Renormalization group study of the electron-phonon interaction in high-Tc cupratesH. C. Fu1, C. Honerkamp2, 3 and D.-H. Lee1, 4, 5
1 Department of Physics, University of California at Berkeley Berkeley, CA 94720, USA
2 Institute for Theoretical Physics, Universität Würzburg D-97074 Würzburg, Germany
3 Max-Planck-Institute for Solid State Research - D-70569 Stuttgart, Germany
4 Material Science Division, Lawrence Berkeley National Laboratory Berkeley, CA 94720, USA
5 Center for Advanced Study, Tsinghua University - Beijing 100084, PRC
received 20 March 2006; accepted in final form 17 May 2006
published online 9 June 2006
We generalize the numerical renormalization group (RG) scheme of Honerkamp et al. (Phys. Rev. B, 63 (2001) 035109), Zanchi et al. (Europhys. Lett., 44 (1997) 235; Phys. Rev. B, 61 (2000) 13609) and Halboth et al. (Phys. Rev. Lett., 85 (2000) 5162) to study the phonon-mediated retarded interactions in the high-Tc cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a x2-y2 symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around . After growing strong, these retarded interaction will trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders.
74.20.Rp - Pairing symmetries (other than s-wave).
74.25.Kc - Phonons.
74.72.-h - Cuprate superconductors (high-Tc and insulating parent compounds).
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