# Pairing from dynamically screened Coulomb repulsion in bismuth

## TL;DR

This paper proposes that superconductivity in bismuth arises from dynamically screened Coulomb interactions, enhanced by plasma modes and electronic structure, rather than conventional electron-phonon coupling, marking a novel mechanism for superconductivity.

## Contribution

It introduces a model showing Coulomb repulsion can induce pairing in bismuth, highlighting the role of plasma modes and Dirac band structure, a departure from traditional phonon-mediated theories.

## Key findings

- Superconductivity in bismuth can be driven by Coulomb interactions alone.
- The presence of a hole pocket significantly enhances pairing instability.
- Acoustic plasma modes are not central to the pairing mechanism 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.