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

Abstract

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 $\frac{1}{2}{e}^2/h$ 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 $\frac{1}{2}{e}^2/h$ Hall conductance quantization of three-dimensional topological insulator surface states, in an experiment which does not require decomposition of signal to separate the contribution of two surfaces. This provides a possible experimental link between quantum Hall physics and axion electrodynamics.

arXiv comment4+6 pages, 5+9 figures

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• Any Axion Insulator Must be a Bulk Three-Dimensional Topological Insulator
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• Distinct quantum anomalous Hall ground states induced by magnetic disorders
• Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures
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• Balanced Quantum Hall Resistor
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• Anomalous Fraunhofer-like patterns in quantum anomalous Hall Josephson junction
• Topological Aspects of Antiferromagnets
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