The Mott insulating state formed from bosons is ubiquitous in solid He-4, cold atom systems, Josephson junction networks and perhaps underdoped high-Tc superconductors. We predict that close to the quantum phase transition to the superconducting state the Mott insulator is not at all as featureless as is commonly believed. In three dimensions there is a phase transition to a low temperature state where, under influence of an external current, a superconducting state consisting of a regular array of wires that each carry a quantized flux of supercurrent is realized. This prediction of the type-II Mott insulator follows from a field theoretical weak-strong duality, showing that this current lattice is the dual of the famous Abrikosov lattice of magnetic fluxes in normal superconductors. We argue that this can be exploited to investigate experimentally whether preformed Cooper pairs exist in high-Tc superconductors.
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