Why the first magic-angle is different from others in twisted graphene bilayers: Interlayer currents, kinetic and confinement energy, and wave-function localization

• Main Authors: Aguilar-Mendez, E. (Author), Espinosa-Champo, A. (Author), Naumis, G.G (Author), Navarro-Labastida, L.A (Author)
• Format: Article
• Language: English
• Published: American Physical Society 2022
• Subjects: Confinement energy; 'current; Current confinement; Current energy; Current kinetics; Energy and wave functions; Graphene; Graphene bilayers; Hamiltonians; Kinetic energy; Kinetics; Localisation; Magic angle; Sub-lattices; Wave functions
• Online Access: View Fulltext in Publisher

 The chiral Hamiltonian for twisted graphene bilayers is analyzed in terms of its squared Hamiltonian which removes the particle-hole symmetry and thus one bipartite lattice, allowing us to write the Hamiltonian in terms of a 2×2 matrix. This brings to the front the three main physical actors of twisted systems: kinetic energy, confinement potential, and an interlayer interaction operator which is divided in two parts: a non-Abelian interlayer operator and an operator which contains an interaction energy between layers. Here, each of these components is analyzed as a function of the angle of rotation as well as in terms of the wave-function localization properties. It is proved that the non-Abelian operator represents interlayer currents between each layer of triangular sublattices, i.e., a second-neighbor interlayer current between bipartite sublattices. A crossover is seen between such contributions, and thus, the first magic-angle is different from other higher-order magic-angles. Such angles are determined by a balance between the negative energy contribution from interlayer currents and the positive contributions from the kinetic and confinement energies. A perturbative analysis performed around the first magic-angle allows us to explore analytically the details of such an energy balance. © 2022 American Physical Society.