Half-integer quantization of Hall conductance in semi-magnetic topological insulator*

The emergence of two-dimensional (2D) Dirac fermions in condensed matter systems, such as graphene and three-dimensional (3D) topological insulators, has greatly deepened quantum Hall physics. The anomalous integer quantization of Hall conductance as observed in graphene is understood by the half-integer topological number of each Dirac cone. However, the Dirac cones always appear in pairs in such 2D lattices, hiding the half-integer number from experimental observations. The 3D topological insulators, on the other hand, can possess a single Dirac cone in each top and bottom surface, serving as an ideal system to explore the half-integer quantization phenomena. Here, we will report the observation of half quantized Hall conductance in ‘semi-magnetic’ topological insulator films, where one of the surfaces is gapped by magnetic doping whereas the opposite one remains non-magnetic and gapless. Using time-domain terahertz magneto-optical spectroscopy as well as electrical transport, we observed half quantized Faraday and Kerr rotations and half quantized Hall conductivity at zero fields. This result provides experimental evidence for the predicted fractional quantized state in 3D topological insulators.