  An intriguing observation on the quantum anomalous Hall effect (QAHE) in
magnetic topological insulators (MTIs) is the dissipative edge states, where
quantized Hall resistance is accompanied by nonzero longitudinal resistance. We
numerically investigate this dissipative behavior of QAHE in MTIs with a
three-dimensional tight-binding model and non-equilibrium Greens function
formalism. It is found that, in clean samples, the geometric mismatch between
the detecting electrodes and the MTI sample leads to additional scattering in
the central Hall bar, which is similar to the effect of splitting gates in the
traditional Hall effect. As a result, while the Hall resistance remains
quantized, the longitudinal resistance deviates from zero due to such
additional scattering. It is also shown that external magnetic fields as well
as disorder scattering can suppress the dissipation of the longitudinal
resistance. These results are in good agreement with previous experimental
observations and provide insight on the fabrication of QAHE devices.

Mesoscale and Nanoscale Physics