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-Fermi-liquid 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/τ(Ω,T)∝Ω2+4π2T2, and show that a factor of 4π2 is the manifestation of the 'first-Matsubara-frequency rule' for boson response, which states that 1/τ(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/τ(Ω,T)∝Ω2+bπ2T2, 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)∝Ω−1/3 at low frequencies and σ′(Ω)∝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.