Order-parameter-node removal in the d-wave superconductor YBa ₂Cu₃O_7-x in a magnetic field

We have measured the in-plane tunneling conductance of optimally doped YBa₂Cu₃O_7-x films/In junctions as a function of magnetic field and film orientation. In zero applied field all samples exhibit a zero bias conductance peak (ZBCP) attributed to the d-wave symmetry of the order parameter. In junctions formed on (110) oriented films, the splitting δ_↓(H) of the ZBCP in decreasing fields applied perpendicular to the CuO₂ planes follows the law δ _↓(H) = A · H^1/2 with A = 1.1 mV/T ^1/2. This law is obeyed up to 16 T for film thickness varying from 600 Å (less than the London penetration depth λ) up to 3200 Å (about twice λ). Since Meissner currents are negligible in decreasing fields and at thickness smaller than λ, this splitting cannot be attributed to a Doppler shift of zero energy surface bound states. The data taken in decreasing fields is quantitatively consistent with a field induced id_xy component of the order parameter. The effect of the Doppler shift is prominent in data taken in increasing fields and in the field hysteresis of the splitting.