Quantum Anomalous Hall Effect in Topological Insulators

The flow of an electrical current in a typical metal experiences dissipation due to scattering of electrons from defects in the crystal lattice. Systems where electricity can flow without resistance are rather unique, and require a mechanism that results in phase coherent transport. The best known examples are superconductors, where electrons form pairs and condense into a Bose–Einstein condensate (see Chapter 16, Volume 1). The quantum Hall effect (QHE) is another example of dissipationless electrical transport that can occur when a large magnetic field is applied to a high mobility two-dimensional (2D) electron gas at absolute zero. Here, the Landau levels caused by the magnetic field result in edge states with a Hall conductance quantized in integer multiples of e 2 / h and where the longitudinal 4-point resistance goes to zero, though the 2-point resistance does not. The integer multiples of the Hall conductance arise from the topology of the wave functions of the quantum Hall state, and are known as Chern numbers [ 1 ]. The realization that the QHE could be understood by using concepts of topology led to a profound reconceptualization of quantum phases of matter. It is now understood that distinct phases can be defined solely by differences in their topology, in the absence of any symmetry breaking.