The high-temperature superconductor gap equation

The expressions for superconducting gap (SG) have been derived using the quantum dynamical many-body theory of electron density of states for high-temperature superconductors (HTSs). The developed two-gap equations depend on the temperature, Fermi energy and renormalized electron and phonon energies that emerge as signatures of anharmonic effects. The computation of the SG compared with the Bardeen-Cooper-Schrieffer gap is found to be in good agreement in the low-temperature region with slight deviation near the critical temperature (T-c). The gap equation reveals anisotropic nature and the reduced gap ratio (2 Delta/k(B)T(C) similar or equal to 7.2- 7.5 for YBa2Cu3O7-delta) is found in the upper limit of the reduced gap ratio for HTSs. Both the SG equations approach the same critical temperature. The pairing potential is derived using the SG equation and numerically analyzed for YBa2Cu3O7-delta, which shows that T-C depends on the strength of the pairing potential and we explore the possibilities to elevate the transition temperature T-c.