  Quantum anomalous Hall effect, with a trademark of dissipationless chiral
edge states for electronics/spintronics transport applications, can be realized
in materials with large spin-orbit coupling and strong intrinsic magnetization.
After Haldane seminal proposal, several models have been presented to
control/enhance the spin-orbit coupling and intrinsic magnetic exchange
interaction. After brief introduction of Haldane model for spineless fermions,
following three fundamental quantum anomalous Hall models are discussed in this
perspective review: (i) low-energy effective four band model for magnetic-doped
topological insulator (Bi,Sb)2Te3 thin films, (ii) four band tight-binding
model for graphene with magnetic adatoms, and (iii) two (three) band spinfull
tight-binding model for ferromagnetic spin-gapless semiconductors with
honeycomb (kagome) lattice where ground state is intrinsically ferromagnetic.
These models cover two-dimensional Dirac materials hosting spinless, spinful
and spin-degenerate Dirac points where various mass terms open a band gap and
lead to quantum anomalous Hall effect. With emphasize on the topological phase
transition driven by ferromagnetic exchange interaction and its interplay with
spin-orbit-coupling, we discuss various symmetry constraints on the nature of
mass term and the materialization of these models. We hope this study will shed
light on the fundamental theoretical perspectives of quantum anomalous Hall
materials.
