Bad-Metallic Behavior of Doped Mott Insulators

TL;DR

This paper explains the bad-metallic behavior in doped Mott insulators by analyzing how charge susceptibility and diffusion contribute to conductivity, supported by numerical results on the Hubbard model.

Contribution

It introduces a framework emphasizing the role of charge susceptibility in bad-metallic behavior, supported by numerical Hubbard model data.

Findings

Charge susceptibility decreases with temperature and doping.

Resistivity scales linearly with temperature and inversely with doping.

Diffusion constant shows weak dependence on temperature and doping.

Abstract

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.