Renormalization Group Study of the Electron-phonon Interaction in the High Tc Cuprates

Abstract

We generalize the numerical renormalization group scheme 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 $x^2-y^2$ symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around $(\pi ,\pi )$. 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.

arXiv comment4 pages, 3 figures, references added, added more details about others' previous studies

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Cited by in corpus (16)

• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Atomic-scale Electronic Structure of the Cuprate d-Symmetry Form Factor Density Wave State
• Interplay between electron-phonon and Coulomb interactions in cuprates
• Checkerboard charge density wave and pseudogap in high-$T_c$ cuprates
• Phonons and d-wave pairing in the two-dimensional Hubbard model
• Interacting electrons on trilayer honeycomb lattices
• Superconducting d-wave stripes in cuprates: Valence bond order coexisting with nodal quasiparticles
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• Self-energy feedback and frequency-dependent interactions in the functional renormalization group flow for the two-dimensional Hubbard model
• Instabilities on graphene's honeycomb lattice with electron-phonon interactions
• A strong coupling critique of spin fluctuation driven charge order in underdoped cuprates
• On the Dichotomy between the Nodal and Antinodal Excitations in High-temperature Superconductors
• Gutzwiller Charge Phase Diagram of Cuprates, including Electron-Phonon Coupling Effects
• Response Theory of the Electron-Phonon Coupling
• Fluctuating Cu-O-Cu Bond model of high temperature superconductivity in cuprates
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization