Local tunneling probe of low-energy Andreev states on (110) Y$_{0.95}$Ca$_{0.05}$Ba$_2$Cu$_3$O$_{7-\delta}$ thin films in an applied magnetic field

Cryomagnetic scanning tunneling spectroscopy (STS) was performed on (110)-oriented Y$_{0.95}$Ca$_{0.05}$Ba$_2$Cu$_3$O$_ {7-\delta}$ thin films, in order to reveal coherence-length scale information on the symmetry of the high-$T_c$ order parameter (OP) in a magnetic field. In zero-field at 4.2K, both spontaneously split and unsplit zero-bias conductance peaks (ZBCP) are seen in the STS spectrum. The two types of peak spectra exhibit increasing splitting in a field applied along the $c$-axis of the film. Both spontaneous and field-induced ZBCP splitting indicate a lifting in the degeneracy of the low- energy Andreev states, consistent with time-reversal symmetry breaking. These results are discussed within the context of the Doppler effect as well as intrinsic \emph{vs.} field-induced complex components in the high-$T_c$ OP.