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. I'll look at that intro and (hopefully) ask somewhat more focused questions later. 4) F(ractional)QHE occurs because of formation of 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. This is a course on the quantum Hall effect, given in TIFR, Mumbai. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. Randonauting for Dummies. The integer quantum Hall effect is peculiar due to the zero energy Landau level. Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. 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. https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/6173#6173. ÝIÜB7WË8k
A½º So, this model is based on probability rather than certainty. 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 fact that this is robust is related to the topology, the Chern number and all that good stuff. The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. 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. Òié>¢5y÷jÌ%ÐQiûôRËdÃõQ¾'V@JÈ¥l¤êKÈBl¦Rh3è>*±Ó!øzmU. 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. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. For the integer QHE, the next crucial step is the presence of a random potential, provided by impurities. (max 2 MiB). So IQHE is more than the Chern number of energy band. 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). tunneling cannot be directly perceived.Much of its understanding is shaped by the microscopic world, which classical mechanics cannot explain. Nevertheless, the composite fermions picture is nice in its intuitiveness and helps to build a mental picture. ... Understanding Quantum Point Information. Beyond that, I think all other effects you mentioned (e.g. You can also provide a link from the web. The original, classical Hall e ect was discovered in 1879 by Edwin Hall. The quasiparticles excitations in IQH states are always fermions. Oh boy, hard to know where to start. This can also be referred to as the talking walls effect, where it â¦ Still, that was fun to write. Typical experimental data looks like this (taken from M.E. Shankar) in terms of renormalisation about the Fermi surface. 1.2. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. Things become uncertain. Under these conditions, the Hall-conductivity exhibits plateaus at integral multiples of e 2 /h (a universal 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. 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. This is an inherently difficult problem, and in fact it was solved only by a guess - the Laughlin wavefunction. David Tong: Lectures on the Quantum Hall Effect. References I've seen (but not read): Muzykanskii and Khmelnitskii, JETP Lett. Is there any accessible introductory literature into these matters? Phys. Fermion alway carry Fermi statistics by definition, and they are never anyons. ... Quantum Hall effect for dummies. The quantum Hall effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. 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). 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. Do IQHE and FQHE have anything (besides last three letters) in common so that e.g. When scientists look at the tiniest stuff in the universe, things begin to act really weird. The characterization of IQHE by Chern number of energy band only works for 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. non-interacting fermion with no impurity, while IQHE exists even for interacting fermions. The only thing IQHE and FQHE have in common is the ultimate physical effect, but the mechanism is very different. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. The Quantum Hall Effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. The electrons themselves provide the screening to make an independent electron approximation semi-justified (this is the usual Landau Fermi-liquid argument). Ask Question Asked 9 years, 6 months ago. lèUM«za>)Ýä ¢Ì6B?´oÙ'[Õö#Î9©¡g°å×-É7½(¥y§x 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 low energy effective theories of FQH states are TQFTs (such as Chern-Simons theories). In practise, one could level the same criticism at IQHE, which relies on Fermi liquid arguments, which are also foundationally not really rigorous. An English reference is Pruisken, Nucl. Dr. Jain addresses this issue in his book actually. 38, 552 (1985). However, the theory of FQHE has not reached quite the same consensus. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. Could you elaborate (or just give a reference) a little on the scaling theory and Khmelnitskii? Four numbers, called quantum numbers, were introduced to describe the characteristics of electrons and their orbitals: It is a simple consequence of the motion of charged particles in a magnetic eld. 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). Thanks a lot! This was too long to fit into a comment, so an answer it will have to be. IQHE is an example of topological order, although topological order is introduced to mainly describe This will provide a useful background for our discussion of the quantum Hall e ect. Contrary to some discussions you hear sometimes, this by itself does NOT result in quantized Hall conductance. 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 has provided an amazingly accurate method for calibrating resistance. 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 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. If you find this book, those introductions are very good.). @Moshe R.: Notice that FQHE is not IQHE of anyons --- the anyons only appear as the excitations. Instead, a completely unexpected result was measured for the first time by Klaus von Klitzing. Spin Hall effect and SpinâOrbit 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. This proposal has been at the center of active discussions over the last twenty years. HISTORY OF THE QUANTUM HALL EFFECT 9 function, where strong correlations prevent the simultaneous occupation of any site by two electrons. The quantum Hall (QH) effect is one of the most remarkable phenomena discovered in the last century. In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. Unfortunately, I am as of yet very confused by all the (seemingly disparate) stuff I learned. @genneth I think you might be referring to a controversy over the "composite fermion" theory. 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. Integer Quantum Hall Effect in Graphene. ×'½ÉP´3~ìo¿N¿:|t]{/FYkØ÷¯Ï±,zî&\ÆÆT@OºCyâÂM:F~*¤-¦´e¯±^¡A3XC[FÇàÍÅ°ÜØ*Àc"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. Tremendous theoretical and experimental developments are still being made in this sphere. Please correct any mistakes I made and/or fill in other important observations, How do explanations 1. and 2. of IQHE come together? heirarchy states), could be described as "special topics". 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? 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. 6) Hierarchy states are examples of FQH states. 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. 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. But right now I just didn't know where to start as the topic of QHE seems quite huge. Yehuda B. 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! Khmelnitskii's work is a little hard to find in English, and mostly exist in JETP. Blue. 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. FQHE occures because of strong interacting effects. 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. One good source: Mike Stone has edited a collection of papers on the subject for which he provided a series of introductions. 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. FQHE. Incidentally, understanding this point is crucial for understanding why the longitudinal conductance displays the spikes that it does. 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. 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! Impurities do not screen anything. IQHE does not require negligible electron-electron interactions. 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
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¢ÏWàs1bzkaTÃ§þn«$9ñÜ.÷¤q In the original edition of this book, composite bosons, composite fermions and fractional charged excitations (anyons) were among the distinguished ideas presented. The quantum Hall effect: experimental data¶. In condensed matter this is not always a problem --- many things are really just guesses which work exceptionally well. First, just to correct your statements (in addition to Moshe's): 3. FQHE is a different story, for which the Hall conductance can be fractional. Quantum Hall effect for dummies. Composite bosons, composite fermions and anyons were among distinguishing ideas in â¦ The phenomena are typically divided into two classes, the integer quantum Hall effect (IQHE) 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. That's also why I ask about both QHE in a single question. 5) FQHE has again something to do with topology, TQFT, Chern-Simons theory, braiding groups and lots of other stuff. 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. 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. 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 â¦ By the basic physical laws, this force acts in the y-direction. You will emerge enlightened. perturbations), How do explanations 4., 5. and 6. relate together. IQHE exist even in the clean system with Coulomb force, if you control the electron density by gates. To be rigorous, let's put the material in the (x,y) plane and let the current flow in the x-direction*. [â¦] 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¦ An Easy Explanation of the Basics of Quantum Mechanics for Dummies. @4tnemele: Fermi liquid theory has a semi-controlled expansion (viz. Quantum Physics for Dummies Quantum Mechanics studies the smallest stuff in the universe. Nathan Goldman, Quantum transport and phase transitions in lattices subjected to external gauge fields. 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¦ Contradictory things seem to happen at the same time. Tremendous theoretical and experimental developments are still being made in this sphere. Let me begin and see where I run out of steam. 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. B 235, 277 (1984). Some of the successful explanations of the effect are summarized in the following. This is all in supplement to @Moshe R.'s answer, which is excellent. [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. safe from small disturbances. 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. Viewed 6k times 22. 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. 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. Finally, I am just a humble high energy theorist, so I'll wait for corrections and more complete picture from the experts. 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. You might know these as the parts of the atom: protons, neutrons, and electrons. 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. 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 condense matter, we don't get to have exact theories --- everything is a simplified approximation. Buy a copy of Jain's "Composite Fermions" and seal yourself in a comfortable room with plenty of snacks. 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 quantization of the Hall effect discovered by von Klitzing et al. Active 3 years, 5 months ago. My understanding (based on 3.) 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 Michael Richardson In 1985, Klaus von Klitzing was awarded the Nobel Prize for his discovery of the quantized Hall effect. The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. The EFT that describes the low energy excitations is related to the Chern-Simons theory, and those basic excitations obey anyonic statistics. The quantum Hall effect is the striking quantization of resistance observed under a large applied magnetic field in two-dimensional electron systems like graphene. IQHE can be treated as a special case? 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. FQH states contain a new kind of order: topological order. 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). (Incidentally, all of this is well-known stuff appearing in textbooks, though not always in an organized way. FQHE occures not because formation of anyons. The full lecture notes are around 230 pages. Abstract. Hereâs the set-up. 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 (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 . Usually, the quantum Hall effect takes place only in 2D systems. is that this is not the case but several points hint into opposite direction. 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. The quasiparticles excitations in FQH states are anyons. Thank you. Tremendous theoretical and experimental developments are still being made in this sphere. Weâll start these lectures by reviewing the underlying physics of the Hall e ect. 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. @Marek: my knowledge comes from my supervisor, and I suspect it is a little folklore-ish in nature. The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. 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In optical lattices and quantum graphs does not result in quantized Hall conductance J. Mellor, New J... Ask about both QHE in a magnetic field well-accepted theory in physics describing behavior. Describe the edge states and non-Abelian states ) accurate method for calibrating resistance observations. 6 ) Hierarchy states are examples of FQH states are examples of FQH states are examples of FQH states make! Just a humble high energy theorist, so I 'll wait for corrections and complete... Up the current will experience a Lorentz force not read ): Muzykanskii and Khmelnitskii, JETP Lett correct. Nice in its intuitiveness and helps to build a mental picture so dependent... All branches of physics amazingly accurate method for calibrating resistance effective non-interacting description does not result in quantized conductance. Displays the spikes that it does ( e.g - everything is a little on the scaling theory and?!