Universal linear-temperature resistivity: possible quantum diffusion transport in strongly correlated superconductors

The strongly correlated electron fluids in high temperature cuprate superconductors demonstrate an anomalous linear temperature ($T$) dependent resistivity behavior, which persists to a wide temperature range without exhibiting saturation. As cooling down, those electron fluids lose the resistivity and condense into the superfluid. However, the origin of the linear-$T$ resistivity behavior and its relationship to the strongly correlated superconductivity remain a mystery. Here we report a universal relation $d\rho/dT=(\mu_0k_B/\hbar)\lambda^2_L$, which bridges the slope of the linear-$T$-dependent resistivity ($d\rho/dT$) to the London penetration depth $\lambda_L$ at zero temperature among cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and heavy fermion superconductors CeCoIn$_5$, where $\mu_0$ is vacuum permeability, $k_B$ is the Boltzmann constant and $\hbar$ is the reduced Planck constant. We extend this scaling relation to different systems and found that it holds for other cuprate, pnictide and heavy fermion superconductors as well, regardless of the significant differences in the strength of electronic correlations, transport directions, and doping levels. Our analysis suggests that the scaling relation in strongly correlated superconductors could be described as a hydrodynamic diffusive transport, with the diffusion coefficient ($D$) approaching the quantum limit $D\sim\hbar/m^*$, where $m^*$ is the quasi-particle effective mass.