We report ${}^{11}\mathrm{B}$ 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 $\sim 40\hspace{0.5em}\mathrm{K}$ in a recently discovered ${\mathrm{MgB}}_2.$ We reported in a previous paper [Phys. Rev. Lett. $87,$ 127001 (2001)] that the results of the nuclear-spin-lattice relaxation rate, ${1/T}_1$ in the SC state revealed the existence of a single large SC gap with $2\Delta {/k}_B{T}_c\sim 5.$ This conclusion is corroborated by the calculation that any two-gap models cannot account for the experimental results. In Al-doped ${\mathrm{MgB}}_2,$ the result of ${1/T}_1$ 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 $\omega \sim 700\hspace{0.5em}\mathrm{K}$ and an electron-phonon coupling constant $\lambda \sim \mathrm{0.87.}$ These results suggest that the high-$T_c$ superconductivity in ${\mathrm{MgB}}_2$ is mediated by the strong electron-phonon coupling with high-frequency phonons.

• Received 11 January 2002

DOI:https://doi.org/10.1103/PhysRevB.66.064516