Tunneling Spectroscopy of Gap Anisotropy in Niobium

The anistropic gap of pure superconducting Niobium has been calculated based on Eliashberg theory with the electron-phonon coupling and phonon density of states computed from density functional theory [1]. Quasiparticle tunneling experiments can in principle reveal the gap structure on the Niobium Fermi surfaces [2]. The tunneling conductance is a convolution of the angle-resolved local density of states on the Fermi surface, the angle-dependent transmission probability, and the derivative of the Fermi distribution function. NIS tunneling normal to different crystalline orientations allows one to determine the gap structure in the high-symmetry directions of the Fermi surface. The gap structure on different sheets can also be revealed if the difference in energy between the gaps for the same direction k/|k| is large compared to 3.5 k_BT. We report results for the tunneling conductance expected for a number of Niobium crystal orientations. Comparison with recent experimental measurements are reported.

[1] Mehdi Zarea, Hikaru Ueki, and J. A. Sauls. “Effects of anisotropy and disorder on the superconducting properties of Niobium,” arXiv:2201.07403 (2022).

[2] E.L. Wolf, Principles of electron tunneling spectroscopy, Oxford University Press (2012).