Things become uncertain. Hereâs the set-up. 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. 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. Suddards, A. Baumgartner, M. Henini and C. J. Mellor, New J. Phys. The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. The only thing IQHE and FQHE have in common is the ultimate physical effect, but the mechanism is very different. The EFT that describes the low energy excitations is related to the Chern-Simons theory, and those basic excitations obey anyonic statistics. @4tnemele: Fermi liquid theory has a semi-controlled expansion (viz. 5) FQHE has again something to do with topology, TQFT, Chern-Simons theory, braiding groups and lots of other stuff. 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! Usually, the quantum Hall effect takes place only in 2D systems. 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. lèUM«za>)Ýä ¢Ì6B?´oÙ'[Õö#Î9©¡g°å×-É7½(¥y§x Ask Question Asked 9 years, 6 months ago. B 235, 277 (1984). Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. 1.2. 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) ⦠It is a simple consequence of the motion of charged particles in a magnetic eld. FQH states contain a new kind of order: topological order. Instead, a completely unexpected result was measured for the first time by Klaus von Klitzing. Do IQHE and FQHE have anything (besides last three letters) in common so that e.g. This is all in supplement to @Moshe R.'s answer, which is excellent. This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics: the quantum Hall effect. In the context of Quantum Hall ⦠Phys. 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. An English reference is Pruisken, Nucl. Typical experimental data looks like this (taken from M.E. Composite bosons, composite fermions and anyons were among distinguishing ideas in ⦠Nevertheless, the composite fermions picture is nice in its intuitiveness and helps to build a mental picture. https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/6173#6173. 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. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. @Marek: my knowledge comes from my supervisor, and I suspect it is a little folklore-ish in nature. 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. 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. 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. 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. Nathan Goldman, Quantum transport in lattices subjected to external gauge fields: The quantum Hall effect in optical lattices and quantum graphs. 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 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? Let me begin and see where I run out of steam. 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. FQHE. Shankar) in terms of renormalisation about the Fermi surface. When scientists look at the tiniest stuff in the universe, things begin to act really weird. Integer Quantum Hall Effect in Graphene. Tremendous theoretical and experimental developments are still being made in this sphere. Incidentally, understanding this point is crucial for understanding why the longitudinal conductance displays the spikes that it does. is that this is not the case but several points hint into opposite direction. Oh boy, hard to know where to start. Is there any accessible introductory literature into these matters? 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. The Quantum Hall Effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. Under these conditions, the Hall-conductivity exhibits plateaus at integral multiples of e 2 /h (a universal constant). 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. safe from small disturbances. Randonauting for Dummies. HISTORY OF THE QUANTUM HALL EFFECT 9 function, where strong correlations prevent the simultaneous occupation of any site by two electrons. 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. Dr. Jain addresses this issue in his book actually. The quasiparticles excitations in FQH states are anyons. 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! ... Quantum Hall effect for dummies. The quantum Hall effect has led to three Nobel Prizes in Physics (1985 von Klitzing; 1998 Tsui, Stormer, Laughlin; 2016 Thouless, Haldane, Kosterlitz). To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. 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. The quantum Hall effect: experimental data¶. The fact that this is robust is related to the topology, the Chern number and all that good stuff. 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. 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. 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. This was too long to fit into a comment, so an answer it will have to be. The original, classical Hall e ect was discovered in 1879 by Edwin Hall. @genneth I think you might be referring to a controversy over the "composite fermion" theory. Beyond that, I think all other effects you mentioned (e.g. (Incidentally, all of this is well-known stuff appearing in textbooks, though not always in an organized way. You can also provide a link from the web. 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. @Moshe R.: Notice that FQHE is not IQHE of anyons --- the anyons only appear as the excitations. non-interacting fermion with no impurity, while IQHE exists even for interacting fermions. perturbations), How do explanations 4., 5. and 6. relate together. The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. 38, 552 (1985). 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). 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. 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). Fermion alway carry Fermi statistics by definition, and they are never anyons. However, the theory of FQHE has not reached quite the same consensus. Some of the successful explanations of the effect are summarized in the following. [â¦] The full lecture notes are around 230 pages. David Tong: Lectures on the Quantum Hall Effect. This is an inherently difficult problem, and in fact it was solved only by a guess - the Laughlin wavefunction. Weâll start these lectures by reviewing the underlying physics of the Hall e ect. 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. This can also be referred to as the talking walls effect, where it ⦠In practise, one could level the same criticism at IQHE, which relies on Fermi liquid arguments, which are also foundationally not really rigorous. References I've seen (but not read): Muzykanskii and Khmelnitskii, JETP Lett. Impurities do not screen anything. This is where we can start with an explanation of the basics of quantum mechanics for dummies. 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 Unfortunately, I am as of yet very confused by all the (seemingly disparate) stuff I learned. Could you elaborate (or just give a reference) a little on the scaling theory and Khmelnitskii? IQHE is an example of topological order, although topological order is introduced to mainly describe 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. 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. In condense matter, we don't get to have exact theories --- everything is a simplified approximation. The low energy effective theories of FQH states are TQFTs (such as Chern-Simons theories). The electrons themselves provide the screening to make an independent electron approximation semi-justified (this is the usual Landau Fermi-liquid argument). 62, 76 (1995), and Khmelnitskii, JETP Lett. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. The phenomena are typically divided into two classes, the integer quantum Hall effect (IQHE) The quantum Hall (QH) effect is one of the most remarkable phenomena discovered in the last century. For the integer QHE, the next crucial step is the presence of a random potential, provided by impurities. heirarchy states), could be described as "special topics". Blue. 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. Yehuda B. ×'½ÉP´3~ìo¿N¿:|t]{/FYkØ÷¯Ï±,zî&\ÆÆT@OºCyâÂM:F~*¤-¦´e¯±^¡A3XC[FÇàÍÅ°ÜØ*Àc"é If you find this book, those introductions are very good.). But right now I just didn't know where to start as the topic of QHE seems quite huge. Contrary to some discussions you hear sometimes, this by itself does NOT result in quantized Hall conductance. (max 2 MiB). Quantum tunneling falls under the domain of quantum mechanics: the study of what happens at the quantum scale. Thanks a lot! This is a course on the quantum Hall effect, given in TIFR, Mumbai. Buy a copy of Jain's "Composite Fermions" and seal yourself in a comfortable room with plenty of snacks. The characterization of IQHE by Chern number of energy band only works for ... Understanding Quantum Point Information. 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. That's also why I ask about both QHE in a single question. You will emerge enlightened. If you also apply a magnetic field in the z-direction, then the electrons that make up the current will experience a Lorentz force. 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. This proposal has been at the center of active discussions over the last twenty years. To be rigorous, let's put the material in the (x,y) plane and let the current flow in the x-direction*. 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). The quantum Hall effect has provided an amazingly accurate method for calibrating resistance. In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. Four numbers, called quantum numbers, were introduced to describe the characteristics of electrons and their orbitals: 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. IQHE exist even in the clean system with Coulomb force, if you control the electron density by gates. The Quantum Hall Effect Michael Richardson In 1985, Klaus von Klitzing was awarded the Nobel Prize for his discovery of the quantized Hall effect. Active 3 years, 5 months ago. 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 . Tremendous theoretical and experimental developments are still being made in this sphere FQH., so I 'll look at that intro and ( hopefully ) ask somewhat focused. 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