Fluctuation Effects in Phase-Frustrated Multiband Superconductors

Abstract

In this paper, we compute the phase diagrams of an effective model of a three-dimensional multiband superconductor which is phase-frustrated by interband Josephson couplings. Four different computations are performed and compared: (i) standard mean field theory, (ii) cluster mean field theory, (iii) large-scale Monte Carlo computations including phase fluctuations but no gauge field fluctuations, and (iv) large-scale Monte Carlo computations including phase fluctuations and gauge field fluctuations. Here, phase fluctuations refer to fluctuations in the phases of the components of the superconducting order parameter. Our findings may be summarized as follows: (i) The standard mean field theory treatment fails in locating correctly the positions of the phase transitions, as well as the character of the transitions between the different states. (ii) A cluster mean field calculations taking into account order parameter fluctuations in a local environment improves the results considerably. This shows that phase fluctuations in the superconducting order parameter are important in these three-dimensional systems. The origin of the strong phase fluctuations is frustration due to interband Josephson couplings. However, 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. (iii) Including all phase fluctuations, but no gauge field fluctuations, in the effective model in large-scale Monte Carlo computations yields results essentially in agreement with the cluster mean field calculations. (iv) Including all phase fluctuations and gauge field fluctuations in the effective model in large-scale Monte Carlo computations shows that the inclusion of gauge field fluctuations is crucial in bringing about the novel chiral metallic state in three dimensions.