Bad-Metallic Behavior of Doped Mott Insulators

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