The Complete Quantum Hall Trio

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Science  12 Apr 2013:
Vol. 340, Issue 6129, pp. 153-154
DOI: 10.1126/science.1237215

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When an electric current I flows through a slab of conductor placed in an external magnetic field H perpendicular to the flow direction, the magnetic field deflects the current-carrying charge particles toward the edge of the conductor and a transverse voltage VT develops across the sample. This effect, discovered by Edwin Hall in 1879 (1), is called the Hall effect. Because the transverse resistance (or Hall resistance) defined as VT/I is proportional to H/n, where n is the sheet carrier density of the sample, the Hall effect has been widely used to quantify the carrier type (electron or hole), density, and mobilities of electronic materials. However, in the 1980s it was found that when the charge carriers are confined to a two-dimensional system (or sheet), the Hall resistance becomes exactly quantized at h/(νe2), where h is the Planck constant, e is the electron charge, and ν is a positive integer, whenever H/n approaches specific values (2). This phenomenon, called the quantum Hall effect (QHE), always requires an external magnetic field. On page 167 this issue (3), Chang et al. have discovered that such exact quantization in the transverse resistance can occur even without an external magnetic field on a thin ferromagnetic topological insulator; the result confirms the long-awaited quantum anomalous Hall effect (QAHE), the final member of the quantum Hall trio (see the figure).