Unifying description of competing chiral and nematic superconducting states in twisted bilayer graphene

TL;DR

This paper unifies the understanding of electron- and phonon-driven superconductivity in twisted bilayer graphene, analyzing the competition between nematic and chiral states and explaining the microscopic origins of their rivalry.

Contribution

It introduces a unified intra-Chern pairing framework that maps electron-driven pairing onto phonon-mediated models, clarifying the competition between nematic and chiral superconducting states in TBG.

Findings

Chiral state hosts unpaired flat bands within the gap, disfavoring it.

Nematic order is locally preferred but incompatible across the Brillouin zone.

Momentum-space frustration favors chiral states at large fillings or weak interactions.

Abstract

We reveal a striking correspondence between electron- and phonon-driven pairing in twisted bilayer graphene (TBG) by mapping an atomistic electronically driven pairing model onto an effective inter-valley, intra-Chern description, originally proposed for phonon-mediated superconductivity. Within the unified framework of intra-Chern pairing, we analyze the competition between nematic and chiral superconducting states. The latter corresponds to the extreme Chern-polarized limit and thus hosts unpaired flat bands within the superconducting gap, which generally disfavors it relative to the nematic states. Crucially, nematic order is locally preferred at each momenta, but the optimal nematic directions are incompatible across the Brillouin zone due to the broken rotation symmetry. This momentum-space frustration enables a chiral ground state at large fillings or weak interactions. Our results thereby both provide a unified understanding of superconductivity in TBG, with a natural cooperation of electron- and phonon-mediated pairing, and clarify the microscopic origin of the competition between the chiral and nematic superconducting states.