Anisotropic Node Removal in d-wave Superconductors under Magnetic Field

A phenomenological model that considers different secondary $id_{xy}$ gap amplitudes and quasiparticle effective charges for each nodal direction, is proposed to explain the observed anisotropic node removal by a magnetic field in high-$T_{c}$ cuprates. Two independent parity-breaking condensates $<\bar{\Psi_{i}}\bigwedge{\Psi}_{i}>$ develop, implying the induction of a magnetic moment per each nodal direction. The model outcomes are in agreement with the experimentally found relation $\Delta_{i}\sim\sqrt{B}$. The secondary gap vanishes through a second-order phase transition at a critical temperature whose value for underdoped nodal-oriented YBCO is estimated to be $\sim 6K$ for a field of 15 T.