Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene

Abstract

We analyze density-wave and Pomeranchuk orders in twisted bilayer graphene. This compliments our earlier analysis of the pairing instabilities. We assume that near half-filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading inter-valley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong coupling approaches, indicating that this order is robust. The other is a mixed state with $120^{\circ }$ complex spin order and orthogonal complex charge order. In addition, we find a weaker, but still attractive interaction in nematic channels, and discuss the type of a nematic order.

arXiv comment15 figures, 48 pages. Version accepted by Phys. Rev. B

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• Parquet renormalization group analysis of weak-coupling instabilities with multiple high-order Van Hove points inside the Brillouin zone
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• The Crossover from Ordinary to Higher-Order van Hove Singularity in a Honeycomb System: A Parquet Renormalization Group Analysis
• Unified picture of superconductivity and magnetism in CeRh${}_2$As${}_2$
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