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Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times2$ matrix operator and physical origin of flat-bands at magic angles
- Source :
- Phys. Rev. B 103, 245418 (2021)
- Publication Year :
- 2021
-
Abstract
- The chiral Hamiltonian for twisted graphene bilayers is written as a $2\times2$ 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.
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. B 103, 245418 (2021)
- Publication Type :
- Report
- Accession number :
- edsarx.2102.09473
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevB.103.245418