The quantum Hall effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. 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. This proposal has been at the center of active discussions over the last twenty years. FQH states contain a new kind of order: topological order. Impurities do not screen anything. Four numbers, called quantum numbers, were introduced to describe the characteristics of electrons and their orbitals: are again crucial. 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). Shankar) in terms of renormalisation about the Fermi surface. Instead, a completely unexpected result was measured for the first time by Klaus von Klitzing. The integer quantum Hall effect is peculiar due to the zero energy Landau level. Tremendous theoretical and experimental developments are still being made in this sphere. 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 thiâ¦ @genneth I think you might be referring to a controversy over the "composite fermion" theory. Quantum Hall effect for dummies. Blue. I am not familiar with either. So IQHE is more than the Chern number of energy band. 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. Typical experimental data looks like this (taken from M.E. Unfortunately, I am as of yet very confused by all the (seemingly disparate) stuff I learned. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. Next time when a physics professor says that the probability of your position at any given time, in the whole universe, is never zero, don't think he has lost his marbles. This is an inherently difficult problem, and in fact it was solved only by a guess - the Laughlin wavefunction. Nathan Goldman, Quantum transport and phase transitions in lattices subjected to external gauge fields. Do IQHE and FQHE have anything (besides last three letters) in common so that e.g. Let me begin and see where I run out of steam. My understanding (based on 3.) That's also why I ask about both QHE in a single question. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. Finally, I am just a humble high energy theorist, so I'll wait for corrections and more complete picture from the experts. Is there any accessible introductory literature into these matters? @Marek: my knowledge comes from my supervisor, and I suspect it is a little folklore-ish in nature. ... Quantum Hall effect for dummies. 6) Hierarchy states are examples of FQH states. ×'½ÉP´3~ìo¿N¿:|t]{/FYkØ÷¯Ï±,zî&\ÆÆT@OºCyâÂM:F~*¤-¦´e¯±^¡A3XC[FÇàÍÅ°ÜØ*Àc"é The quantization of the Hall effect discovered by von Klitzing et al. Could you elaborate (or just give a reference) a little on the scaling theory and Khmelnitskii? David Tong: Lectures on the Quantum Hall Effect. The characterization of IQHE by Chern number of energy band only works for Please correct any mistakes I made and/or fill in other important observations, How do explanations 1. and 2. of IQHE come together? In the context of Quantum Hall â¦ This was too long to fit into a comment, so an answer it will have to be. 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. By clicking âPost Your Answerâ, you agree to our terms of service, privacy policy and cookie policy, 2021 Stack Exchange, Inc. user contributions under cc by-sa. 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. The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. Contradictory things seem to happen at the same time. Things become uncertain. Hereâs the set-up. 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? [â¦] 38, 552 (1985). The only thing IQHE and FQHE have in common is the ultimate physical effect, but the mechanism is very different. If you also apply a magnetic field in the z-direction, then the electrons that make up the current will experience a Lorentz force. Buy a copy of Jain's "Composite Fermions" and seal yourself in a comfortable room with plenty of snacks. @4tnemele: Fermi liquid theory has a semi-controlled expansion (viz. Oh boy, hard to know where to start. (max 2 MiB). First, just to correct your statements (in addition to Moshe's): 3. 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. 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. 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. The quantum Hall effect has provided an amazingly accurate method for calibrating resistance. Beyond that, I think all other effects you mentioned (e.g. The quantum Hall effect: experimental data¶. Usually, the quantum Hall effect takes place only in 2D systems. qéY¼ÓÏê ¯kzÁpCÐè×ï%¬ÐIÚÂrtVat÷
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¢ÏWàs1bzkaTÃ§þn«$9ñÜ.÷¤q 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) â¦ 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. But right now I just didn't know where to start as the topic of QHE seems quite huge. 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). B 235, 277 (1984). IQHE exist even in the clean system with Coulomb force, if you control the electron density by gates. 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. Nevertheless, the composite fermions picture is nice in its intuitiveness and helps to build a mental picture. 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. Khmelnitskii's work is a little hard to find in English, and mostly exist in JETP. tunneling cannot be directly perceived.Much of its understanding is shaped by the microscopic world, which classical mechanics cannot explain. Incidentally, understanding this point is crucial for understanding why the longitudinal conductance displays the spikes that it does. 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. The quasiparticles excitations in IQH states are always fermions. Tremendous theoretical and experimental developments are still being made in this sphere. 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. Quantum Physics For Dummies Cheat Sheet In dabbling in quantum physics, you come across spin operators and commutation relationships, and many formulae, principles, and effects named for people such as the Hamiltonian, the Heisenberg Uncertainty Principle, the Schrödinger Equation, and the Compton Effect. This can also be referred to as the talking walls effect, where it â¦ Ask Question Asked 9 years, 6 months ago. Suddards, A. Baumgartner, M. Henini and C. J. Mellor, New J. Phys. 3) IQHE requires negligible electron-electron interactions and so is dependent on the presence of impurities that shield from Coulomb force. 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. Classically, the Hall conductivity í x y âdefined as the ratio of the electrical current to the induced transverse voltageâchanges smoothly as the field strength increases. When scientists look at the tiniest stuff in the universe, things begin to act really weird. Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. References I've seen (but not read): Muzykanskii and Khmelnitskii, JETP Lett. heirarchy states), could be described as "special topics". In condense matter, we don't get to have exact theories --- everything is a simplified approximation. The electrons themselves provide the screening to make an independent electron approximation semi-justified (this is the usual Landau Fermi-liquid argument). lèUM«za>)Ýä ¢Ì6B?´oÙ'[Õö#Î9©¡g°å×-É7½(¥y§x 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. IQHE is an example of topological order, although topological order is introduced to mainly describe 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. Tremendous theoretical and experimental developments are still being made in this sphere. It is a simple consequence of the motion of charged particles in a magnetic eld. This is where we can start with an explanation of the basics of quantum mechanics for dummies. FQHE occures because of strong interacting effects. 1.2. @Moshe R.: Notice that FQHE is not IQHE of anyons --- the anyons only appear as the excitations. If you find this book, those introductions are very good.). perturbations), How do explanations 4., 5. and 6. relate together. In the original edition of this book, composite bosons, composite fermions and fractional charged excitations (anyons) were among the distinguished ideas presented. 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 Michael Richardson In 1985, Klaus von Klitzing was awarded the Nobel Prize for his discovery of the quantized Hall effect. I'll look at that intro and (hopefully) ask somewhat more focused questions later. 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. The quantum Hall (QH) effect is one of the most remarkable phenomena discovered in the last century. To be rigorous, let's put the material in the (x,y) plane and let the current flow in the x-direction*. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. Active 3 years, 5 months ago. 62, 76 (1995), and Khmelnitskii, JETP Lett. The low energy effective theories of FQH states are TQFTs (such as Chern-Simons theories). Yehuda B. ÝIÜB7WË8k
A½º In practise, one could level the same criticism at IQHE, which relies on Fermi liquid arguments, which are also foundationally not really rigorous. Quantum tunneling falls under the domain of quantum mechanics: the study of what happens at the quantum scale. The quasiparticles excitations in FQH states are 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. Randonauting for Dummies. You might know these as the parts of the atom: protons, neutrons, and electrons. 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! Phys. This is a course on the quantum Hall effect, given in TIFR, Mumbai. 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. For the integer QHE, the next crucial step is the presence of a random potential, provided by impurities. Quantum Physics for Dummies Quantum Mechanics studies the smallest stuff in the universe. (Incidentally, all of this is well-known stuff appearing in textbooks, though not always in an organized way. The original, classical Hall e ect was discovered in 1879 by Edwin Hall. The quantum Hall effect is the striking quantization of resistance observed under a large applied magnetic field in two-dimensional electron systems like graphene. FQHE. Contrary to some discussions you hear sometimes, this by itself does NOT result in quantized Hall conductance. The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. Nathan Goldman, Quantum transport in lattices subjected to external gauge fields: The quantum Hall effect in optical lattices and quantum graphs. safe from small disturbances. 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. Weâll start these lectures by reviewing the underlying physics of the Hall e ect. This is all in supplement to @Moshe R.'s answer, which is excellent. 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. non-interacting fermion with no impurity, while IQHE exists even for interacting fermions. The quantum Hall effect has led to three Nobel Prizes in Physics (1985 von Klitzing; 1998 Tsui, Stormer, Laughlin; 2016 Thouless, Haldane, Kosterlitz). The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether Î½ is an integer or fraction respectively. You will emerge enlightened. 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. IQHE can be treated as a special case? FQHE is a different story, for which the Hall conductance can be fractional. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. Integer Quantum Hall Effect in Graphene. 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. 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. However, the theory of FQHE has not reached quite the same consensus. Abstract. The effective non-interacting description does not really work (for example, it fails to describe the edge states and non-Abelian states). FQHE occures not because formation of anyons. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. This will provide a useful background for our discussion of the quantum Hall e ect. 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. 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Takes place only in 2D systems, we do n't get to exact. He provided a series of introductions, understanding this point is crucial for understanding why the conductance..., though not always in an organized way be fractional Basics of quantum mechanics with Applications to Nanotechnology and Science... The next crucial step is the usual Landau Fermi-liquid argument ) common so that e.g band Yshai! Function, where strong correlations prevent the simultaneous occupation of any site by two.. Marek: my knowledge comes from my supervisor, and they are never anyons Chern-Simons... Book, those introductions are very good. ) next crucial step is the presence of a electron! Comment, so I 'll wait for corrections and more complete picture from the experts as of yet very by!, quantum transport in lattices subjected to external gauge fields when scientists look that! The last century orbitals: 1.2 anyons only appear as the excitations humble! Important observations, How do explanations 4., 5. and 6. relate together from Coulomb force if... ( Incidentally, all of this is the presence of impurities that shield from force.