Optical Conductivity and Spatial Inhomogeneity in Cuprate Superconductors

Abstract

We present an overview of the microwave and millimeter wave response of cuprate superconductors, emphasizing two basic types of low-frequency optical conductivity, σ (ω), that these materials exhibit. The first type, exemplified by ultra-pure and stoichiometric YBa 2 Cu 3 O 7−δ (YBCO) single crystals, is well described by a single component originating from the Drude response of thermal quasiparticles. In other cuprate systems that have been studied σ (ω) has an additional component beyond the quasiparticle contribution, also centered at ω = 0. The existence of this peak has not been widely appreciated because most of its spectral weight lies in the " terahertz gap " between microwave and infrared regimes. After re-viewing the evidence for this spectral feature in a wide variety of cuprate compounds, we trace its origin to quenched spatial variation in the superfluid density, ρ s . We show that the trends in optical conductiv-ity as a function of hole carrier concentration in a series of Bi 2 Sr 2 Ca 1−y Dy y Cu 2 O 8+δ (BSCCO) thin films can be understood by adding a component generated by spatial inhomogeneity to the quasiparticle Drude peak. We conclude by discussing the role of optical conductivity measurements in investigating the existence, origin, and importance of inhomogeneity in cuprate superconductors. 7.1. Introduction 7.1.1. Optical Conductivity of Superconductors The dynamical conductivity, σ (q, ω), is the linear response function that relates current density to electric field. The q → 0 limit of σ (q, ω) is referred to as the optical conductivity, or σ (ω), because it describes the response of the medium to electromagnetic waves with wavelength much longer than the characteristic length scales of condensed electronic systems. The real part of the optical conductivity, σ 1 (ω), describes the dissipation of electromagnetic energy in the medium, while the imaginary part, σ 2 (ω), describes screening of the applied field. Measurement of σ (ω) in a superconductor is a powerful method for probing the dynam-ics of quasiparticle excitations and the size of the energy gap. According to BCS theory, there are three dissipative processes that determine σ 1 (ω) in a superconductor: superfluid acceler-ation, pair creation, and quasiparticle scattering. The first is the work required to accelerate electrons to achieve the Meissner screening current. This contribution appears as a δ-function at zero frequency in σ 1 (ω), whose spectral weight is the superfluid density, ρ s . The latter