Quantum nucleation and thermal activation of vortex rings in high-Tc superconductors

Vortex-ring nucleation by thermal activation and quantum-tunneling processes in high-Tc superconductors is discussed. The nonlinear resistance scales as e1/2-(J/J)1/2. Thermal activation yields a critical index of 1/2=1, while quantum tunneling (without normal current dissipation) yields a critical index of 1/2=2. Current-voltage characteristics were measured on both disordered (low-Jc), ordered (c axis normal to the film plane, high-Jc) Y-Ba-Cu-O films, and microbridges below Tc. The data were examined in terms of both thermal-activation and quantum-nucleation models. For the disordered films, the 1/2=1 scaling law is in reasonable agreement with data, while 1/2=2 scaling is required to explain the results of the ordered films at low temperatures. For the microbridges, the 1/2=2 scaling extends even to high temperatures.