Dual proximity effect near superconductor-insulator transition

We show that quantum vortex-loop proliferation may be one possible explanation of the super-long-range proximity effect observed in an insulating underdoped cuprate, using the dual theory of quantum vortices. As a test of this scenario, we propose that a dual proximity effect experiment can confirm the superfluid motion of the quantum vortices in the vortex-proliferated insulator and can measure the divergent correlation lengths near the superconductor-insulator transition.