Energy gap,Tc, and density of states in high-temperature superconductors for retardeds- andd-wave interactions

We employ strong-coupling theory to investigate the effect of the form of the spectral function ${\mathrm{\alpha }}^2$F for isotropic and anisotropic interactions on the tunneling density of states N(ω), ${\mathrm{T}}_{\mathrm{c}}$, and the ratio 2Δ/${\mathit{k}}_{\mathit{B}}$ ${\mathit{T}}_{\mathit{c}}$. Resistivity data are used to fix the isotropic coupling constant ${\lambda }_0$∼1. This severely restricts the results for s-wave pairing; high-energy spectral weight is required in addition to phonons. The anisotropic interaction is not restricted by the resistivity and thus with d-wave pairing a variety of data, including the linear behavior of N(ω) within the gap, can be fitted without high-energy interactions.