The transport properties of strongly correlated materials, such as vanadates, cobaltates, cuprates, Kondo semiconductors and organic demiconductors show the non-Fermi-liquid behavior. One common feature of these vastly different materials is that the resistivity rises linearly with temperature above the Ioffe-Regel limit. Another common feature is that they are formed by doping away from a Mott-Hubbard insulating state. Starting from this observation, and the ubiquity of non-Fermi-liquid materials, we provide a simple explanation for the transport properties.

The linear resistivity is derived using the general properties of the transport relaxation time for a strongly correlated material. The phenomenological results are substantiated by calculating the transport coefficients of the Falicov-Kimball model which, like the Hubbard or periodic Anderson model, has a gap in the excitation spectrum but, unlike these other models, admits an exact solution at arbitrary doping and temperature.
We show that the resistivity ρ(T) and thermopower α(T) of doped Mott-Hubbard systems exhibit simple universal features. (i) Close to the insulating phase, ρ(T) has a sharp lowtemperature upturn and α(T) has a large peak centered at temperature T. (ii) At moderate doping, ρ(T) becomes a linear function, while the peak of α(T) decreases and shifts to lower temperatures; α(T) changes sign for T>>Tα. (iii) At the highest doping, we find that ρ(T) ~ ρ0+AT², and that α(T) is a monotonic function, negative for electron doping and positive for hole doping. This universal behavior follows from the general properties of the transport relaxation time of a doped Mott-Hubbard systems. The high-temperature behavior of α(T) can also be explained by the Kelvin formula and the fact that the chemical potentials for doped Mott insulators display similar behavior at high T.

 

[1] V. Zlatić, G. Boyd and J.K. Freericks, PRL 109, 266601 (2012).
[2] V. Zlatić, G. Boyd and J.K. Freericks, Phys. Rev. B 89, 55101 (2014).
[3] G. Boyd, V. Zlatić and J.K. Freericks, Phys. Rev. B 91, 075118 (2015).