CHEMICAL EQUILIBRIUM MODEL FOR HIGH-TC AND HEAVY FERMION SUPERCONDUCTORS: THE DENSITY OF STATES

Abstract

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.