Electronic Raman scattering in HgBa_{2}Ca_{2}Cu_{3}O_{8+\delta} single crystals. Analysis of the superconducting state

Electronic Raman-scattering measurements have been performed on ${\mathrm{HgBa}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ single crystals in the superconducting state. Pure electronic Raman spectra with no phonon structures hindering the analysis of the electronic continuum have been obtained. As a consequence, the spectra in the pure ${B}_{1g}$ and ${B}_{2g}$ symmetries are directly and reliably analyzed and the pure ${A}_{1g}$ contribution can be easily identified. Below the critical temperature ${T}_{c},$ two electronic structures at $2\ensuremath{\Delta}\ensuremath{\sim}6.4{k}_{B}{T}_{c}$ and $2\ensuremath{\Delta}\ensuremath{\sim}9.4{k}_{B}{T}_{c}$ are clearly seen. Both are observed simultaneously in pure ${A}_{1g}$ symmetry, the highest energy one being located at the energy of the ${B}_{1g}$ maximum. These two maxima disappear at ${T}_{c}$ and do not soften significantly as the temperature is raised up to ${T}_{c}.$ The low-energy frequency dependence of the ${B}_{1g}$ electronic response is strongly linear, for various excitation lines in the 476.5\char21{}647.1 nm range. Such experimental data cannot be reconciled with a pure ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry. Instead, they strongly advocate in favor of an anisotropic superconducting gap with two distinct gap maxima and of nodes existing outside the [110] and $[1,1\ifmmode\bar\else\textasciimacron\fi{},0]$ directions in k space. We discuss in detail the simplest order parameter compatible with our experimental findings.