Bad-metallic behavior of doped Mott insulators

Employing Nernst-Einstein decomposition $\ensuremath{\sigma}={e}²{\ensuremath{\chi}}_cD$ of the conductivity $\ensuremath{\sigma}$ onto charge susceptibility (compressibility) ${\ensuremath{\chi}}_c$ and diffusion constant $D$, we argue that the bad-metallic behavior of $\ensuremath{\sigma}$ in the regime of high temperatures and lightly doped insulator is dominated by the strong temperature and doping dependence of ${\ensuremath{\chi}}_c$. In particular, we show how at small dopings ${\ensuremath{\chi}}_c$ strongly decreases towards undoped-insulating values with increasing temperature and discuss a simple picture leading to the linear-in-temperature resistivity with the prefactor increasing inversely with decreasing concentration $(p)$ of doped holes, $\ensuremath{\rho}\ensuremath{\propto}T/p$. On the other hand, $D$ shows weak temperature and doping dependence in the corresponding regime. We support our arguments by numerical results on the two-dimensional Hubbard model and discuss the proposed picture from the experimental point of view.