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Fluctuation effects in phase-frustrated multiband superconductors

We compare the phase-diagrams of an effective theory of a three-dimensional multi-band superconductor obtained within standard and cluster mean-field theories, and in large-scale Monte Carlo simulations. In three dimensions, mean field theory fails in locating correctly the positions of the phase transitions, as well as the character of the transitions between the different states. A cluster mean-field calculations taking into account order-parameter fluctuations in a local environment improves the results considerably for the case of extreme type-II superconductors where gauge-field fluctuations are negligible. The large fluctuations in the multi-component superconducting order parameter originate with strong frustration due to interband Josephson-couplings. A novel chiral metallic phase found in previous works using large scale Monte-Carlo computations, is not obtained either within the single-site mean-field theory or the improved cluster mean-field theory of order parameter fluctuations. In three-dimensional superconductors, this unusual metallic phase originates with gauge-field fluctuations.