Impact of multiband effects on non-Fermi-liquid transport phenomena in bilayer nickelates

Recently discovered high-$T_c$ superconductivity in thin-film bilayer nickelates La$_3$Ni$_2$O$_7$ under ambient pressure has attracted great interest. Non-Fermi-liquid transport behaviors, such as $T$-linear resistivity and a positive Hall coefficient that increases at low temperatures, have been reported in this system. In this study, we analyze the non-Fermi-liquid transport phenomena in the thin-film bilayer nickelate La$_3$Ni$_2$O$_7$ using a multiorbital tight-binding model. In La$_3$Ni$_2$O$_7$, the cold spots composed of Ni $d_{x^2-y^2}$ orbital emerge, since the spin fluctuations cause stronger quasiparticle damping $γ$ in the Ni $d_{z^2}$ orbital. Notably, in the present study, we derive a rigorous formula for the Hall coefficient $R_H$ incorporating the $γ$ in the quasi-quantum metric (qQM) term. We find that the $T$ dependence of $γ$ in the qQM term is important in determining $R_H$. In La$_3$Ni$_2$O$_7$, the $T$ dependence of $R_H$ becomes pronounced due to the competition between the positive contribution from the hole band and the negative contribution from the electron band. Moreover, the qQM term plays an important role in describing the Nernst coefficient and other transport phenomena involving the second derivative velocity $v^{μν}$.