Doping dependence of electron-electron scattering in Na$_x$CoO$_2$

The in-plane resistivity $\rho$ was measured down to 40 mK for a single crystal of Na$_x$CoO$_2$ ($x$ = 0.75), which has spin-density-wave order below $T_c$ = 22 K. We show its Fermi-liquid ground state by observing a $T^2$ dependence of $\rho$ at low temperature, $\Delta \rho = AT^2$. The measured value of coefficient $A$ = 2.60 $\mu \Omega$ cm K$^{-2}$ is about 100 and 3 times of that in Na$_{0.31}$CoO$_2$ and Na$_ {0.70}$CoO$_2$, respectively, indicating an increase of electron-electron scattering upon Na doping. The enormous $A$, and the moderate electron specific heat coefficient $\gamma$, gives an even larger Kadowaki-Woods ratio $A/\gamma^2$ than that previously reported in Na$_{0.70}$CoO$_2$ (Li {\it et al.}, Phys. Rev. Lett. {\bf 93}, 056401 (2004)).