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

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Summary

Introduction

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].

Model Hamiltonian and Calculation of SC Order Parameter
Result and Discussion
Conclusion

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