Kekule CDW versus 3-sublattice SDW in magic-angle twisted bi-layer graphene by Fermi surface nesting

By exact numerical calculation of the energy spectrum of a nearest-neighbor electron hopping model for twisted bi-layer graphene (tBLG) at the magic angle[1], we find evidence for nesting of the Fermi surfaces of the flat central bands near half filling. The electron hops over the simplest lattices of bi-layer graphene at commensurate twist angles, with no subcells in the moire pattern. The nesting vector of the Fermi surfaces coincides with the separation between moire valleys in the energy spectrum. We show that this is compatible with Kekule spiral CDW order on the graphene scale within a mean-field description of the Hubbard model for tBLG. It is based on the above nearest-neighbor electron hopping description[1]. We also find that the nested Fermi surfaces are unstable to the formation of SDW order with three sublattices. These results shall be compared to recent experimental observations of Kekule spiral CDW order in twisted bi-layer graphene and in twisted tri-layer graphene at the magic angle[2][3]. Competition between the Kekule CDW and the 3-sublattice SDW shall also be explored.

[1] J.P. Rodriguez, "Flat Electron Bands with Bad Valley Quantum Numbers in Twisted Bi-Layer Graphene", arXiv:2410.18594 .

[2] K.P. Nuckolls et al., "Quantum Textures of the Many-Body Wavefunction in Magic-Angle Graphene", Nature 620, 525 (2023).

[3] H. Kim et al., "Imaging Inter-Valley Coherent Order in Magic-Angle Twisted Trilayer Graphene", Nature 623, 942 (2023).