How semimetallic bismuth superconducts at half a millikelvin
In plain words
Bismuth crystals, with roughly one mobile electron per hundred thousand atoms, become superconducting at about half a thousandth of a kelvin. Standard theory gives no reliable prediction at such low density with such light carriers.
Precise statement
High-purity Bi single crystals superconduct at $T_{c} \sim 0.53\,\mathrm{mK}$ (Prakash et al., Science 2017) with carrier density about $3e17\,\mathrm{cm}^{-3}$, Fermi energies of order $25\,\mathrm{meV}$ comparable to the Debye energy of order $10\,\mathrm{meV}$, so the Migdal adiabatic approximation fails. Compute $T_{c}$ from a controlled theory (Dirac-like bands with phonon coupling and screening) and determine the pairing symmetry. An answer is a mechanism giving $T_{c}$ within a factor of about 2 together with the predicted gap symmetry.
What would settle it
A non-adiabatic pairing calculation reproducing $0.53\,\mathrm{mK}$ and the measured critical field, tested by the isotope or pressure dependence of $T_{c}$.