The link between s and d components of electron boson coupling constants in one band d wave Eliashberg theory for high Tc superconductors

The phenomenology of overdoped high Tc uperconductors can be described by a one band d wave Eliashberg theory where the mechanism of superconducting coupling is mediated by antiferromagnetic spin fluctuations and whose characteristic energy Ω0 scales with Tc according to the empirical law Ω0 = 5.8 kBTc. This model presents universal characteristics that are independent of the critical temperature such as the link between the s and d components of electron boson coupling constants and the invariance of the ratio 2∆/kBTc. This situation arises from the particular structure of Eliashberg's equations which, despite being non-linear equations, present solutions with these simple properties.