Classically, the Hall conductivity í x y âdefined as the ratio of the electrical current to the induced transverse voltageâchanges smoothly as the field strength increases. Òié>¢5y÷jÌ%ÐQiûôRËdÃõQ¾'[email protected]JÈ¥l¤êKÈBl¦Rh3è>*±Ó!øzmU. In some respects, FQHE is like a IQHE of electrons with extra flux "bound" to them (through an effective interaction due to Coulomb repulsion); in this picture, all the messiness (impurities), etc. Blue. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. @4tnemele: Fermi liquid theory has a semi-controlled expansion (viz. Let me begin and see where I run out of steam. Contradictory things seem to happen at the same time. FQH states contain a new kind of order: topological order. 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). 3) IQHE requires negligible electron-electron interactions and so is dependent on the presence of impurities that shield from Coulomb force. ... Quantum Hall effect for dummies. The Quantum Hall Effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. is that this is not the case but several points hint into opposite direction. The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. Yehuda B. When scientists look at the tiniest stuff in the universe, things begin to act really weird. This can also be referred to as the talking walls effect, where it â¦ Some of the successful explanations of the effect are summarized in the following. 1.2. An English reference is Pruisken, Nucl. (max 2 MiB). Quantum tunneling falls under the domain of quantum mechanics: the study of what happens at the quantum scale. 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. 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. 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. 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. This proposal has been at the center of active discussions over the last twenty years. ×'½ÉP´3~ìo¿N¿:|t]{/FYkØ÷¯Ï±,zî&\ÆÆ[email protected]ºCyâÂM:F~*¤-¦´e¯±^¡A3XC[F­ÇàÍÅ°ÜØ*Àc"é 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. The quantum Hall effect has provided an amazingly accurate method for calibrating resistance. Four numbers, called quantum numbers, were introduced to describe the characteristics of electrons and their orbitals: We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. Under these conditions, the Hall-conductivity exhibits plateaus at integral multiples of e 2 /h (a universal constant). But right now I just didn't know where to start as the topic of QHE seems quite huge. 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 EFT that describes the low energy excitations is related to the Chern-Simons theory, and those basic excitations obey anyonic statistics. 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! Please correct any mistakes I made and/or fill in other important observations, How do explanations 1. and 2. of IQHE come together? Things become uncertain. Abstract. Tremendous theoretical and experimental developments are still being made in this sphere. This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics: the quantum Hall effect. Is there any accessible introductory literature into these matters? The full lecture notes are around 230 pages. That's also why I ask about both QHE in a single question. My understanding (based on 3.) Buy a copy of Jain's "Composite Fermions" and seal yourself in a comfortable room with plenty of snacks. @genneth I think you might be referring to a controversy over the "composite fermion" theory. Hereâs the set-up. 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 first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. 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). 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 ï¬eld 1 . The effective non-interacting description does not really work (for example, it fails to describe the edge states and non-Abelian states). The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values at certain level This is where we can start with an explanation of the basics of quantum mechanics for dummies. 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? Phys. The characterization of IQHE by Chern number of energy band only works for 4) F(ractional)QHE occurs because of formation of anyons. 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! Oh boy, hard to know where to start. The fact that this is robust is related to the topology, the Chern number and all that good stuff. You can also provide a link from the web. FQHE occures not because formation of anyons. Khmelnitskii's work is a little hard to find in English, and mostly exist in JETP. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. Quantum Hall effect for dummies. David Tong: Lectures on the Quantum Hall Effect. Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. IQHE is an example of topological order, although topological order is introduced to mainly describe 6) Hierarchy states are examples of FQH states. IQHE exist even in the clean system with Coulomb force, if you control the electron density by gates. Integer Quantum Hall Effect in Graphene. 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). ÝIÜB7WË8kA½º The only thing IQHE and FQHE have in common is the ultimate physical effect, but the mechanism is very different. In the context of Quantum Hall â¦ One good source: Mike Stone has edited a collection of papers on the subject for which he provided a series of introductions. 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 quantization of the Hall effect discovered by von Klitzing et al. 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. The original, classical Hall e ect was discovered in 1879 by Edwin Hall. Weâll start these lectures by reviewing the underlying physics of the Hall e ect. Viewed 6k times 22. Ask Question Asked 9 years, 6 months ago. This is an inherently difficult problem, and in fact it was solved only by a guess - the Laughlin wavefunction. The Quantum Hall Effect Michael Richardson In 1985, Klaus von Klitzing was awarded the Nobel Prize for his discovery of the quantized Hall effect. Thanks a lot! You might know these as the parts of the atom: protons, neutrons, and electrons. In the original edition of this book, composite bosons, composite fermions and fractional charged excitations (anyons) were among the distinguished ideas presented. 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. 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. The quasiparticles excitations in IQH states are always fermions. 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. IQHE can be treated as a special case? Instead, a completely unexpected result was measured for the first time by Klaus von Klitzing. ... Understanding Quantum Point Information. The phenomena are typically divided into two classes, the integer quantum Hall effect (IQHE) 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. 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. In practise, one could level the same criticism at IQHE, which relies on Fermi liquid arguments, which are also foundationally not really rigorous. 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. I am not familiar with either. This was too long to fit into a comment, so an answer it will have to be. 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¦ This is a course on the quantum Hall effect, given in TIFR, Mumbai. FQHE is a different story, for which the Hall conductance can be fractional. The quasiparticles excitations in FQH states are anyons. 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. are again crucial. 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. There is a book that covers exactly the questions you asked: If you are short of time (or money) - the book is based on his thesis: Click here to upload your image 5) FQHE has again something to do with topology, TQFT, Chern-Simons theory, braiding groups and lots of other stuff. [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. 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. By clicking âPost 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 (QHE), which was previously known for two-dimensional (2-D) systems, was predicted to be possible for three-dimensional (3-D) â¦ The quantum Hall effect: experimental data¶. An Easy Explanation of the Basics of Quantum Mechanics for Dummies. You will emerge enlightened. Still, that was fun to write. In condensed matter this is not always a problem --- many things are really just guesses which work exceptionally well. qéY¼ÓÏê ¯kzÁpCÐè×ï%¬ÐIÚÂrtVat÷ «+ ¢ÏWàs1bzkaTÃ§þn«$9ñÜ.÷­¤q Could you elaborate (or just give a reference) a little on the scaling theory and Khmelnitskii? First, just to correct your statements (in addition to Moshe's): 3. The integer quantum Hall effect is peculiar due to the zero energy Landau level. @Marek: my knowledge comes from my supervisor, and I suspect it is a little folklore-ish in nature. So IQHE is more than the Chern number of energy band. I'll look at that intro and (hopefully) ask somewhat more focused questions later. 62, 76 (1995), and Khmelnitskii, JETP Lett. 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. In condense matter, we don't get to have exact theories --- everything is a simplified approximation. Typical experimental data looks like this (taken from M.E. The quantum Hall (QH) effect is one of the most remarkable phenomena discovered in the last century. 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. So, this model is based on probability rather than certainty. Usually, the quantum Hall effect takes place only in 2D systems. 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). [â¦] Dr. Jain addresses this issue in his book actually. Quantum Physics for Dummies Quantum Mechanics studies the smallest stuff in the universe. If you also apply a magnetic field in the z-direction, then the electrons that make up the current will experience a Lorentz force. lèUM«za>)Ýä ¢Ì6B?´oÙ'[Õö#Î9©¡g°å×-É7½(¥y§x The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. To be rigorous, let's put the material in the (x,y) plane and let the current flow in the x-direction*. Composite bosons, composite fermions and anyons were among distinguishing ideas in â¦ HISTORY OF THE QUANTUM HALL EFFECT 9 function, where strong correlations prevent the simultaneous occupation of any site by two electrons. FQHE. For the integer QHE, the next crucial step is the presence of a random potential, provided by impurities. 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. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. Tremendous theoretical and experimental developments are still being made in this sphere. The electrons themselves provide the screening to make an independent electron approximation semi-justified (this is the usual Landau Fermi-liquid argument). The low energy effective theories of FQH states are TQFTs (such as Chern-Simons theories). FQHE occures because of strong interacting effects. Tremendous theoretical and experimental developments are still being made in this sphere. Finally, I am just a humble high energy theorist, so I'll wait for corrections and more complete picture from the experts. By the basic physical laws, this force acts in the y-direction. (Incidentally, all of this is well-known stuff appearing in textbooks, though not always in an organized way. 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. 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. Impurities do not screen anything. 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. 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. Thank you. Incidentally, understanding this point is crucial for understanding why the longitudinal conductance displays the spikes that it does. safe from small disturbances. Do IQHE and FQHE have anything (besides last three letters) in common so that e.g. Unfortunately, I am as of yet very confused by all the (seemingly disparate) stuff I learned. https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/6173#6173. 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. Randonauting 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. 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. perturbations), How do explanations 4., 5. and 6. relate together. The higher cleaniness is just a result of the composite IQHE being a bit more fragile; notice that for Anderson localisation to occur in 2D, one just needs a sufficiently large sample with arbitrarily small impurities. The quantum Hall effect has led to three Nobel Prizes in Physics (1985 von Klitzing; 1998 Tsui, Stormer, Laughlin; 2016 Thouless, Haldane, Kosterlitz). Nevertheless, the composite fermions picture is nice in its intuitiveness and helps to build a mental picture. Suddards, A. Baumgartner, M. Henini and C. J. Mellor, New J. Phys. tunneling cannot be directly perceived.Much of its understanding is shaped by the microscopic world, which classical mechanics cannot explain. @Moshe R.: Notice that FQHE is not IQHE of anyons --- the anyons only appear as the excitations. This is all in supplement to @Moshe R.'s answer, which is excellent. Nathan Goldman, Quantum transport in lattices subjected to external gauge fields: The quantum Hall effect in optical lattices and quantum graphs. 38, 552 (1985). Spin Hall effect and SpinâOrbit Torques An Overview Sergio O. Valenzuela [email protected] [email protected] ICREA and Institut Catalá Nanociència iNanotecnologia, ICN2 ... Quantum manipulation and Coupling of spin states Adapted, C. Chappert, Université Paris Sud. IQHE does not require negligible electron-electron interactions. 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). It is a simple consequence of the motion of charged particles in a magnetic eld. If you find this book, those introductions are very good.). However, the theory of FQHE has not reached quite the same consensus. 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. Shankar) in terms of renormalisation about the Fermi surface. Beyond that, I think all other effects you mentioned (e.g. This will provide a useful background for our discussion of the quantum Hall e ect. 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. heirarchy states), could be described as "special topics". Active 3 years, 5 months ago. non-interacting fermion with no impurity, while IQHE exists even for interacting fermions. Fermion alway carry Fermi statistics by definition, and they are never anyons. References I've seen (but not read): Muzykanskii and Khmelnitskii, JETP Lett. The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. 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. Contrary to some discussions you hear sometimes, this by itself does NOT result in quantized Hall conductance. 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. Nathan Goldman, Quantum transport and phase transitions in lattices subjected to external gauge fields. 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This model is based on quantum hall effect for dummies rather than certainty ( for example, it to...