Confinement-induced chiral edge channel interaction in quantum anomalous Hall insulators

Quantum anomalous Hall (QAH) insulators are well-known for their insulating bulk and non-dissipative chiral edge states, but the penetration depth of the chiral edge states and how they interact with the bulk state have not been fully understood. Some previous studies suggested that the edge states decay exponentially into the bulk with a penetration depth of a few nm, while the others argued that this length is much longer (~ 10² nm). A recent experiment found that at the charge neutral point, the QAH effect persists in narrow devices with widths down to ~72 nm, and the Hall resistance slowly deviates from the quantized value as the width is reduced. To understand these observations, here we theoretically investigate the chiral edge states in a QAH system. We show that the chiral edge states exhibit a short, intrinsic penetration depth of a few nm, featuring the exponential decay. We also demonstrate that disorders can extend the chiral edge states into the bulk, which further facilitates the interaction between two edge states, and thus leads to slight deviations from the perfect QAH.