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.

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• Superconductivity in the vicinity of a ferroelectric quantum phase transition
• Thermal plasmon resonantly enhances electron scattering in Dirac/Weyl semimetals
• Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals
• Kohn-Luttinger Correction to Tc in a Phonon Superconductor
• Synthesizing Coulombic superconductivity in van der Waals bilayers
• The field theory of a superconductor with repulsion
• Twists and turns of superconductivity from a repulsive dynamical interaction
• Quantum phase transition in a clean superconductor with repulsive dynamical interaction
• Acoustic plasmons in type-I Weyl semimetals
• Theoretical determination of the effect of a screening gate on plasmon-induced superconductivity in twisted bilayer graphene
• Odd-frequency pairing and time-reversal symmetry breaking for repulsive interactions
• The shear viscosity of interacting graphene
• Competing phases and critical behavior in three coupled spinless Luttinger liquids
• Acoustic plasmons and isotropic short-range interaction in two-component electron liquids
• The Effect of Repulsion on Superconductivity at Low Density