Surface edge state and half-quantized Hall conductance in topological insulators

We study the surface local density of states and the transport properties of a three-dimensional (3D) topological insulator (TI) in the presence of a uniform spin-splitting Zeeman field. We find chiral edge states exist on the gapped surfaces of the 3D TI, which can be considered as interface states between domains of massive and massless Dirac fermions. Effectively these states are the result of splitting of a perfect interface conducting channel. This picture is confirmed by the Landauer-Buttiker calculations in four-terminal Hall bars made of 3D TIs. It is demonstrated that the difference between the clockwise and counterclockwise transmission coefficients of the two neighboring terminals is approximately one-half, which suggests that the half-quantized Hall conductance can be manifested in an appropriate experimental setup. We also predict that the quantized anomalous Hall effect exists in thin films of TIs where such effective Zeeman felds are present.