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, σ (ω T). This review consists of three parts, addressing the following three aspects of optical response: (1) the role of momentum relaxation; (2) ω/T scaling of the optical conductivity of a Fermi-liquid metal, and (3) the optical conductivity of non-Fermiliquid metals. In the first part (section 2), we analyze the interplay between the contributions to the conductivity from normal and umklapp electron-electron scattering. As a concrete example, we consider a two-band metal and show that although its optical conductivity is finite it does not obey the Drude formula. In the second part (sections 3 and 4), we re-visit the Gurzhi formula for the optical scattering rate, 1/(ω T) α ω2 + 4φ2T2, and show that a factor of 4φ2 is the manifestation of the first-Matsubara-frequency rule for boson response, which states that 1/(ω 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/(ω T)α ω2 + bφ2T2, differs significantly from b = 4 in most of the cases. We suggest that the deviations from Gurzhi scaling may be due to the presence of elastic but energy-dependent scattering, which decreases the value of b below 4, with b = 1 corresponding to purely elastic scattering. In the third part (section 5), we consider the optical conductivity of metals near quantum phase transitions to nematic and spin-density-wave states. In the last case, we focus on composite scattering processes, which give rise to a non-Fermi-liquid behavior of the optical conductivity at T = 0: σ(ω)α ω-1/3 at low frequencies and σ(ω)α ω-1 at higher frequencies. We also discuss ω/T scaling of the conductivity and show that σ( ω, T) in the same model scales in a non-Fermi-liquid way, as T4/3ω-5/3.