Josephson-frustrated superconductors in a magnetic field

Abstract

We study the effect of an externally imposed rotation or magnetic field on frustrated multiband superconductors and 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 $U(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$-symmetric system, where essentially only the $U(1)$ 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 ${Z}_{2}$ sector. At low enough vorticity there is a corresponding vortex-lattice phase featuring a ${Z}_{2}$ phase transition. We argue that this transition phase should be readily observable in experiments.