Pair formation and phase ordering

Pairing can establish a local binding or gap scale before a system develops phase-coherent transport. An actual superconducting transition temperature depends on both the pair scale and the phase stiffness. Low carrier density or weak interlayer coupling can make phase ordering the lower scale even when the pairing amplitude is appreciable. A minimum or smooth interpolation of two estimated scales is a qualitative guide, not a substitute for a self-consistent theory of the crossover.