Transport properties of strongly correlated Fermi systems

In our short review, we consider the transport properties of strongly correlated Fermi systems like heavy fermion metals and high-$T_c$ superconductors. Their transport properties are defined by strong inter-particle interaction forming flat bands in these compounds. Indeed, in contrast to the behavior of the transport properties of conventional metals, the strongly correlated compounds exhibit the linear in temperature resistivity, $\rho(T)\propto T$. We analyze the magnetoresistance and show that it under the application of magnetic field becomes negative. It is shown that near a quantum phase transition, when the density of electronic states diverges, semiclassical physics remains applicable to describe the resistivity $\rho$ of strongly correlated metals due to the presence of a transverse zero-sound collective mode, representing the phonon mode in solids. We demonstrate that when $T$ exceeds the extremely low Debye temperature $T_D$, the resistivity $\rho(T)$ changes linearly with $T$, since the mechanism of formation of the $T$-dependence $\rho(T)$ is similar electron-phonon mechanism, which predominates at high temperatures in ordinary metals. Thus, in the region of $T$-linear resistance, electron-phonon scattering leads to a lifetime of $\tau$ quasiparticles practically independent of the material, which is expressed as the ratio of the Planck constant $\hbar$ to the Boltzmann constant constant $k_B$, $T\tau\sim \hbar/k_B$. We explain that due to the non-Fermi-liquid behavior the real part of the frequency-dependent optical conductivity $\sigma^R_{opt}(\omega)$ exhibits a scaling behavior, and demonstrates the unusual power law behavior $\sigma^R_{opt}(\omega)\propto\omega^{-1}$, rather than the well-known one shown by conventional metals, $\sigma^R_{opt}(\omega)\propto\omega^{-2}$.