Evidence for strong-coupling s-wave superconductivity in MgB 2: 11B-NMR study of MgB 2 and the related materials

Abstract

We report the results of nuclear spin–lattice relaxation time, T 1 of 11B in MgB 2, Al-doped MgB 2 and NbB 2. A T 1 T=constant behavior was observed in the normal state, indicating the absence of strong magnetic correlation. In the superconducting (SC) state, 1/ T 1 shows a tiny coherence peak just below T c and decreases exponentially, demonstrating an s-wave superconductivity. The magnitude of SC gap is estimated as 2 Δ/ k B T c∼5, which is quite larger than the weak-coupling value in the BCS theory, 2 Δ/ k B T c=3.5. This rules out a possibility for the multiple SC gaps that was suggested in many literatures. The anisotropy in the upper critical field was also corroborated by the T 1 measurement on a bulk polycrystalline sample. In NbB 2 with a low value of T c=5 K, the T 1 measurement revealed the distinct coherence peak just below T c, followed by an exponential decrease with a magnitude of SC gap 2 Δ/ k B T c=3.1. These data are consistent with the weak-coupling BCS theory. As Al 3+ is substituted for Mg 2+, 1/ T 1 T, which is proportional to the square of the density of states at the Fermi level N( E F), decreases. The variation in T c against the relative changes in N( E F) deduced from 1/ T 1 T is well fitted in terms of the McMillan equation by assuming a characteristic phonon frequency ω ∼ 700 K and an electron–phonon coupling constant λ ∼ 0.87. Thus obtained values are in good agreement with the values suggested by the theoretical works. The high- T c superconductivity in MgB 2 is shown to occur through the strong coupling with high frequency phonons.