Order-parameter-node removal in the d-wave superconductor YBa 2 Cu 3 O 7-x in a magnetic field

We have measured the in-plane tunneling conductance of optimally doped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ 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 ${\ensuremath{\delta}}_{\ensuremath{\downarrow}}(\mathrm{H})$ of the ZBCP in decreasing fields applied perpendicular to the ${\mathrm{CuO}}_{2}$ planes follows the law ${\ensuremath{\delta}}_{\ensuremath{\downarrow}}(\mathrm{H})=\mathrm{A}\ensuremath{\cdot}{\mathrm{H}}^{1/2}$ with $\mathrm{A}=1.1{\mathrm{m}\mathrm{V}/\mathrm{T}}^{1/2}.$ This law is obeyed up to 16 T for film thickness varying from 600 \AA{} (less than the London penetration depth \ensuremath{\lambda}) up to 3200 \AA{} (about twice \ensuremath{\lambda}). Since Meissner currents are negligible in decreasing fields and at thickness smaller than \ensuremath{\lambda}, 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 ${\mathrm{id}}_{\mathrm{xy}}$ 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.