Quadratic Dirac fermions and the competition of ordered states in twisted bilayer graphene

TL;DR

This paper proposes that quadratic Dirac fermions with enhanced interaction effects explain the complex phase diagram of twisted bilayer graphene, including insulating, magnetic, and superconducting states, aligning with recent experimental findings.

Contribution

It introduces a quadratic Dirac fermion model with RG analysis that captures the phase diagram and experimental phenomena in twisted bilayer graphene, differing from previous strong-coupling approaches.

Findings

Reproduces the phase diagram with insulating, magnetic, and superconducting states.

Explains STM and tunneling experimental results.

Predicts nematic and nodal superconductivity near half-filling.

Abstract

Magic-angle twisted bilayer graphene (TBG) exhibits a captivating phase diagram as a function of doping, featuring superconductivity and a variety of insulating and magnetic states. The bands host Dirac fermions with a reduced Fermi velocity; experiments have shown that the Dirac dispersion reappears near integer fillings of the moir\'e unit cell -- referred to as the $\textit{Dirac revival}$ phenomenon. The reduced velocity of these Dirac states leads us to propose a scenario in which the Dirac fermions possess an approximately quadratic dispersion. The quadratic momentum dependence and particle-hole degeneracy at the Dirac point results in a logarithmic enhancement of interaction effects, which does not appear for a linear dispersion. The resulting non-trivial renormalisation group (RG) flow naturally produces the qualitative phase diagram as a function of doping -- with nematic and insulating states near integer fillings, which give way to superconducting states past a critical relative doping. The RG method further produces different results to strong-coupling Hartree-Fock treatments: producing T-IVC insulating states for repulsive interactions, explaining the results of very recent STM experiments, alongside nodal $A_2$ superconductivity near half-filling, whose properties explain puzzles in tunnelling studies of the superconducting state. The model explains a diverse range of additional experimental observations, unifying many aspects of the phase diagram of TBG.