The chemical equilibrium model is based on the idea of correlated electron pairs, which in singlet state can exist as quasimolecules in the superfluid and normal states of a superconductor. These preformed pairs are bosons which can undergo a Bose-Einstein condensation in analogy with the superfluidity of 4 He+ 3 He -mixture. The bosons (B++) and the fermions (h+) are in chemical equilibrium with respect to the reaction B++⇌ 2 h+, at any temperature. The mean densities of bosons and fermions (quasiholes) nB(T) and nh(T) are determined from the thermodynamics of the equilibrium reaction in terms of a single function f(T). By thermodynamics the function f(T) is connected to equilibrium constant φ (T) by 1-f(T)= [1+φ(T)]-1/2. Using a simple power law, known to be valid near T=0, for the chemical constant φ(T)=α/t2γ, t=T/T*, the mean density of quasiholes is given in closed form. This enables one to calculate the corresponding density of states (DOS) D(E)=NS/N(0), by solving an integral equation. The NIS-tunneling conductivity near T=0, given by D(E) compares well with the most recent experiments: D(E)~ Eγ, for small E and a finite maximum of right size, corresponding to "finite quasiparticle lifetime". The corresponding SIS-tunneling conductivity is obtained from a simple convolution and is also in agreement with recent break junction experiments of Hancotte et al. The position of the maximum can be used to obtain the scaling temperature T*, which comes close to the one measured by Hall coefficient in the normal state. A simple explanation for the spingap effect in NMR is given.
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.
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