Evidence for high-frequency phonon mediated S-wave superconductivity: ¹¹B NMR study of Al-doped MgB₂

We report ¹¹B NMR studies that address the underlying two superconducting (SC) gaps model and a possible mechanism for interpreting a high SC transition temperature (T_c) of ∼40 K in a recently discovered MgB₂. We reported in a previous paper [Phys. Rev. Lett. 87, 127001 (2001)] that the results of the nuclear-spin-lattice relaxation rate, 1/T₁ in the SC state revealed the existence of a single large SC gap with 2Δ/k_BT_c∼5. This conclusion is corroborated by the calculation that any two-gap models cannot account for the experimental results. In Al-doped MgB₂, the result of 1/T₁ in the SC state revealed that a size in the SC gap is not changed by substituting Al for Mg. The reduction in T_c by Al doping is shown to be due to the decrease of the density of states N(E_F) at the Fermi level. According to the McMillan equation, an experimental relation between T_c and the relative change in N(E_F) allowed us to estimate a characteristic phonon frequency ω ∼700 K and an electron-phonon coupling constani λ∼0.87. These results suggest that the high-T_c superconductivity in MgB₂ is mediated by the strong electron-phonon coupling with high-frequency phonons.