The quantum Hall effect: experimental data¶. That's also why I ask about both QHE in a single question. Is there any accessible introductory literature into these matters? [1.1] in 1980 is a remarkable macroscopic quantum phenomenon which occurs in two-dimensional electron systems at low temperatures and strong perpendicular magnetic fields. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. Quantum Hall effect for dummies. Dr. Jain addresses this issue in his book actually. Could you elaborate (or just give a reference) a little on the scaling theory and Khmelnitskii? Under these conditions, the Hall-conductivity exhibits plateaus at integral multiples of e 2 /h (a universal constant). IQHE exist even in the clean system with Coulomb force, if you control the electron density by gates. Usually, the quantum Hall effect takes place only in 2D systems. By the basic physical laws, this force acts in the y-direction. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. This was too long to fit into a comment, so an answer it will have to be. The phenomena are typically divided into two classes, the integer quantum Hall effect (IQHE) Nevertheless, most people are far happier to accept that interactions may be neglected entirely, than somehow incorporating part of the interaction into a topological order, and neglecting the rest. Blue. HISTORY OF THE QUANTUM HALL EFFECT 9 function, where strong correlations prevent the simultaneous occupation of any site by two electrons. The full lecture notes are around 230 pages. The electrons themselves provide the screening to make an independent electron approximation semi-justified (this is the usual Landau Fermi-liquid argument). Viewed 6k times 22. 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. @Moshe R.: Notice that FQHE is not IQHE of anyons --- the anyons only appear as the excitations. Thank you. perturbations), How do explanations 4., 5. and 6. relate together. This proposal has been at the center of active discussions over the last twenty years. If you find this book, those introductions are very good.). However, it is clear that since the basic ingredient is the strong Coulomb interaction, without a systematic (the above is very much ad hoc) treatment it is impossible to be confident about the range of validity of the theory. FQH states contain a new kind of order: topological order. Let me begin and see where I run out of steam. In practise, one could level the same criticism at IQHE, which relies on Fermi liquid arguments, which are also foundationally not really rigorous. The Quantum Hall effect is the observation of the Hall effect in a two-dimensional electron gas system (2DEG) such as graphene and MOSFETs etc. non-interacting fermion with no impurity, while IQHE exists even for interacting fermions. This is all in supplement to @Moshe R.'s answer, which is excellent. The quantum Hall effect (QHE) and its relation to fundamental physical constants was discovered in 1980 by Klaus von Klitzing for which he received a Nobel prize in 1985. Contradictory things seem to happen at the same time. lèUM«za>)Ýä ¢Ì6B?´oÙ'†[Õö#Î9©¡g°å×-É7ˆ½(¥y§žx The integer quantum Hall effect is peculiar due to the zero energy Landau level. The Quantum Hall Effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction respectively. 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. The quantum Hall (QH) effect is one of the most remarkable phenomena discovered in the last century. Things become uncertain. The Quantum Hall Effect Michael Richardson In 1985, Klaus von Klitzing was awarded the Nobel Prize for his discovery of the quantized Hall effect. @Marek: my knowledge comes from my supervisor, and I suspect it is a little folklore-ish in nature. Despite Jain's obvious bias towards promoting his own perspective, I think this book remains the best introduction to the physics of the quantum hall effect. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. IQHE can be treated as a special case? The modern work tends to proceed via a field theory or replica theory model of disorder, and derive an effective non-linear $\sigma$-model for the diffusive transport, and from there find a scaling theory. Nathan Goldman, Quantum transport and phase transitions in lattices subjected to external gauge fields. Active 3 years, 5 months ago. B 235, 277 (1984). 38, 552 (1985). In the original edition of this book, composite bosons, composite fermions and fractional charged excitations (anyons) were among the distinguished ideas presented. FQHE is a different story, for which the Hall conductance can be fractional. This implies that at least for some phases of operation of the device, the carriers are confined in a potential such that the motion is only permitted in a restricted direction thus, quantizing the motion in thi… Oh boy, hard to know where to start. An Easy Explanation of the Basics of Quantum Mechanics for Dummies. 17 $\begingroup$ In the past few days I've become increasingly intrigued by the QHE, mainly thanks to very interesting questions and answers that have appeared here. You will emerge enlightened. @genneth I think you might be referring to a controversy over the "composite fermion" theory. Instead, a completely unexpected result was measured for the first time by Klaus von Klitzing. Nevertheless, the composite fermions picture is nice in its intuitiveness and helps to build a mental picture. In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. ÝIÜB7WË8k…A½º 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. The integer quantum Hall effect is very well understood, and can be simply explained in terms of single-particle orbitals of an electron in a magnetic field (see Landau quantization). Suddards, A. Baumgartner, M. Henini and C. J. Mellor, New J. Phys. The quantum Hall effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. The two-dimensional electron gas has to do with a scientific model in which the electron gas is free to move in two dimensions, but tightly confined in the third. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. Whilst I respect Jain's works, it is worthwhile pointing out that his books is obviously a biased view of the problem, and does not necessarily reflect a consensus of the community! For the fractional effect you need very pure samples, since it is driven by strong Coulomb intercations between the degenerate electrons in each Landau levels. Randonauting for Dummies. IQHE is an example of topological order, although topological order is introduced to mainly describe ... Quantum Hall effect for dummies. 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. In the context of Quantum Hall … This is a course on the quantum Hall effect, given in TIFR, Mumbai. 3) IQHE requires negligible electron-electron interactions and so is dependent on the presence of impurities that shield from Coulomb force. In condense matter, we don't get to have exact theories --- everything is a simplified approximation. The effective non-interacting description does not really work (for example, it fails to describe the edge states and non-Abelian states). In this case Coulomb interaction can't be neglected but it turns out an effective non-interacting description emerges with particles obeying parastatistics and having fractional charge. Beyond that, I think all other effects you mentioned (e.g. However, the theory of FQHE has not reached quite the same consensus. Incidentally, it is worth pointing out that some of the recent literature on topological insulators actually contain some of the cleanest expositions of the IQHE. 62, 76 (1995), and Khmelnitskii, JETP Lett. At this point, it is fair to say that IQHE is well understood, the prevailing theory being a combination of topological states, impurity effects, and 2-parameter scaling theory (of both longitudinal and transverse conductances, ala Khmelnitskii). FQHE. tunneling cannot be directly perceived.Much of its understanding is shaped by the microscopic world, which classical mechanics cannot explain. Fermion alway carry Fermi statistics by definition, and they are never anyons. 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. Thanks a lot! I am not familiar with either. Tremendous theoretical and experimental developments are still being made in this sphere. This is an inherently difficult problem, and in fact it was solved only by a guess - the Laughlin wavefunction. 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). Finally, I am just a humble high energy theorist, so I'll wait for corrections and more complete picture from the experts. FQHE occures not because formation of anyons. Impurities do not screen anything. Buy a copy of Jain's "Composite Fermions" and seal yourself in a comfortable room with plenty of snacks. The quantum Hall effect has led to three Nobel Prizes in Physics (1985 von Klitzing; 1998 Tsui, Stormer, Laughlin; 2016 Thouless, Haldane, Kosterlitz). Quantum Physics for Dummies Quantum Mechanics studies the smallest stuff in the universe. is that this is not the case but several points hint into opposite direction. David Tong: Lectures on the Quantum Hall Effect. Please correct any mistakes I made and/or fill in other important observations, How do explanations 1. and 2. of IQHE come together? 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. 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. You can also provide a link from the web. Tremendous theoretical and experimental developments are still being made in this sphere. Tremendous theoretical and experimental developments are still being made in this sphere. Then one can show that each Landau level contributes a fixed value to the Hall conductance, and therefore that conductance counts the number of filled Landau levels. qé•Y¼ÓÏê ¯kzÁpC‰Ðè×ï%¬ÐIځÂr€tžVat÷ «+ ¢ÏˆWà‹s1bz€kaT€Ã§þn«$9ñܞ.÷­¤q Do IQHE and FQHE have anything (besides last three letters) in common so that e.g. Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/6173#6173. 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. The quantum Hall effect has provided an amazingly accurate method for calibrating resistance. The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. 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. The quantum Hall effect is the striking quantization of resistance observed under a large applied magnetic field in two-dimensional electron systems like graphene. The fact that this is robust is related to the topology, the Chern number and all that good stuff. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. You might know these as the parts of the atom: protons, neutrons, and electrons. 4) F(ractional)QHE occurs because of formation of anyons. Typical experimental data looks like this (taken from M.E. If you also apply a magnetic field in the z-direction, then the electrons that make up the current will experience a Lorentz force. In this case Coulomb interaction can't be neglected but it turns out an effective non-interacting description emerges with particles obeying parastatistics and having fractional charge, FQHE has again something to do with topology, TQFT, Chern-Simons theory, braiding groups and lots of other stuff, FQHE has something to do with hierarchy states, Most importantly, do these points make sense? My understanding (based on 3.) The quantum Hall effect (QHE) refers to a set of phenomena and associated phases of matter found in two-dimensional electron gases subjected to a large perpendicular magnetic field 1 . Four numbers, called quantum numbers, were introduced to describe the characteristics of electrons and their orbitals: Composite bosons, composite fermions and anyons were among distinguishing ideas in … […] Abstract The quantum Hall effect is a set of phenomena observed at low temperature in a two-dimensional electron gas subject to a strong perpendicular magnetic field. (max 2 MiB). The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. The quantization of the Hall effect discovered by von Klitzing et al. 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). This will provide a useful background for our discussion of the quantum Hall e ect. 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. Some of the successful explanations of the effect are summarized in the following. 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. The quantum Hall effect (QHE), which was previously known for two-dimensional (2-D) systems, was predicted to be possible for three-dimensional (3-D) … One good source: Mike Stone has edited a collection of papers on the subject for which he provided a series of introductions. Phys. Unfortunately, I am as of yet very confused by all the (seemingly disparate) stuff I learned. The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. The quasiparticles excitations in FQH states are anyons. This is also related to the hierarchical states because one can imagine binding more flux to the anyonic excitations and getting more IQHE states of those. , and I suspect it is a course on the quantum Hall in... 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