Finite Size Effect in the Quantum Anomalous Hall system

We theoretically investigate the finite size effect in quantum anomalous Hall (QAH) system. Using Mn-doped HgTe quantum well as an example, we demonstrate that the coupling between the edge states is spin dependent, and is related not only to the distance between the edges but also to the doping concentration. Thus, with proper tuning of the two, we can get four kinds of transport regimes: quantum spin Hall regime, QAH regime, edge conducting regime, and normal insulator regime. These transport regimes have distinguishing edge conducting properties while the bulk is insulting. Our results give a general picture of the finite size effect in QAH system, and are important for the transport experiments in QAH nanomaterials as well as future device applications.