Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene

TL;DR

This paper introduces an SU(4) spin-valley-fermion model to study superconductivity in twisted bilayer graphene, revealing multiple competing pairing states and nematic tendencies driven by SU(4) fluctuations.

Contribution

It proposes a novel SU(4) fluctuation-mediated framework for understanding diverse superconducting and ordered states in TBG, highlighting the role of valley and spin symmetries.

Findings

Identification of various pairing states including $f$-wave, $i$-wave, $d+id$, and $p+ip$ with topological properties.

Demonstration of nematic superconductivity arising from near-degenerate order parameters.

Revealing the influence of SU(4) fluctuations on lifting degeneracies and promoting different orders.

Abstract

We propose an SU(4) spin-valley-fermion model to investigate the superconducting instabilities of twisted bilayer graphene (TBG). In this approach, bosonic fluctuations associated with an emergent SU(4) symmetry, corresponding to combined rotations in valley and spin spaces, couple to the low-energy fermions that comprise the flat bands. These fluctuations are peaked at zero wave-vector, reflecting the "ferromagnetic-like" SU(4) ground state recently found in strong-coupling solutions of microscopic models for TBG. Focusing on electronic states related to symmetry-imposed points of the Fermi surface, dubbed here "valley hot-spots" and "van Hove hot-spots", we find that the coupling to the itinerant electrons partially lifts the huge degeneracy of the ferro-SU(4) ground state manifold, favoring inter-valley order, spin-valley coupled order, ferromagnetic order, spin-current order, and valley-polarized order, depending on details of the band structure. These fluctuations, in turn, promote attractive pairing interactions in a variety of closely competing channels, including a nodeless $f$-wave state, a nodal $i$-wave state, and topological $d+id$ and $p+ip$ states with unusual Chern numbers $2$ and $4$, respectively. Nematic superconductivity, although not realized as a primary instability of the system, still appears as a consequence of the near-degeneracy of superconducting order parameters that transform as one-dimensional and two-dimensional irreducible representations of the point group $D_{6}$.