Coherence length and vortex filament in the boson-fermion model of superconductivity

Abstract

The boson-fermion model of high-${\mathit{T}}_{\mathit{c}}$ superconductivity is based on the dominance of the ‘‘s-channel’’ reaction 2e→φ→2e, where φ is a local field, representing phenomenologically the pair state. We show that in this model the coherence length ξ can be calculated and is very small, consistent with observation. This, in turn, justifies the local-field approximation. The relevance of Bose-Einstein condensation is discussed; in this theory, the critical temperature can be much higher than that in the BCS theory. We also examine the vortex filament and the critical magnetic fields ${\mathit{H}}_{\mathit{c}1}$ and ${\mathit{H}}_{\mathit{c}2}$.