Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times 2$ matrix operator and physical origin of flat-bands at magic angles

Abstract

The chiral Hamiltonian for twisted graphene bilayers is written as a $2\times 2$ matrix operator by a renormalization of the Hamiltonian that takes into account the particle-hole symmetry. This results in an effective Hamiltonian with an average field plus and effective non-Abelian gauge potential. The action of the proposed renormalization maps the zero-mode region into the ground state. Modes near zero energy have an antibonding nature in a triangular lattice. This leads to a phase-frustration effect associated with massive degeneration, and makes flat-bands modes similar to confined modes observed in other bipartite lattices. Suprisingly, the proposed Hamiltonian renormalization suggests that flat-bands at magic angles are akin to floppy-mode bands in flexible crystals or glasses, making an unexpected connection between rigidity topological theory and magic angle twisted two-dimensional heterostructures physics.

References in corpus (2)

• Landau levels in twisted bilayer graphene and semiclassical orbits
• Floquet engineering of twisted double bilayer graphene

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