Quantum Anomalous Hall Insulators

Topological insulators are materials that insulate in bulk yet feature topologically protected, conductive surface states. These surface states 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 (Bi1-xSbx)2Te3 [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 the Hall resistance in a QAH material to one part in one million at zero external magnetic field[3].

The novelty of the QAH state of matter opens the door to a variety of exciting experiments and applications. For instance, the zero-field quantized Hall resistance can serve as a known resistance while a Josephson voltage standard can play the role of a known voltage. By combining the two in a single cryostat it is possible to produce a highly accurate quantum current sensor that operates in the nA regime. Such a current sensor was previously impossible because most material systems that display a quantized Hall resistance require large external magnetic fields which destroy the superconductivity necessary for a Josephson device to produce a known voltage. The unidirectional dissipationless transport displayed in the QAH state can also be utilized to construct nonrecripocrial microwave circuit elements. Microwave elements that exhibit a nonreciprocal response to electromagnetic radiation are essential in quantum computation. The isolation provided by the nonreciprocity allows small signals to propagate up from the qubit to classical circuit elements but prevents noise from the electronics and thermal fluctuations from perturbing the qubit.