  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.
