Superconducting pairing and the two-gap nature of Al and C dopedMgB2: screened phonon-pairing mechanism

Abstract

A simplified two-band model for describing the longitudinal dielectric function for a layeredMgB2 system has been developed to reveal the attractive pairing mechanismleading to the superconducting state. A model dielectric function forσ andπ bandcarriers is set up that fulfils the appropriate sum rules on the electronic and ionic polarizabilities.The value of the in-layer electron–phonon coupling strength and the Coulomb screening parameterfor σ (π) band carriers is obtained from the residues of the dielectric function. It is noticed that theσ-holes in the two-dimensional boron planes via the screened phonon coupling isresponsible for the attractive interaction and the superconductor is in the strongcoupling regime. Within this framework, the superconducting transition temperatureTc ofMgB2 is estimated as 42 K and the pressure derivative ofTc isnegative. The isotope effect, coherence length, magnetic penetration depth, and volume derivative ofTc are alsoestimated to be consistent with the earlier results. Within the two-band model of superconductivityin MgB2, we place particular emphasis on intraband channels, carriers either inσ orπ bands,as interband effects are negligible. In such a situation the superconductivity originates from eitherσ orπ band carriers. The implications of the effective interactive potential with bothσ andπ carriers and its analysis are discussed.