Superconductivity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-gallium probed on the atomic scale by normal and Josephson tunneling

We investigate superconducting gallium in its $\ensuremath{\alpha}$ phase using scanning tunneling microscopy and spectroscopy at temperatures down to about 100 mK. High-resolution tunneling spectroscopies using both superconducting and normal tips show that superconducting $\ensuremath{\alpha}$-Ga is accurately described by Bardeen-Cooper-Schrieffer theory, with a gap ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{Ga}}=163\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{eV}$ on the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ga}(112)$ facet, with highly homogeneous spectra over the surface, including atomic defects and step edges. Using a superconducting Pb tip, we furthermore study the low-bias conductance features of the Josephson junction formed between the tip and sample. The features are accurately described by dynamical Coulomb blockade theory, highlighting $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ga}$ as a possible platform for surface science studies of mesoscopic superconductivity.