Theoretical Study of Screening Dependence of Aluminium Doped MgB_2

The screening dependence of superconducting state parameters (\lambda, \mu^\ast, T_\rm c, \alpha and N_0V) of six alloys of aluminium doped MgB_2 systems are studied in the BCS–Eliashberg–McMillan framework by employing five forms of dielectric screening function, viz. random phase approximation (RPA), Harrison, Geldart and Vosko (GV), Hubbard and Overhauser in conjunction with Ashcroft's potential. It is observed that electron-phonon coupling strength \lambda and Coulomb pseudopotential \mu^\ast are quite sensitive to the form of dielectric screening, whereas transition temperature T_\rm c, isotope effect exponent \alpha and effective interaction strength N_0V show weak dependence on the form of dielectric screening function. It is found that the RPA form of dielectric screening function yields the best results for transition temperature T_\rm c for all alloys of the Mg-Al-B system. The results obtained using GV screening are much higher than the experimental results. This shows that all the four dielectric screenings used here almost describe superconductivity in all the alloys of the Mg-Al-B system, but the GV screening is not suitable for such an alloy system.