Why the anti-nodal quasiparticle dispersion is so flat in the superconducting cuprates?

Abstract

The emergence of the coherent quasiparticle peak and the development of the peak-dip-hump structure in the anti-nodal region below T c is the most prominent non-BCS signature of the under-doped high-T c cuprates, in which no coherent quasiparticle can be defined in the anti-nodal region above T c. The peak-dip-hump structure has been commonly interpreted as the result of the coupling of the electron to some Bosonic mode. However, such an electron–Boson coupling picture does not answer the question of why the quasiparticle dispersion is so flat in the anti-nodal region, a behavior totally unexpected for Bogoliubov quasiparticle in a d-wave BCS superconductor. Here we show that the sharp quasiparticle peak in the anti-nodal region should be understood as a new pole in the electron Green’s function generated by the strong coupling of the electron to diffusive spin fluctuation around the antiferromagnetic wave vector Q = (π, π), rather than a nearly free Bogoliubov quasiparticle in a d-wave BCS superconductor. More specifically, we find that the normal self-energy of the electron from the scattering with the diffusive spin fluctuation manifests itself mainly as a level repulsion effect and is responsible for the reduction of both the quasiparticle dispersion and the quasiparticle dissipation rate in the anti-nodal region. We argue that the peak-dip separation in the anti-nodal spectrum should not be interpreted as the energy of the pairing glue.