Phys. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. Could you elaborate (or just give a reference) a little on the scaling theory and Khmelnitskii? The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance takes on the quantized values where is the elementary charge and is Planck's constant. If you also apply a magnetic field in the z-direction, then the electrons that make up the current will experience a Lorentz force. Some of the successful explanations of the effect are summarized in the following. This is where we can start with an explanation of the basics of quantum mechanics for dummies. The key problem with current FQHE theories is the lack of a detailed quantitative theory of how the interaction brings about the new order --- one usually simply posits the state and show that it is gapped, i.e. The low energy effective theories of FQH states are TQFTs (such as Chern-Simons theories). You might know these as the parts of the atom: protons, neutrons, and electrons. 62, 76 (1995), and Khmelnitskii, JETP Lett. The quantum Hall effect has led to three Nobel Prizes in Physics (1985 von Klitzing; 1998 Tsui, Stormer, Laughlin; 2016 Thouless, Haldane, Kosterlitz). @genneth I think you might be referring to a controversy over the "composite fermion" theory. IQHE does not require negligible electron-electron interactions. The quantization of the Hall effect discovered by von Klitzing et al. 4) F(ractional)QHE occurs because of formation of anyons. The only thing IQHE and FQHE have in common is the ultimate physical effect, but the mechanism is very different. ... Understanding Quantum Point Information. In the context of Quantum Hall â¦ Is there any accessible introductory literature into these matters? You can also provide a link from the web. 3) IQHE requires negligible electron-electron interactions and so is dependent on the presence of impurities that shield from Coulomb force. FQH states contain a new kind of order: topological order. This is all in supplement to @Moshe R.'s answer, which is excellent. First, here are some random points that I've been able to gather, 1) I(nteger)QHE occurs due to the presence of Landau levels, 2) IQHE is an embodiment of topological order and the states are characterized by the Chern number that tells us about topologically inequivalent Hamiltonians defined on the Brillouin zone. Oh boy, hard to know where to start. Abstract. But right now I just didn't know where to start as the topic of QHE seems quite huge. Please correct any mistakes I made and/or fill in other important observations, How do explanations 1. and 2. of IQHE come together? Randonauting for Dummies. Impurities however provide the basic scattering potential to achieve some Anderson localisation, which is crucial for actually getting the plateaus --- otherwise one would never get any resistance at all! This is a course on the quantum Hall effect, given in TIFR, Mumbai. However, my point is that for FQHE we have, https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/6188#6188, http://www.amazon.com/Quantum-transport-lattices-subjected-external/dp/3639163869, http://theses.ulb.ac.be/ETD-db/collection/available/ULBetd-04012009-152422/, I(nteger)QHE occurs due to the presence of Landau levels, IQHE is an embodiment of topological order and the states are characterized by the Chern number that tells us about topologically inequivalent Hamiltonians defined on the Brillouin zone, IQHE requires negligible electron-electron interations and so is dependent on the presence of impurities that shield from Coulomb force, F(ractional)QHE occurs because of formation of anyons. Questions related to the quantum Hall effect (the quantisation of resistivity observed when a 2-dimensional electron gas system is subjected to a strong perpendicular magnetic field), as well as formulations of states, topological properties, and applications. 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