Effects of phonon interaction on the pairing in the high-T$c$ superconductors

Abstract

We study the effects of phonon interaction on the superconducting pairing in the background of a d-wave gap, mediated by antiferromagnetic (AFM) spin fluctuations, using coupled BCS gap equations. We found that phonon interaction can induce a s-wave component to the d-wave gap in the (D+S) form with an interaction anisotropy and in the (D+$i$S) form without anisotropy, respectively. In either case, however, T${}_c$ is not enhanced compared to the pure d-wave pairing without phonon interaction. On the other hand, anisotropic phonon interaction can dramatically enhance the d-wave pairing itself and therefore T${}_c$, together with the AFM spin fluctuation interaction. This (D${}_{AFM}$ + D${}_{ph}$) type pairing exhibits strongly reduced isotope coefficient despite the large enhancement of T${}_c$ by phonon interaction. Finally, we study the combined type of (D${}_{AFM}$ + D${}_{ph}$ +$i$S)) gap and calculate the penetration depth and specific heat to be compared with the experiments.

arXiv comment9 pages, 10 figures

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• Enhanced superconductivity due to forward scattering in FeSe thin films on SrTiO3 substrates
• Aspects of electron-phonon interactions with strong forward scattering in FeSe Thin Films on SrTiO${}_3$ substrates
• Pairing Mechanism of the Heavily Electron Doped FeSe Systems: Dynamical Tuning of the Pairing Cutoff Energy
• Isotope effect and the role of phonon in the Fe-based superconductors
• Phonon Boost Effect on the $S^{\pm }$-wave Superconductor with Incipient Band