The discovery of the quantum hall effect has proven that topology is an imperative element of the quantum description of condensed matter systems. The last decade has seen the discovery of topological insulators, materials that insulate in bulk yet feature conductive surface states. These surface states are protected by topological invariants and host spin-momentum locked electron states, which are profoundly visible in transport as the bulk of the material is highly resistive. Furthermore, in such topological insulators, the topological protection of the surface states makes them robust against disorder and impurities. Topological insulators are therefore highly relevant for laboratory and commercial applications.

Two dimensional films of topological insulators have states on their one dimensional boundary, like a two-lane highway around the coast of an island. The two directions of travel are spin protected, meaning all the electrons traveling in one lane are spin up and all the electrons traveling in the other lane are spin down. This type of electronic transport is called the quantum spin hall effect [1]. Given the existence of one lane, time reversal symmetry mandates the existence of the other. The spatial proximity of the two lanes leads to backscattering between them, as if the electrons make U-turns. Backscattering is encouraged by time-reversal symmetry breaking impurities, but even higher quality materials only exhibit mean free paths of microns.

Doping a topological insulator with ferromagnetic ions breaks time reversal symmetry, allowing one highway lane to exist without the other. Such behavior, called the quantum anomalous hall effect (QAHE), has been realized in magnetically doped (Bi_{1-x}Sb_{x})_{2}Te_{3 }[2]. Electric transport in QAH films is relegated to a single chiral edge mode, which propagates either clockwise or counterclockwise around the boundary of the material, depending on the direction of magnetization. Since there are no states available into which a conduction electron may scatter, QAH materials conduct with virtually no dissipation along their length. As such, we were able to demonstrate the quantization of transport in a QAH material to at least one part in ten-thousand[3].

The novelty of the QAH state of matter leaves a wealth of intriguing questions. The quantum anomalous hall state is a playground for the device physicist. We use macroscopic transport measurements of QAH devices patterned in interesting geometries to address questions about microscale physics. Specifically, we are interested in the role of magnetic domains in the QAH phase as well as in exotic physics (including Majorana modes) resulting from combining QAH materials with superconductors. We are also interested in questions relating to the materials science aspect of QAH materials. Despite the theory, QAH devices are slightly dissipative. We would like to understand the nature and source of this dissipation, in the hope that future QAH materials will exhibit ideal chiral transport at higher temperatures.

Figure 1: Precise quantization of the quantum anomalous hall effect, including zero longitudinal resistance, achived in a hall bar of a magnetic topological insulator. Figure from ref [3].

[1] M. Konig, S. Weidmann, C. Brune, et al. Science 318 (2007)

[2] C. Z. Chang, J. Zhang, X. Feng, et al. Science 340 (2013)

[3] A. J. Bestwick, E. J. Fox, X. Kou, et al. PRL 114 (2015).