Abstract
We formulate a Model Hamiltonian of two band superconductivity for Magnesium Diboride superconductors (MgB<sub>2</sub>). It is a conventional BCS type metallic superconductor which has the highest critical temperature T<sub>c</sub>=39K. It is assumed that the superconductivity in MgB<sub>2</sub> 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<sub>0</sub>, where t<sub>0</sub> is the hopping integral. To make all the physical quantities dimensionless, we divide 2t<sub>0</sub> in each of the physical quantities. We then calculate the gap ratio 2∆(0)/K<SUB>B</SUB>T<sub>c</sub> for both the bands. It is seen form our theoretical model that the two bands of MgB<sub>2</sub> 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.
Highlights
One of the common, conventional BCS type of superconductor is Magnesium Diboride MgB
Boron atoms are arranged like graphite sheets which are segregated by Magnesium atoms
We have reviewed the experimental observations of MgB superconductors
Summary
Conventional BCS type of superconductor is Magnesium Diboride MgB. Four sheets, two 3D sheets from the π bonding with antibonding ( B − 2P ) and other two nearly cylindrical sheets from 2D σ bonding (B − 2P , ) [13, 14] Experiments such as point-contact spectroscopy [15], specific heat measurement [4, 5], scanning tunneling microscopy [16] and Raman spectroscopy [17], critical current measurement [18] clearly explain the existence of two distinct superconducting gaps with small gaps ∆ 0 =2.8 ± 0.05 MeV and large gap ∆ 0 =7.1 ± 0.1 MeV [19].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
