Abstract
The quantum Hall (QH) effect1 is observed in two-dimensional electronic systems (2DES’s) subjected to a strong, uniform, transverse external magnetic field. Experi mentally, such systems are realized as inversion layers that form at the interfaces of heterostructures (e.g., GaAs/Al x Ga1−xAs) in the presence of an electric field (gate voltage) perpendicular to the structures. To develop an idea of the orders of magnitude involved in QH systems, we recall that sample sizes are typically of a few tenths of a mm times a few mm, whereas the charge carrier densities, n = n electron - n hole, are of the order of 1011/cm2, and the magnetic fields, B c , range from about 0.1 T up to 30 T. Moreover, experiments are performed at very low temperatures, T, typically between 10 mK and 100 mK. An important quantity characterizing QH systems is the filling factor v. denoting by Φ o = h/e = 4.14 · 10−11 Tcm2 the magnetic flux quantum and by B c,⊥ the component of the magnetic field B c perpendicular to a 2DES, the filling factor is defined by v = nΦo/B c,⊥.
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Fröhlich, J., Studer, U.M., Thiran, E. (1994). An ADE-O Classification of Minimal Incompressible Quantum Hall Fluids. In: Fannes, M., Maes, C., Verbeure, A. (eds) On Three Levels. NATO ASI Series, vol 324. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2460-1_23
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