  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.
