Cuprate interband model and doping dependence of the coherence length

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The free energy expansion of a two-band pair-transfer superconductor is developed. A critical in temperature and a noncritical coherence length appear. The effective in-plane ξab, Hc₂ c ξab-2 and the thermodynamic critical magnetic field (Hc₀) on the whole hole doping (p) scale are calculated for a "typical'' cuprate. A doping-prepared bare spectrum with normal state gaps quenched by doping has been used. The coherence length ξab falls with p first rapidly. A moderate enhancement starts when the "cold'' defect band overlap with the valence band is reached. At overdoping ξab rises markedly. The Hc₂ c curve shows a maximum before Tcmax. The bell-like Hc₀-curve follows closely Tc, superconducting gaps, and superfluid density. The theoretical ξab(p) nonmonotonic curve on the whole doping scale agrees with a recent experimental finding.