Intermediately coupled phonon and charge fluctuation induced superconductivity in MgB2 probed by a three square well approach

A three square well model is developed, which allows one to easily calculate the correlation between the coupling strength parameters and superconducting transition temperature (T-c), pressure and volume derivative of T-c and isotope effect exponent for MgB2. Upon considering the three interactions, namely, electron-phonon, electron-plasmon and Coulomb, the analytical solutions for the energy gap equation allow us to understand the relative interplay of these interactions. The values of the coupling strength and of the Coulomb interaction parameter indicate that the superconductor is in the intermediate coupling regime. The superconducting transition temperature of MgB2 for the 2D band is estimated as 41 K for lambda(sigma)(ph) approximate to 0.45, lambda(sigma)(pl) approximate to 0.1 and mu(sigma)* approximate to 0.28. We present correlation curves of T-c with various coupling strengths as electron-phonon (lambda(sigma)(ph)), electron-plasmon (lambda(sigma)(pl)) and the Coulomb screening parameter (mu(sigma)*). The present approach also explains the reported boron isotope effect and the pressure derivative of T-c in the test material. We suggest from these results that both the plasmons and phonons within the framework of a three square well scheme consistently explain the effective electron-electron interaction leading to superconductivity in MgB2. The implications of the effective interactive potential with both sigma and pi carriers and its analysis are discussed.