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

• Received 10 May 1991

DOI:https://doi.org/10.1103/PhysRevB.45.3048