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arXiv · 2102.09473

Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times2$ matrix operator and physical origin of flat-bands at magic angles

Gerardo G. Naumis·Leonardo A. Navarro-Labastida·Enrique Aguilar-Méndez·Abdiel Espinosa-Champo
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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.

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Gerardo G. Naumis, Leonardo A. Navarro-Labastida, Enrique Aguilar-Méndez, Abdiel Espinosa-Champo. 2021-02-18. Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times2$ matrix operator and physical origin of flat-bands at magic angles. https://doi.org/10.1103/physrevb.103.245418

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