q-Analog of the gap equation for cuprates

The q -deformed algebraic method based on the extension of the number concept as proposed by Gauss [1] is used to obtain a q -analog to the gap equation for the cuprates using a tight-binding model. The conventional s -wave symmetry along with the d x 2 - y 2 wave order parameter are considered to understand the effect of q -fermionic theory which is a generalization or deformation of the usual Fermi theory. The dependence of the gap and/or the critical temperature on doping for various values of q is studied. Specific heat and the phase diagram are found to be explicitly dependent on the parameter and the well-known hump-like behavior is detected for q > 1. Moreover, the position of the maximum in T c in the phase diagram depends on the value of q and also on the value of the coupling.