Energy gap anisotropy in bulk Pb via tunneling

Abstract

We have recently reported a successful tunneling technique for investigating energy gap anisotropy in single crystal Pb. Data from twelve individual junctions are presented here. Two energy gaps Δ 1 and Δ 2 (Δ 2 Δ 1) were apparent in all of the characteristics. The observed anisotropy of the tunneling currents associated with the two gaps suggested that Δ 2 is due to electrons from the 2nd zone hole-surface, while Δ 1 is due to electrons from the 3rd zone electron-surface. Δ 1(0) showed a maximum variation of 5% over the tunneling directions studied. Previously it was reported that Δ 2(0) remained relatively constant but new data indicate that it varies by about 5% in the vicinity of [001]. The extremal values of 2Δ 1(0) were 2.48±0.01 meV and 2.36±0.01 meV while for 2Δ 2(0) they were 2.74±0.01 meV and 2.88±0.01 meV. The temperature dependence of the d V/d I curves shows that all the gaps have the same transition temperature, which is a characteristic of true anisotropy. The relative amplitudes of the phonon structures in d 2 V/d I 2 were found to depend on the tunneling direction.