Optical response of correlated electron systems

Recent progress in experimental techniques has made it possible to extract detailed information on dynamics of carriers in a correlated electron material from its optical conductivity, $\sigma(\Omega, T)$. This review consists of three parts, addressing the following three aspects of optical response: 1) the role of momentum relaxation, 2) $\Omega/T$ scaling of the optical conductivity of a Fermi-liquid metal, and 3) optical conductivity of non-Fermi-liquid metals. In the first part (Sec. II), we analyze the interplay between the contributions to the conductivity from normal and umklapp scattering. In the second part (Secs. III and IV), we re-visit the Gurzhi formula for the optical scattering rate, $1/\tau(\Omega,T)\propto\Omega^2+4\pi^2 T^2$, and show that a factor of $4\pi^2$ is the manifestation of the "first-Matsubara-frequency rule", which states that $1/\tau(\Omega,T)$ must vanish upon analytic continuation to the first boson Matsubara frequency. However, recent experiments show that the coefficient $b$ in the Gurzhi-like form, $1/\tau(\Omega,T)\propto\Omega^2+b\pi^2 T^2$, differs significantly from $b=4$ in most of the cases. We suggest that the discrepancy may be due to the presence of elastic scattering, which decreases the value of $b$ below $4$, with $b=1$ corresponding to purely elastic scattering. In the third part (Sec. V), we consider the optical conductivity of metals near quantum phase transitions to nematic and spin-density-wave (SDW) states. In the last case, we focus on "composite" scattering processes, which give rise to a non-Fermi--liquid behavior of the optical conductivity: $\sigma'(\Omega,T)\propto \Omega^{-1/3}$ at low frequencies and $\sigma'(\Omega,T)\propto \Omega^{-1}$ at higher frequencies. We also discuss $\Omega/T$ scaling and show that $\sigma'(\Omega,T)$ in the same model scales in a non-Fermi-liquid way, as $T^{4/3}\Omega^{-5/3}$.