Reduction of the twisted bilayer graphene chiral Hamiltonian into a 2 ×2 matrix operator and physical origin of flat bands at magic angles
The chiral Hamiltonian for twisted graphene bilayers is written as a 2 ×2 matrix operator by a renormalization of the Hamiltonian that takes into account the particle-hole symmetry. This results in an effective Hamiltonian written in terms of Pauli matrices with three contributions: a kinetic term, a confinement potential, and a non-Abelian gauge field. The action of the proposed renormalization maps zero-mode flat bands into ground states. On each graphene layer, 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-band modes similar to confined modes observed in other bipartite lattices. At magic angles, it is shown that the intralayer frustration is exactly zero. Surprisingly, 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 twisted two-dimensional superconductor systems.
Physical Review B
- Pub Date:
- June 2021
- Condensed Matter - Mesoscale and Nanoscale Physics;
- Condensed Matter - Materials Science
- Phys. Rev. B 103, 245418 (2021)