Superconducting Gap Nodal Surface and Fermi Surface: their partial overlap in cuprates

An actively debated issue in the experimental study of high-Tc cuprate superconductors [1,11,16] is the symmetry and detailed k-dependence of the gap function ∆k. We suggest a form of ∆k, based on physical arguments and numerical results, which is in qualitative agreement with the available experimental results. The form that we suggest is a generalised version of an early suggestion of Anderson [2] in the context of cuprates and even an earlier suggestion of Cohen [3] in the context of sodium metal. In our scenerio, what is of primary importance is the vanishing of gap function on patches of the fermi surface(FS), leading to a gapless superconducting state with finite density of states for quasiparticle excitations at the chemical potential. That is, in the vicinity of finite portions of the FS the gap function has a non-zero value ∆k ≈ ∆1 and in the vicinity of the rest of the portions on the FS the gap function has the form ∆k ≈ (|k|−kF )∆2. Here ∆1 and ∆2 are finite and are weakly dependent on the wave vector k. The issue of the symmetry of the gap function in the context of the above suggestions is discussed at the end of this paper. The local constraint on double occupancy in the conducting CuO2 layer of the cuprates has non-trivial consequence on the structure of the gap function. In a simple tight binding one band large-U Hubbard model or the t − J model of the CuO2 layers (for which there is ample theoretical and experimental evidence) this implies essentially zero on-site pairing amplitude in the superconducting state: ∆ii ≡ 〈ci↑c † i↓〉 = 0, which in k-space means