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But right now I just didn't know where to start as the topic of QHE seems quite huge. 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. Quantum tunneling falls under the domain of quantum mechanics: the study of what happens at the quantum scale. 38, 552 (1985). This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics: the quantum Hall effect. It is a simple consequence of the motion of charged particles in a magnetic eld. Shankar) in terms of renormalisation about the Fermi surface. 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. [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. 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. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. Impurities do not screen anything. ÝIÜB7WË8kA½º The quantum Hall effect has provided an amazingly accurate method for calibrating resistance. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. 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. Khmelnitskii's work is a little hard to find in English, and mostly exist in JETP. 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. 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. 5) FQHE has again something to do with topology, TQFT, Chern-Simons theory, braiding groups and lots of other stuff. This was too long to fit into a comment, so an answer it will have to be. Òié>¢5y÷jÌ%ÐQiûôRËdÃõQ¾'V@JÈ¥l¤êKÈBl¦Rh3è>*±Ó!øzmU. The Quantum Hall Effect Michael Richardson In 1985, Klaus von Klitzing was awarded the Nobel Prize for his discovery of the quantized Hall effect. 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¦ Usually, the quantum Hall effect takes place only in 2D systems. Nathan Goldman, Quantum transport in lattices subjected to external gauge fields: The quantum Hall effect in optical lattices and quantum graphs. So IQHE is more than the Chern number of energy band. I am not familiar with either. https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/6173#6173. 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. 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. 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? 6) Hierarchy states are examples of FQH states. The Quantum Hall Effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. 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 low energy effective theories of FQH states are TQFTs (such as Chern-Simons theories). 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. Contrary to some discussions you hear sometimes, this by itself does NOT result in quantized Hall conductance. This is where we can start with an explanation of the basics of quantum mechanics for dummies. Is there any accessible introductory literature into these matters? In practise, one could level the same criticism at IQHE, which relies on Fermi liquid arguments, which are also foundationally not really rigorous. The original, classical Hall e ect was discovered in 1879 by Edwin Hall. 4) F(ractional)QHE occurs because of formation of anyons. 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. Four numbers, called quantum numbers, were introduced to describe the characteristics of electrons and their orbitals: For the integer QHE, the next crucial step is the presence of a random potential, provided by impurities. 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. Viewed 6k times 22. 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). Abstract. 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. Some of the successful explanations of the effect are summarized in the following. Quantum Hall effect for dummies. HISTORY OF THE QUANTUM HALL EFFECT 9 function, where strong correlations prevent the simultaneous occupation of any site by two electrons. The quantum Hall effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. 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. Contradictory things seem to happen at the same time. 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. An Easy Explanation of the Basics of Quantum Mechanics for Dummies. The quasiparticles excitations in FQH states are anyons. 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. 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. In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. I'll look at that intro and (hopefully) ask somewhat more focused questions later. 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¦ Still, that was fun to write. If you also apply a magnetic field in the z-direction, then the electrons that make up the current will experience a Lorentz force. 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). 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. Oh boy, hard to know where to start. FQHE is a different story, for which the Hall conductance can be fractional. FQH states contain a new kind of order: topological order. In the context of Quantum Hall â¦ Randonauting for Dummies. An English reference is Pruisken, Nucl. This will provide a useful background for our discussion of the quantum Hall e ect. Yehuda B. ... Understanding Quantum Point Information. You might know these as the parts of the atom: protons, neutrons, and electrons. Let me begin and see where I run out of steam. @Moshe R.: Notice that FQHE is not IQHE of anyons --- the anyons only appear as the excitations. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. References I've seen (but not read): Muzykanskii and Khmelnitskii, JETP Lett. 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. lèUM«za>)Ýä ¢Ì6B?´oÙ'[Õö#Î9©¡g°å×-É7½(¥y§x @4tnemele: Fermi liquid theory has a semi-controlled expansion (viz. FQHE occures not because formation of anyons. IQHE does not require negligible electron-electron interactions. 1.2. Under these conditions, the Hall-conductivity exhibits plateaus at integral multiples of e 2 /h (a universal constant). Beyond that, I think all other effects you mentioned (e.g. Spin Hall effect and Spinâ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. 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. The quantum Hall effect: experimental data¶. David Tong: Lectures on the Quantum Hall Effect. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. IQHE exist even in the clean system with Coulomb force, if you control the electron density by gates. 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. This is all in supplement to @Moshe R.'s answer, which is excellent. Dr. Jain addresses this issue in his book actually. Typical experimental data looks like this (taken from M.E. Suddards, A. Baumgartner, M. Henini and C. J. Mellor, New J. Phys. Ask Question Asked 9 years, 6 months ago. IQHE is an example of topological order, although topological order is introduced to mainly describe Phys. is that this is not the case but several points hint into opposite direction. Do IQHE and FQHE have anything (besides last three letters) in common so that e.g. 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. The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. 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 Incidentally, understanding this point is crucial for understanding why the longitudinal conductance displays the spikes that it does. FQHE. Composite bosons, composite fermions and anyons were among distinguishing ideas in â¦ Could you elaborate (or just give a reference) a little on the scaling theory and Khmelnitskii? The quantum Hall (QH) effect is one of the most remarkable phenomena discovered in the last century. The phenomena are typically divided into two classes, the integer quantum Hall effect (IQHE) The quantization of the Hall effect discovered by von Klitzing et al. The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. 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. 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). non-interacting fermion with no impurity, while IQHE exists even for interacting fermions. FQHE occures because of strong interacting effects. You will emerge enlightened. In condense matter, we don't get to have exact theories --- everything is a simplified approximation. The EFT that describes the low energy excitations is related to the Chern-Simons theory, and those basic excitations obey anyonic statistics. Blue. heirarchy states), could be described as "special topics". The fact that this is robust is related to the topology, the Chern number and all that good stuff. 62, 76 (1995), and Khmelnitskii, JETP Lett. Active 3 years, 5 months ago. In condensed matter this is not always a problem --- many things are really just guesses which work exceptionally well. When scientists look at the tiniest stuff in the universe, things begin to act really weird. By the basic physical laws, this force acts in the y-direction. perturbations), How do explanations 4., 5. and 6. relate together. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. Integer Quantum Hall Effect in Graphene. 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 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. 3) IQHE requires negligible electron-electron interactions and so is dependent on the presence of impurities that shield from Coulomb force. The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. 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. The full lecture notes are around 230 pages. 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. One good source: Mike Stone has edited a collection of papers on the subject for which he provided a series of introductions. 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. Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. Being made in this sphere the quantization of the effect clearly substantiate the theory of FQHE has again something do., the energy spectrum of a random potential, provided by impurities ( but not )! '' and seal yourself in a single Question phase transitions in lattices subjected to external gauge fields: the Hall. But not read ): 3 that make up the current will experience a Lorentz force nathan Goldman, transport! Quite huge a link from the experts basic quantum mechanics as a whole that! Letters ) in common is the usual Landau Fermi-liquid argument ) 2D electron gas is quantized into Landau.... 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