Effects of gap anisotropy on the electromagnetic response of high-Tc superconductors.

Abstract

We study the nature of the electromagnetic absorption in a superconductor with an anisotropic energy gap and a nonspherical Fermi surface that is either completely closed or open along the direction of the c axis of the crystal. The real part of the electromagnetic conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}$(q,\ensuremath{\omega}) has been calculated for a wide range of the normal-state collision frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ and the parameter Q=max{\ensuremath{\Vert}q\ensuremath{\cdot}${\mathbf{V}}_{\mathit{F}}$\ensuremath{\Vert}}, where q is the incident wave vector of the electromagnetic wave and ${\mathbf{V}}_{\mathit{F}}$ is quasiparticle velocity at the Fermi surface. For simplicity, the model gap parameter \ensuremath{\Delta}(k) is assumed to vary only with the angle \ensuremath{\theta} between the direction k^ of the quasiparticle wave vector and the c axis of the crystal (chosen to be the z direction). We employ a formulation for calculating the linear conductivity in which the collision frequency is directly related to the imaginary part of the single-particle self-energy resulting from various elastic and inelastic collisions.In the presence of gap anisotropy, there is finite absorption below the in-plane gap 2${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$, assumed to be the maximum energy gap. We find that with a bilevel gap parameter consisting of an in-plane value ${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$, a c-axis value of about 1/4 to 1/3 of ${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$, and a sharp transition between them at \ensuremath{\Vert}cos\ensuremath{\theta}\ensuremath{\Vert}\ensuremath{\sim}0.5, we are able to fit quite well the experimental infrared absorption data for the single crsytal ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$, in which q is along the c axis. With \ensuremath{\Elzxh}Q\ensuremath{\ll}${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$, the observed data in the region \ensuremath{\omega}2${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$/\ensuremath{\Elzxh} can be fitted even with a low normal-state collision frequency derived from the normal-state dc conductivity. However, we find that to get a good fit in the region beyond \ensuremath{\omega}=2${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$/\ensuremath{\Elzxh}, ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ must necessarily be large and close to 2.5${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$/\ensuremath{\Elzxh}. Whether this type of frequency-dependent ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ implies electron-electron collision effects in the normal state beyond the normal Fermi-liquid picture or wether this is merely due to the existence of another inelastic scattering channel in the system with a low threshold, cannot be resolved unambiguously.