Quasiparticle tunneling spectra of the high-Tc mercury cuprates:: Implications of the d-wave two-dimensional van Hove scenario

Quasiparticle tunneling measurements of the high-temperature superconductors HgBa2Can-1CunO2n+2+delta (Hg-12(n-1)n,n=1,2,3) are considered in the context of d(x2-y2) symmetry of the superconducting order parameter and a two-dimensional (2D) van Hove singularity (vHs) related to saddle points in the electronic band structure. Normal-metal-insulator-superconductor tunneling spectra taken at 4.2 K with a scanning tunneling microscope on Hg-1212 c-axis epitaxial films, as well as on Hg-1201 and Hg-1223 polycrystalline samples, show distinct gap characteristics which cannot be easily reconciled with the simple s-wave BCS density of states. The data are analyzed with the nodal d-wave gap function Delta(k)=Delta(0)(cos k(x)-cos k(y))/2 and the 2D tight-binding electronic dispersion xi(k)=-2t(cos k(x) + cos k(y))+4t'(cos k(x) cos k(y))-mu, using the quasiparticle tunneling formalism for elastic and specular transmission. The analysis indicates a highly directional and energy-dependent spectral weighting, related to the gap anisotropy and band-structure dependence of the tunneling matrix element \T\(2), and successfully explains the observed gap spectra. Values for the d-wave gap maximum are determined to be Delta(0) approximate to 33, 50, and 75 meV, respectively, for optimally doped Hg-1201, Hg-1212, and Hg-1223, corresponding to reduced-gap ratios of 2 Delta(0)/k(B)T(c) approximate to 7.9, 9.5, and 13. These ratios are substantially larger than the BCS weak-coupling limit of 3.54. A comparison with data from other high-T-c cuprates indicates an overall trend of 2 Delta(0)/k(B)T(c) rising with T-c, in violation of BCS universality.