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Superconducting qubit circuits require high quality low critical current density Josephson tunnel junctions. We have developed high quality epitaxial NbN/AlN/NbN tunnel junctions with critical current density, Jc, ranging from as low as a few A/cm2 to a few tens of kA/cm2. In this work, we measured current-voltage characteristics for junctions with a Jc ~ 32 A/cm2 in the temperature range from 17...
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