▎ 摘　　要

Flat band electronic modes in twisted graphene bilayers are responsible for superconducting and other highly correlated electron-electron phases. Although some hints were known of a possible connection between the quantum Hall effect and zero flat band modes, it was not clear how such connection appears. Here the electronic behavior in twisted bilayer graphene is studied using the chiral model Hamiltonian. As a result, it is proved that for high-order magic angles, the zero flat band modes converge into coherent Landau states with a dispersion sigma 2 = 1/3 alpha, where alpha is a coupling parameter that incorporates the twist angle and energetic scales. Then it is proved that the square of the Hamiltonian, which is a 2 x 2 matrix operator, turns out to be equivalent in a first approximation to a two-dimensional quantum harmonic oscillator. The interlayer currents between graphene's bipartite lattices are identified with the angular momentum term while the confinement potential is an effective quadratic potential. By considering the zero-mode equation, the boundary conditions, and a scaling argument, a limiting quantization rule for high-order magic angles is obtained, i.e., alpha m+1 - alpha m = 3/2, where m is the order of the angle. From there, an equipartition and quantization of the kinetic, confinement, and angular momentum contributions is found. All these results are in very good agreement with numerical calculations.