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Josephson-frustrated superconductors in a magnetic field

We study the effect of an externally imposed rotation or magnetic field on frustrated multiband superconductors/superfluids. The frustration originates with multiple superconducting bands crossing the Fermi surface in conjunction with interband Josephson-couplings with a positive sign. These couplings tend to frustrate the phases of the various components of the superconducting order parameter. This in turn leads to an effective description in terms of a $\groupUZ$-symmetric system, where essentially only the $\groupU$-sector couples to the gauge-field representing the rotation or magnetic field. By imposing a large enough net vorticity on the system at low temperatures, one may therefore reveal a resistive vortex liquid state which will feature an unusual additional phase transition in the $\groupZ$-sector. At low enough vorticity there is a corresponding vortex-lattice phase featuring a $\groupZ$ phase transition. We argue that this Ising transition phase should be readily observable in experiments.