Recently, Prakash et al. have discovered bulk superconductivity in single crystals of bismuth, which is a semimetal 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 Tc in the s-wave channel without breaking time-reversal symmetry.
|Journal||Physical Review B|
|State||Published - 5 Dec 2017|
Bibliographical noteFunding Information:
We thank Srinivasan Ramakrishnan, Lucile Savary, Jorn Venderbos, Inti Sodemann, Yuki Nagai, Brian Skinner, and Anshul Kogar for many helpful discussions and for pointing out important papers. We also thank Nandini Trivedi and Andrew Dane for pointing out Ref.  . J.R. acknowledges a scholarship by the Gordon and Betty Moore Foundation under the EPiQS initiative under Grant No. GBMF4303. P.A.L. acknowledges the support of DOE under Grant No. FG02-03ER46076.
© 2017 American Physical Society.