Hole doped high-T c cuprate superconductors are strongly correlated electronic systems. In these materials, various electronic orders are often found, but whether they support or compete with superconducting order is not unambiguous. Superconductivity normally manifests itself by a superconducting gap in the electronic density of states (EDOS). In cuprates, a gap appears even in the normal state called the pseudogap (PG). For certain doping range, spin density wave and charge density wave coexist with superconductivity by inducing corresponding additional gaps in the EDOS. In this study, we have tried to obtain expression for superconducting transition temperature, T c by solving the BCS (Bardeen-Cooper-Schrieffer) energy gap equation in the presence of depleted EDOS of various origins and types. We have been successful to solve the weak-coupling BCS integral equation analytically in some special cases and also in the general case by using numerical integration. We have found that depending on conditions these non-pairing gaps/orders can enhance as well as reduce T c .

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Irrespective of the class they belong to, all the hole doped high-T c cuprate superconductors show an anti-correlation between the superconducting transition temperature and the characteristic pseudogap energy in the underdoped region. The doping dependent pseudogap in the quasiparticle spectral density is believed to remove low-energy electronic states and thereby reduce the superconducting condensate. Impurities within the CuO 2 plane, on the other hand, break Cooper pairs in the unitarity limit and diminish superfluid density. Both pseudogap in pure cuprates and impurity scattering in disordered cuprates reduces T c very effectively. In this study we have compared and contrasted the mechanisms of T c degradation due to pseudogap and impurity scattering in hole doped cuprates. We have suggested a framework where both these factors can be treated on somewhat equal footing. Beside impurity and pseudogap dependent superconducting transition temperature, the proposed scenario has been employed to investigate the disorder and hole content dependent isotope exponent in high-T c cuprates in this work.