Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics

We report on the scaling behavior of V-doped (Bi,Sb)_{2}Te_{3} samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a two-dimensional integer quantum Hall state, we observe a dimensional crossover to three spatial dimensions as a function of layer thickness. In the limit of a sufficiently thick layer, we find scaling behavior matching the flow diagram of two parallel conducting topological surface states of a three-dimensional topological insulator each featuring a fractional shift of 1/2e^{2}/h in the flow diagram Hall conductivity, while we recover the expected integer quantum Hall behavior for thinner layers. This constitutes the observation of a distinct type of quantum anomalous Hall effect, resulting from 1/2e^{2}/h Hall conductance quantization of three-dimensional topological insulator surface states, in an experiment which does not require decomposition of the signal to separate the contribution of two surfaces. This provides a possible experimental link between quantum Hall physics and axion electrodynamics.