Evolution of Low-Energy Andreev States under an Applied Supercurrent in YBa$_2$Cu$_3$O$_{7-\delta}$

We present scanning tunneling spectroscopy measurements on current-carrying YBa$_2$Cu$_3$O$_{7-\delta}$ thin-film strips at 4.2K, showing the evolution of the phase-sensitive low-energy Andreev states. In the low-current regime, well below the Landau depairing limit, the Andreev states are anomalously suppressed, suggesting nanoscale dephasing of the \emph{d}-wave order parameter. Measurements are also made at higher applied current levels to probe possible \emph{local} chiral states in the pairing symmetry. These results will be discussed in the context of order parameter non-rigidity in the high-$T_c$ cuprates.