Abstract
We study electronic ordering instabilities of twisted bilayer graphene with $n=2$ electrons per supercell, where correlated insulator state and superconductivity are recently observed. Motivated by the Fermi surface nesting and the proximity to Van Hove singularity, we introduce a hot-spot model to study the effect of various electron interactions systematically. Using renormalization group method, we find $d$/$p$-wave superconductivity and charge/spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density wave state has a gapped energy spectrum at $n=2$ and yields a single doubly-degenerate pocket upon doping to $n>2$. The intertwinement of density wave and superconductivity and the quasiparticle spectrum in the density wave state are consistent with experimental observations.
Highlights
Superconductivity was discovered near a correlated insulator state in bilayer graphene with a small twist angle θ ≈ 1.1° [1,2], where the moirepattern creates a superlattice with a periodicity of about 13 nm
We study interaction-driven ordering instabilities of twisted bilayer graphene around the filling n 1⁄4 2 using renormalization group (RG) by patching the Brillouin zone where the density of states (DOS) is considerably larger than other parts
We introduce a hot-spot model for twisted bilayer graphene and the notion of Fermi surface nesting in hot spots
Summary
Superconductivity was discovered near a correlated insulator state in bilayer graphene with a small twist angle θ ≈ 1.1° [1,2], where the moirepattern creates a superlattice with a periodicity of about 13 nm. This is rather different from the case of a Mott insulator in the strong coupling limit, which would become insulating at much higher temperature Based on these considerations, in this work, we take a weak-coupling approach to study ordered states driven by electron correlation in twisted bilayer graphene. When multiple hot spots are present at a given energy, various scattering processes among them may interfere with each other, leading to intertwined density wave and superconducting instabilities Such hot-spot models were studied with the renormalization group (RG) approach in the context of cuprates [30,31,32,33,34], and recently, by Nandkishore et al, in the context of doped monolayer graphene [35]. We introduce a hot-spot model for twisted bilayer graphene and the notion of Fermi surface nesting in hot spots
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