We consider the effect of thermal fluctuations on the phase of the superconducting order parameter of the Abrikosov flux-line-lattice state of a type-II superconductor. While in the electrodynamic gauges usually chosen there are apparently divergent phase fluctuations, we show that the gauge-invariant phase has a finite average value. Thus, conventional superconducting long-range order is present in a three-dimensional flux line lattice.

• Received 31 January 1990

DOI:https://doi.org/10.1103/PhysRevB.42.906