An Empirical Pair-breaking Picture for the Non-linear Meissner Effect in   d-wave Superconductors
  A empirical model is proposed for the observed variation of the London penetration depth of cuprate superconductors with applied magnetic field $H$ below the lower critical field H_c1. It is suggested that the Doppler shift of the quasi-particle energies near the d-wave nodes could cause pair-breaking and that this could be responsible for the non-linear Meissner effect (NLME) investigated in recent experiments. This picture gives a somewhat better description of the observed temperature and field dependencies than the original theory proposed by Yip and Sauls. A calculation based on weak-coupling BCS theory suggests that when there is a finite supercurrent, the state for which pairs are broken in a small angular range around the nodes can have a lower free energy than the d_x^2-y^2 state. 
J.R. Cooper