Spectroscopic Evidence for Anisotropic S-Wave Pairing Symmetry in MgB2

Scanning tunneling spectroscopy of superconducting MgB$_2$ ($T_c = 39$ K) were studied on high-density pellets and c-axis oriented films. The sample surfaces were chemically etched to remove surface carbonates and hydroxides, and the data were compared with calculated spectra for all symmetry-allowed pairing channels. The pairing potential ($\Delta_k$) is best described by an anisotropic s-wave pairing model, with $\Delta_k = \Delta_{xy} \sin ^2 \theta_k + \Delta_z \cos ^2 \theta_k$, where $\theta_k$ is the angle relative to the crystalline c-axis, $\Delta_z \sim 8.0$ meV, and $\Delta_{xy} \sim 5.0$ meV.