UPPER CRITICAL FIELD OF UNCONVENTIONAL SUPERCONDUCTORS FROM CHEMICAL EQUILIBRIUM

We have shown previously that many normal state properties of high Tc superconductors in zero magnetic field can be understood in terms of a single universal function f(t) in the scaled variable t=T/T*, where T* is connected with temperature independent gap 2Δ=2kBT*, which gives the binding energy of a pair in analogy with dissociation of molecules. The function f(t) determines the fraction of bosons (B++) and fermions (h+) at temperature T and it is obtained from the mathematical treatment of chemical equilibrium with respect to the reaction B++⇌ 2h+. Since for magnetic fields of reasonable strength the Zeeman energy is much smaller than the pseudo gap Δ~100K-800K, the function f(t) in the normal state is largely independent of magnetic field. The main effect of the magnetic field is to increase the tendency for bosons to localize. This means that the critical density nL for delocalization in the ab-plane direction and the critical density for superfluidity nc (≳ nL) both increase with magnetic field. This causes the corresponding temperatures TBL(H) and Tc(H) to go down with the field. Assuming a power law dependence nc(H)/nc(0)=1+AHμ, the upper critical fields for several heavy fermion compounds are shown to fall into a single curve. The purpose here is to show that the upper critical field Hc2(y) (y=Tc(H)/Tc(0)) can be expressed in a simple way in terms of f(t). We show that this theory predicts all the shapes of Hc2(y) observed in several unconventinal superconductors such as Tl 2 Ba 2 CuO 6+δ, with Tc=15 K.