Microscopic Study of Two Band Superconductivity in Magnesium Diboride Superconductor (MgB2)

Abstract

We formulate a Model Hamiltonian of two band superconductivity for Magnesium Diboride superconductors (MgB2). It is a conventional BCS type metallic superconductor which has the highest critical temperature Tc=39K. It is assumed that the superconductivity in MgB2 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=8t0, where t0 is the hopping integral. To make all the physical quantities dimensionless, we divide 2t0 in each of the physical quantities. We then calculate the gap ratio 2∆(0)/KBTc for both the bands. It is seen form our theoretical model that the two bands of MgB2 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.