On the break in the single-particle energy dispersions and the ‘universal’ nodal Fermi velocity in the high-temperature copper oxide superconductors

Abstract

Recent data from angle-resolved photoemission experiments published by Zhou et al. [Nature, 423, 398 (2003)] concerning a number of hole-doped copper-oxide-based high-temperature superconductors reveal that in the nodal directions of the underlying square Brillouin zones (i.e. the directions along which the d-wave superconducting gap is vanishing) the Fermi velocities for some finite range of k inside the Fermi sea and away from the nodal Fermi wave vector k F are to within an experimental uncertainty of approximately 20% the same both in all the compounds investigated and over a wide range of doping concentrations and that, in line with earlier experimental observations, at some characteristic wave vector k ☆ away from k F ( typically amounts to approximately 5% of ) the Fermi velocities undergo a sudden change, with this change (roughly speaking, an increase for ) being the greatest (smallest) in the case of underdoped (overdoped) compounds. We demonstrate that these observations establish four essential facts: firstly, the ground-state momentum distribution function must be discontinuous at k = k ☆; with and denoting the measured velocities close to and , we obtain in which is the ‘Fermi’ velocity corresponding to the case in which (for two-body interaction potentials of shorter range than the Coulomb potential, whereby ); secondly, the single-particle spectral function must at k = k ☆ possess a coherent contribution corresponding to a well-defined quasiparticle excitation at an energy of approximately 70 meV below the Fermi energy; thirdly, the amount of discontinuity in at the nodal Fermi points must be small and ideally vanishing; fourthly, the long range of the two-body Coulomb potential is of vital importance for realization of a certain aspect of the observed behaviour in the Fermi velocities (specifi- cally) in the underdoped regime. The condition conforms with the observation through an earlier angle-resolved photoemission experiment by Valla et al. [Science, 285, 2110 (1999)], on the optimally doped compound Bi2Sr2CaCu2O8 + δ, which shows that the imaginary part of the self-energy along the nodal directions of the Brillouin zone and in the vicinity of the nodal Fermi points satisfies the scaling behaviour characteristic of marginal Fermi-liquid metallic states, for which is indeed vanishing. We present arguments advocating the viewpoint that the observed ‘kink’ in the measured energy dispersions cannot be a direct consequence of electron-phonon interaction, although a finite may possibly arise from this interaction. In other words, even though possibly vital, the role played by phonons in bringing about the latter ‘kink’ must be indirect. Our approach further provides a consistent interpretation of the observed sudden decrease in the width of the so-called ‘momentum distribution curve’ on ‖k| increasing above .