c-axis resistivity, pseudogap, superconductivity and Widom line in doped Mott insulators

TL;DR

This paper investigates the temperature and doping dependence of c-axis resistivity in doped Mott insulators, revealing its connection to a hidden first-order transition and Widom line, using advanced computational methods on the Hubbard model.

Contribution

It demonstrates how the c-axis resistivity behavior is governed by a pseudogap to metal transition and the Widom line in the Hubbard model, linking transport properties to underlying phase transitions.

Findings

Resistivity shows metallic and semi-conducting regimes depending on doping and temperature.

The resistivity jump across the transition becomes a crossover at higher temperatures.

Resistivity behavior aligns with the Widom line and pseudogap temperature, indicating a hidden first-order transition influence.

Abstract

Layered doped Mott insulators, such as the cuprates, show unusual temperature dependence of the resistivity. Intriguingly, the resistivity perpendicular to the CuO$_2$ planes, $\rho_c(T)$, shows both metallic ($d\rho_c/dT > 0$) and semi-conducting ($d\rho_c/dT<0$) behavior. We shed light on this puzzle by calculating $\rho_c$ for the two-dimensional Hubbard model within plaquette cellular dynamical mean-field theory and strong-coupling continuous-time quantum Monte Carlo as the impurity solver. The temperature, $T$, and doping, $\delta$, dependencies of $\rho_c$ are controlled by the first-order transition between pseudogap and correlated metal phases from which superconductivity can emerge. On the large doping side of the transition $\rho_c(T)$ is metallic, while on the low-doping side $\rho_c(T)$ changes from metallic to semi-conducting behavior with decreasing $T$. As a function of doping, the jump in $\rho_c$ across the first-order transition evolves into a sharp crossover at higher temperatures. This crossover coincides with the pseudogap temperature $T^*$ in the single-particle density of states, the spin susceptibility and other observables. Such coincidence in crossovers is expected along the continuation of the first-order transition into the super-critical regime, called the Widom line. This implies that not only the dynamic and the thermodynamic properties but also the DC transport in the normal state are governed by the hidden first-order transition. $\rho_c(T)$ has a high-temperature quasi-linear regime where it can exceed the Mott-Ioffe-Regel limit and when it has a minimum it is nearly parallel to the Widom line.