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On the Nature of the Quantum Anomalous Hall Effect

Kolloquium der Abteilung 2

The importance of the Quantum Hall effect in metrological standards is well established, but its implementation in many situations is hindered by its requirements of a strong magnetic field. Recently, a new material class, magnetically doped topological insulators, has been shown to exhibit an effect, dubbed Quantum Anomalous Hall Effect, with completely novel physical origins and providing a quantized Hall plateau without needing magnetic field.

The effect was first reported in 2013 [1], and very quickly captured the imagination of the field, because of both the beautiful fundamental physics which lead to its existence, and the practical potential it offers for a zero-field resistance standard. The effect was originally reported in a 5 quintuple layer (~5 nm) thick layer of Cr0.15(Bi0.1Sb0.9)1.85Te3, and has since been reproduced in layers ranging in thickness from about 4 to 10 QL, using either Cr or V as the magnetic doping. While the span between 4 and 10 QL may at first not appear very significant, a more careful consideration of the issue reveals that such would be a naive view as it has been experimentally verified in Bi2Se3 that at a thickness of about 6 QL, hybridization between the two surfaces causes a gap to open in the surface state band structure, and delimits the regime between two dimensional (2D) and three dimensional (3D) topological insulator (TI) behavior.

This distinction is all the more interesting given the different theoretical views into the origins of the QAHE in these two regimes. The interpretation presented in the original report, is applicable to a 2D TI, and invokes a lifting of the band inversion of one of the two spin species due to exchange interaction from the internal magnetic field. The theoretical prediction of the QAHE in 3D systems [2] is much more subtle and invokes a correction to the Maxwell equations analogous to the axion term in quantum chromodynamics.

In this talk I will show that proper analysis of the transport characteristics during magnetization reversal can directly reveal [3] the effects of axion corrections to the electromagnetic action, and thus clearly establishes that the 2D and 3D quantum anomalous Hall effects are fundamentally different. I will further discuss the current understand of the underlying origin of the effect in both cases, as well as the various mysteries which remain to be explained in this exciting new playground of physics.


[1]     C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang, L. Lu, X.-C. Ma, and Q.-K. Xue, “Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator” Science, vol. 340, no. 6129, pp. 167 – 170, April 2013.

[2]     K. Nomura and N. Nagaosa, “Surface-quantized anomalous Hall current and the magnetoelectric effect in magnetically disordered topological insulators” Phys. Rev. Lett., vol. 106, no. 166802, April 2011.

[3]     S. Grauer, K. M. Fijalkowski, S. Schreyeck, M. Winnerlein, K. Brunner, R. Thomale, C. Gould, and L. W. Molenkamp, “Scaling of the quantum anomalous Hall effect as an indicator of axion electrodynamicsPhys. Rev. Lett., vol. 118, no. 246801, June 2017.