The study focused on the theoretical investigation of superconducting gap parameters, density of states, electronic specific heat and condensation energy of two-band iron based superconductor MgB2. By developing a canonical two band BCS Hamiltonian containing a Fermi Surface of P(π)- and d(σ)-bands for the given system and by using the double time temperature dependent Green’s function formalism, we obtained mathematical expressions for superconducting order parameters for the electron intra-band (Δ_p ), hole intra-band (Δ_d ), inter-band between the two bands (Δ_pd ) and superconducting transition temperature (T_C ). Furthermore, we obtained the density of states for each intra-band, N(ε), electronic specific heat (C_es)and condensation energy (E_c ) for MgB2. By using the experimental values and by considering some plausible approximations of the parameters in the obtained expressions, phase diagrams of superconducting order parameters for Δ_p, Δ_d,Δ_pd versus temperature and superconducting transition temperature (T_C )versus the inter-band pairing potential (V_pd ) are plotted. We also plotted the density of states for the electron intra-band, N_p (ε)and hole intra-band, N_p (ε) versus excitation energy (ε) at T=0K, and the variation of density of states with temperature, electronic specific heat for the electron intra-band (C_p)and hole intra-band(C_p)versus temperature are plotted. Similarly, phase diagrams of condensation energy (E_c ) versus temperature, inter-band pairing potential and superconducting transition temperature are plotted for the material. Our results are in agreement with previous findings.
