Nonlinear Meissner effect in CuO superconductors

Recent theories of the NMR in the CuO superconductors are based on a spin-singlet ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ order parameter. Since this state has nodal lines on the Fermi surface, nonlinear effects associated with low-energy quasiparticles become important, particularly at low temperatures. We show that the field dependence of the supercurrent, below the nucleation field for vortices, can be used to locate the positions of the nodal lines of an unconventional gap in momentum space, and hence test the proposed ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ state.