Magnetic field -induced phase transition in a $d_{x^2-y^2}$-wave superconductor at low temperatures

Abstract

We consider, within BCS weak coupling theory, the instability of a $d_{x^2-y^2}$-wave superconductor to a state of mixed symmetry $d+iq$, $q=d_{xy},s$. In zero magnetic field we show that there is a large and physically reasonable range of interaction strengths for which a pure $d_{x^2-y^2}$ state is stable down to T=0. In this case a magnetic field, assumed to couple to quasiparticles via their Doppler shifts in the vortex superflow field, is shown to induce a phase transition at $T=T_c^*\sim \sqrt{H}$. Below $T_c^*$, the density of states remains gapless but its field dependence is substantially supressed. The theory explains many features of recent striking thermal conductivity measurements on BSCCO by Krishana et al.

This paper has been withdrawn due to an error discovered by the Authors in their treatment of the Doppler shifts of quasiparticles and quasiholes