Andreev reflections at large ferromagnet/high-T_C superconductor area junctions with rough interface

Sub-gap conductance at a large area junction with a rough interface of a ferromagnet and a high-T$_{C}$ superconductor is superimposed by multiple peaks which is not expected from an ideal point contact Andreev reflection process. We demonstrate this phenomenon by measuring resistance as a function of bias voltage of a Co/Y$_{1}$Ba$_{2}$Cu$_{3}$O$_{7-delta}$ junction with contact area 50 x 70 $mu$ $m^{2}$ at various temperatures. In order to analyze such Andreev reflection data, the interface is assumed to have random potentials which can create local electric fields. The Blonder-Tinkham-Klapwijk theory is modified with the inclusion of a broadening parameter due to finite life time effects of quasi particles. An additional voltage drop due to local electric fields at the rough interface has been included in terms of an extra energy shift which may be related to the asymmetry of normalized resistance data. Spin polarization has been introduced for the ferromagnet. The presented model explains the multi-peak nature and asymmetry of Andreev reflection data experimentally observed at large area junctions. Extension of the model also interprets the experimentally observed anomalous enhancement of resistance peaks in the sub-gap region which may result from crossing the critical current limit across the junction.