No abstract

We formulate a Model Hamiltonian of two band superconductivity for Magnesium Diboride superconductors (MgB 2 ). It is a conventional BCS type metallic superconductor which has the highest critical temperature T c =39K. It is assumed that the superconductivity in MgB 2 arises due to metallic nature of the 2D sheets. From band structure calculations, it is observed that two types of bands i.e. σ and π bands are located at Fermi surface. Here, we consider phonon mediated superconductivity in which σ band is dominant over π band i.e. σ band is more coupled to a superconductor with much higher coupling. We consider a model Hamiltonian with mean field approach and solve this by calculating equations of motion of Green functions for a single particle. We determine the quasi-particle energy from the poles of the Green functions. We derive the single particle correlation functions and determine the two SC order parameters for both σ and π band. Here, the two SC order parameters for the bands are solved self-consistently and numerically. The conduction bandwidth (W) is considered as W=8t 0 , where t 0 is the hopping integral. To make all the physical quantities dimensionless, we divide 2t 0 in each of the physical quantities. We then calculate the gap ratio 2∆(0)/K B T c for both the bands. It is seen form our theoretical model that the two bands of MgB 2 superconductors have two different SC gaps with the same critical temperature. We also observe the variation of dispersion curves of quasi-particles for different temperature parameters for both σ and π band.