Title: Pairing from dynamically screened Coulomb repulsion in bismuth,
Abstract: Recently, Prakash et. al. have discovered bulk superconductivity in single
crystals of bismuth, which is a semi metal with extremely low carrier density.
At such low density, we argue that conventional electron-phonon coupling is too
weak to be responsible for the binding of electrons into Cooper pairs. We study
a dynamically screened Coulomb interaction with effective attraction generated
on the scale of the collective plasma modes. We model the electronic states in
bismuth to include three Dirac pockets with high velocity and one hole pocket
with a significantly smaller velocity. We find a weak coupling instability,
which is greatly enhanced by the presence of the hole pocket. Therefore, we
argue that bismuth is the first material to exhibit superconductivity driven by
retardation effects of Coulomb repulsion alone. By using realistic parameters
for bismuth we find that the acoustic plasma mode does not play the central
role in pairing. We also discuss a matrix element effect, resulting from the
Dirac nature of the conduction band, which may affect $T_c$ in the $s$-wave
channel without breaking time-reversal symmetry.