Experimental indications for the role of the van Hove singularity (vHs) in the electronic density of states of high Tc superconductors are discussed. It is argued that (i) like the resistivity, the measured temperature and doping dependences of the normal state electronic specific heat of YBCO are consistent with the existence of a vHs and (ii) the doping dependence of Tc in the underdoped and optimally doped regimes may be accounted for mainly by a vHs. Further, we discuss the suppression of the quasiparticle scattering rate below Tc, and the coherence lengths in the hole-doped materials and NCCO. Assuming that the same mechanism for superconductivity operates in the electron-doped and the hole-doped cuprates, we argue that the bosonic mode that causes the superconductivity is strongly influenced by the doping in the overdoped regime. We further argue that this boson involves an energy scale larger than that of phonons and is only weakly coupled to the charge carriers.
Effects of finite superconducting coherence lengths and of phase gradients in topological SN and SNS junctions and rings
