Self-consistent Eliashberg theory, Tc, and the gap function in electron-doped cuprates

Details Self-consistent Eliashberg theory, Tc, and the gap function in electron-doped cuprates Self-consistent Eliashberg theory, Tc, and the gap function in electron-doped cuprates

2010-10-05

arxiv.org/abs/1010.0994v1

Physics

Condensed Matter

Superconductivity

14 pp, 11 figures, submitted to PRB

Scientific paper

We consider normal state properties, the pairing instability temperature, and the structure of the pairing gap in electron-doped cuprates. We assume that the pairing is mediated by collective spin excitations, with antiferromagnetism emerging with the appearance of hot spots. We use a low-energy spin-fermion model and Eliashberg theory up to two-loop order. We justify ignoring vertex corrections by extending the model to N >>1 fermionic flavors, with 1/N playing the role of a small Eliashberg parameter. We argue, however, that it is still necessary to solve coupled integral equations for the frequency dependent fermionic and bosonic self-energies, both in the normal and superconducting state. Using the solution of the coupled equations, we find an onset of d-wave pairing at Tc ~ 30 K, roughly three times larger than the one obtained previously [P. Krotkov and A. Chubukov, Phys. Rev. B 74, 014509 (2006)], where it was assumed that the equations for fermionic and bosonic self-energies decouple in the normal state. To obtain the momentum and frequency dependent d-wave superconducting gap D(k,w), we derive and solve the non-linear gap equation together with the modified equation for the bosonic self energy which below Tc depends on the pairing gap. We find that the gap is a non-monotonic function of momentum along the Fermi surface, with its node along the zone diagonal and its maximum some distance away from it. We obtain 2D/Tc ~ 4. We argue that the value of Tc, the non-monotonicity of the gap, and 2D/Tc ratio are all in good agreement with the experimental data on electron-doped cuprates.

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