C-axis persistent current and Cooper-pair tunnelling through intrinsic Josephson junctions in a ring-shaped YBa$_2$Cu$_3$O$_{7-\delta}$ film

We present the direct experimental observation of the temperature dependence of the persistent current I$_{cj}$ due to tunneling Cooper pairs along the c-axis intrinsic Josephson junctions integrated into YBa$_2$Cu$_3$O$_{7-\delta}$ ring-shaped thin films. The measured I$_{cj}$ exhibits a linear temperature dependence over a wide range of temperatures well below T$_c$. Similar behavior was observed in different samples, confirming the reproducibility of the fabrication technique and the reliability of the results. Our fabrication and measurement techniques which allowed us to observe ``pure'' Cooper pair tunneling persistent current are superior to other techniques that are unable to separate Cooper pair from quasi-particles tunneling currents.