This can also be referred to as the talking walls effect, where it … 6) Hierarchy states are examples of FQH states. It is formal --- the idea is to justify that such a picture makes sense and predicts the right (say) excitations, but there's no "derivation" to be had to get it. 1.2. Could you elaborate (or just give a reference) a little on the scaling theory and Khmelnitskii? 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. https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/6173#6173. FQH states contain a new kind of order: topological order. IQHE is an example of topological order, although topological order is introduced to mainly describe Thank you. Thanks a lot! The quantum mechanical model of the atom uses complex shapes of orbitals (sometimes called electron clouds), volumes of space in which there is likely to be an electron. The only thing IQHE and FQHE have in common is the ultimate physical effect, but the mechanism is very different. Spin Hall effect and Spin‐Orbit Torques An Overview Sergio O. Valenzuela SOV@icrea catSOV@icrea.cat ICREA and Institut Catalá Nanociència iNanotecnologia, ICN2 ... Quantum manipulation and Coupling of spin states Adapted, C. Chappert, Université Paris Sud. ... Quantum Hall effect for dummies. For the integer QHE, the next crucial step is the presence of a random potential, provided by impurities. To be rigorous, let's put the material in the (x,y) plane and let the current flow in the x-direction*. ×'½ÉP´3~Šìžoœˆ¿•N‹¿:|t]{/FY†k“Ø“÷¯Ï±,zî&\ÆÆT@OºŸCyâ’ÂM:F~*¤-¦—´e¯±^¡A3XC[F­Çà͂ŰÜØ*Àc"é This is a course on the quantum Hall effect, given in TIFR, Mumbai. 4) F(ractional)QHE occurs because of formation of anyons. Oh boy, hard to know where to start. Quantum Hall effect for dummies. Buy a copy of Jain's "Composite Fermions" and seal yourself in a comfortable room with plenty of snacks. FQHE. @Moshe R.: Notice that FQHE is not IQHE of anyons --- the anyons only appear as the excitations. Nathan Goldman, Quantum transport and phase transitions in lattices subjected to external gauge fields. qé•Y¼ÓÏê ¯kzÁpC‰Ðè×ï%¬ÐIځÂr€tžVat÷ «+ ¢ÏˆWà‹s1bz€kaT€Ã§þn«$9ñܞ.÷­¤q Incidentally, understanding this point is crucial for understanding why the longitudinal conductance displays the spikes that it does. When scientists look at the tiniest stuff in the universe, things begin to act really weird. Active 3 years, 5 months ago. Work on this aspect is on going (but to be fair, somewhat stalled --- it is sufficiently hard theoretically speaking that one is really looking for some fundamental break through in mathematics to finish it off). Tremendous theoretical and experimental developments are still being made in this sphere. You can visualize each one of them as an electron moving in a circle whose radius is quantized (determined by the Landau level) and whose center can be anywhere (resulting in the degeneracy). Impurities do not screen anything. By the basic physical laws, this force acts in the y-direction. The quasiparticles excitations in IQH states are always fermions. Chapter 3 is devoted to the transport characteristics of the integer quantum Hall effect, and the basic aspects of the fractional quantum Hall effect are described in chapter 4. B 235, 277 (1984). As such, one will come across in the literature many different theories, which emphasise different aspects of the phenomenon, and have differing amounts of complexity and quantitative accuracy. @genneth I think you might be referring to a controversy over the "composite fermion" theory. IQHE can be treated as a special case? Tremendous theoretical and experimental developments are still being made in this sphere. So IQHE is more than the Chern number of energy band. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. If you find this book, those introductions are very good.). In condensed matter this is not always a problem --- many things are really just guesses which work exceptionally well. Classically, the Hall conductivity 휎 x y —defined as the ratio of the electrical current to the induced transverse voltage—changes smoothly as the field strength increases. Fermion alway carry Fermi statistics by definition, and they are never anyons. The integer QH effect was discovered in 1980 by Klaus von Klitzing, while the fractional QH effect was discovered in 1982 by Daniel Tsui, Horst Strömer and Arthur Gossard. In the context of Quantum Hall … This was too long to fit into a comment, so an answer it will have to be. Tremendous theoretical and experimental developments are still being made in this sphere. Together with a detailed introduction by the editor, this volume serves as a stimulating and valuable reference for students and research workers in condensed matter physics and for those with a particle physics background. An Easy Explanation of the Basics of Quantum Mechanics for Dummies. Here’s the set-up. Things become uncertain. I'll go by the order you wrote your questions and make comments: When you quantize electrons in a magnetic field, you get Landau levels: discrete energy levels which are highly degenerate. My understanding (based on 3.) You might know these as the parts of the atom: protons, neutrons, and electrons. The characterization of IQHE by Chern number of energy band only works for https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/29032#29032, https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/6155#6155. 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! Òié>¢5y÷jÌ%›ÐžQˆiûôRËdÃõ€Q¾'V@›JȔ¥l¤êKÈBl¦Rh˜3è>*±Ó!øzm€U. Under these conditions, the Hall-conductivity exhibits plateaus at integral multiples of e 2 /h (a universal constant). Landau quantization only talks about electron states while topological picture doesn't mention them at all (they should be replaced by global topological states that are stable w.r.t. Randonauting for Dummies. 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