Impurity, electron–phonon and electron–electron contributions to electrical resistivity of single-crystal Mg1−xAlxB2 Original Research Article

The electrical resistivity of Mg1−xAlxB2 superconductor is analysed from the generalised Bloch–Gruneisen equation and the Debye and Einstein temperatures are estimated by formulating an effective interaction with the long-range Coulomb, van der Waals interaction and the short-range repulsive interaction within the Hafemeister and Flygare approach. Due to inherent two energy gaps, the elastic scatterings of electron from impurities have first been estimated and within a two-band picture, the impurity-limited resistivity due to π band carrierʹs ρ0π is larger as compared to the contribution from σ band carriers. The inelastic scattering of σ band carriers with acoustic phonons dominates over the π band carriers with optical phonons much below T≈θD/2. An investigation exhibiting the mechanism of Mg1−xAlxB2 (x=0.0, 0.1, 0.2) was accomplished by comparing the resistivity estimated by considering both phonons with that of the reported metallic resistivity; accordingly ρdiff=[ρexp−{ρ0+ρe–ph (=ρac+ρop)}] has been analysed through electron–electron scattering. The quadratic temperature dependence of ρdiff=[ρexp−{ρ0+ρe–ph(=ρσe–ph+ρπe–ph)}] is understood in terms of inelastic electron–electron scattering.