  We propose a magnetic dual of the Coulomb blockade effect for quantum
nucleation of flux vortex pairs in high-Tc superconducting (HTS) films and
grain boundaries in zero applied field. The magnetic blockade instability
occurs at {\theta} = {\pi}, where {\theta} is the "vacuum" or theta angle. The
{\theta} term has recently been discussed in the context of several other
systems, including charge and spin density waves, topological insulators, the
quantum Hall effect, and spontaneous CP violation. Our model predicts a sharp
pair creation threshold current at {\theta} = {\pi}, analogous to the Coulomb
blockade voltage of a tunnel junction, and explains the observed thickness
dependence of critical currents in HTS coated conductors. We use the
Schr\"odinger equation to compute the evolving macrostate amplitudes, coupled
by a generalized tunneling matrix element. The simulations yield excellent
quantitative agreement with measured voltage-current characteristics of
bi-crystal and other HTS grain boundary junctions. The model also predicts
non-sinusoidal behavior in the voltage oscillations resulting from
time-correlated vortex tunneling.
