Abstract In this PhD research work, we have theoretically investigated the nature of high-temperature superconductivity in two-band (electron and hole) model for the isovalent-doped ironbased superconductor BaFe 2 (As 1{x P at x = 0.32. We have considered the effects of the electron and hole intra-band superconducting pairing interactions including the interband pair interaction between the two bands in two-band model for the superconductor BaFe 2 (As 1{x P x ) 2 x ) 2 . The dissertation is presented in three main parts. In the first part of the research work, we have theoretically investigated the superconducting order parameters, superconducting transition temperature, density of states and condensation energy in two-band model for the iron-based superconductor BaFe 2 (As . In this study we have considered the effect of all the possible interactions in the electron and hole intra bands, and the inter-band between the two bands in the Bardeen, Cooper and Schrieffer (BCS) mean field approximation (MFA) level for BaFe 2 (As 1{x P . By formulating a system Hamiltonian in two-band model and by employing the retarded double time temperature dependent Green’s function formalism, we have obtained the expressions for the temperature dependence of superconducting order parameters in the electron intra-band, D e (T); hole intra-band, D h (T); inter-band, D eh x ) 2 (T) and in the combined intra-inter band, D intra{inter (T) for the superconductor BaFe 2 (As 1{x P . By using the experimental values and by considering some plausible approximations of the parameters in the obtained expressions, phase diagrams of superconducting order parameters, D x ) 2 e , D h , D versus temperature are plotted. In this research work we obtained that, the values of the total superconducting order parameters at zero temperature due to the effect of all the intra-inter band pairings is, D (0) ' 25 meV which demonstrates the contribution of combined intra-inter band pairing in the two-band model on strengthing the pairing mechanism of high-temperature superconductivity in BaFe intra{inter 2 (As 1{x P . We have also obtained the mathematical expression for the dependence of the superconducting transition temperature (T C ) on the inter-band pairing potential (V eh x ) 2 ) and the phase diagram is plotted. A dramatic enhancements of T C (T C = 49 K) is demonstrated by increasing V for the iron-based superconductor BaFe 2 (As 1{x P x ) 2 eh . Moreover, we obtained the mathematical expressions for the dependence of density of states on excitation energy and temperature in the electron and hole intra-bands and phase diagrams are plotted for BaFe 2 (As 1{x P . Furthermore, we have investigated the dependence of condensation energy (E c x ) 2 eh 1{x P x ) and D 2 intra{inter ) on temperature, inter-band pairing potential and superconducting transition temperature and phase diagrams are plotted based on the obtained mathematical expressions for BaFe 2 (As 1{x P x ) 2 . In the second part of the research work, we have theoretically investigated the possible coexistence of superconductivity and spin density wave (SDW) in two-band model for the iron-based superconductor BaFe 2 (As 1{x P . We are particularly interested in whether the transition between the two states is first order or the two pure phases are separated by an intermediate phase with the coexistence of superconductivity and SDW orders. By formulating a system Hamiltonian in two-band model for the given system and by employing the retarded double time temperature dependent Green’s function formalism, we obtained mathematical expressions for the dependence of superconducting transition temperature (T C ) on SDW order parameter (D SDW x ) 2 ) in the electron and hole intra-bands, and in the inter-band. By using the experimental values and by considering some plausible approximations of the parameters in the obtained expressions, phase diagrams of T in the electron and hole intra-bands, and in the inter-band are plotted for BaFe . Furthermore, we obtained the mathematical expression for the dependence of SDW transition temperature (T SDW ) on the SDW order parameter (D ) and the phase diagram of T SDW versus D SDW is plotted for BaFe 2 (As 1{x P x ) 2 SDW . By merging the phase diagrams we demonstrated the possible coexistence of superconductivity and spin density wave (SDW) in the electron and hole intra-bands, and in the inter-band for the iron-based superconductor BaFe 2 (As 1{x P x ) 2 . Similarly, the third part of this research work focuses on the theoretical investigation of upper critical magnetic field (H C2 ), Ginzburg-Landau coherence length (x ) and GinzburgLandau penetration depth (l GL GL ) in two-band model for the iron-based superconductor BaFe 2 (As 1{x P . By employing the phenomenological Ginzburg-Landau (GL) free energy density functional theory in two-band model in the presence of two superconducting order parameters, we obtained the expressions for the temperature dependence of upper critical magnetic field, H x ) 2 (T); the angular dependence of upper critical magnetic field, H C2 C2 (q) and the temperature dependence of GL coherence length, x (T) and GL penetration depth, l GL (T) for the superconductor BaFe 2 (As 1{x P x ) 2 GL . By using the experimental values in the obtained expressions, the phase diagrams for the temperature dependence of upper critical magnetic fields parallel, H kc C2 (T) and perpendicular, H ?c C2 (T) to the crystallographic c-axis are plotted for BaFe 2 (As 1{x P x ) 2 C versus D 2 (As . Similarly, using the obtained expression the 1{x SDW P x ) 2phase diagram for the angular dependence of upper critical magnetic field, H (q) is plotted for BaFe 2 (As 1{x P . We demonstrated that, the upper critical magnetic field along the ab-plane is greater than along the crystallographic c-axis for BaFe x ) 2 2 (As . The higher upper critical magnetic field values observed in BaFe 2 (As 1{x P x ) 2 1{x indicate the importance of the iron-based superconductors for electrical power and magnet applications. Furthermore, the phase diagrams for the temperature dependence of GL coherence lengths in the ab-plane, x (T) are plotted. We also plotted the phase diagrams for the temperature dependence of GL penetration depths in the ab-plane, l ab GL (T) and along the c-axis, x and along the c-axis, l c GL c GL (T). Finally, the phase diagrams for the GL characteristic parameters, k c GL and k ab GL are plotted and the large values indicate that, BaFe 2 (As is extreme type-II iron-based superconductor. Our results allow us to draw some general conclusions and seem to provide a framework for the interpretation of some of the universal properties of high-temperature iron-based superconductors. The results we obtained in this research work are in broad agreement with previous experimental findings. Keywords: BaFe 2 (As 1{x P , high-temperature superconductivity, iron-based superconductors, two-band model, Green’s function, Ginzburg-Landau theory, order parameters, density of states, condensation energy, spin density wave, upper critical magnetic field. x ) 2 P 1{x x ) P 2 x C2 ) 2 ab GL (T)