Infrared studies of the superconducting energy gap and normal-state dynamics of the high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

A detailed study of infrared properties (reflectivity, conductivity, and dielectric response), emphasizing reproducible results from fully oxygenated ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ crystals (${\mathit{T}}_{\mathit{c}}$≃93 K) and films, is presented. The extrapolated values of ${\mathrm{\sigma }}_1$(ω) at low frequency are roughly consistent with the measured temperature-dependent dc resistivity. Although not well understood, this infrared conductivity can be interpreted in terms of a frequency-dependent scattering rate of ∼kT+ħω, with a low-frequency mass enhancement of roughly 2 to 4 associated with a carrier-spin related interaction. Infrared measurements polarized along the c axis suggest a conductivity anisotropy of roughly 40:1 near ${\mathit{T}}_{\mathit{c}}$ in the normal state. In the superconducting state an energy scale of 2${\mathrm{\Delta }}_{\mathit{c}}$≃3${\mathit{kT}}_{\mathit{c}}$ is suggested by c-axis polarized measurements, while a much larger characteristic energy of 2${\mathrm{\Delta }}_{\mathit{a}\mathrm{-}\mathit{b}}$≃8${\mathit{kT}}_{\mathit{c}}$ is evident in the (a-b)-plane conductivity. From the area missing from the conductivity up to this very large gap, a reasonable estimate (≃1700 Å) for the (a-b)-plane penetration depth is obtained. Evidence for non-BCS temperature dependence, strong pair breaking scattering, and possible fluctuation effects is discussed. A comparison to infrared data from ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8\mathrm{-}\mathit{y}}$ shows a similarly large energy scale, 2${\mathrm{\Delta }}_{\mathit{a}\mathrm{-}\mathit{b}}$≃8${\mathit{kT}}_{\mathit{c}}$; for the cubic ${\mathrm{Ba}}_{0.6}$ ${\mathrm{K}}_{0.4}$ ${\mathrm{BiO}}_3$ superconductor a more conventional energy scale, 2Δ≃4${\mathit{kT}}_{\mathit{c}}$ is observed. The unusually large energy scale obtained from the (a-b)-plane measurements of the layered cuprates lies far beyond the range of previously studied superconducting energy gaps (2Δ≃3 to 5${\mathit{kT}}_{\mathit{c}}$).