textrm{H}}$ near the AF QCP have high-temperature region, governed mainly by the $\Sigma$ CVC, and low-temperature region, governed mainly by the $\Sigma$ CVC and the MT CVC. Third, in case away from the AF QCP, the MT CVC leads to a considerable effect on only $R_{\textrm{H}}$ at low temperatures, although $R_{\textrm{H}}$ at high temperatures and $\rho_{ab}$ at all temperatures considered are sufficiently described by including only the $\Sigma$ CVC. I also achieved the qualitative agreement with several experiments of Sr$_{2}$RuO$_{4}$ or Sr$_{2}$Ru$_{0.975}$Ti$_{0.025}$O$_{4}$. Moreover, I showed several better points of this theory than other theories.