The model for non-Abelian field topology for the multilayer fractional quantum anomalous Hall device - Shen, Jie; Dong, Wen Qi; Shi, Xuewei; Wang, Jing; Wang, Yang; Liu, Han Min (Frontiers in Physics, 2022)
From recent empirical discovery of Quantum Anomalous Hall Effect (QAHE), the interaction of the particle with spin-orbit coupling (SOC) plays an essential role in the cause of QAHE, which includes three terms: external, internal, and chiral symmetric terms. Then the non-Abelian quantum field theory was adopted to analyze and prove the conjecture on the causes that can lead to Fractional Quantum Hall Effect (FQHE). The spontaneously topological chiral symmetry breaking is the main contribution to FQHE, which also includes two terms: the hopping of sublattice, and Coulomb energy by the interaction of many-body particles. More generally, this exciton possesses an intermediate characteristic between the Wannier regimes and displays a peculiar two-dimensional wavefunction in the three-dimensional FQHE states. Finally, a bilayer three-dimensional model is proposed to implement FQHE on lattice by incorporating ferromagnetic dopants into three-dimensional topological insulative thin films. This paper theoretically predicts FQHE on the basis of other reports that have experimentally verified the rationality of the proposed model in magnetic topological insulators.