Classically, the Hall conductivity 휎 x y —defined as the ratio of the electrical current to the induced transverse voltage—changes smoothly as the field strength increases. FQHE occures not because 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. The Quantum Hall Effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. qé•Y¼ÓÏê ¯kzÁpC‰Ðè×ï%¬ÐIځÂr€tžVat÷ «+ ¢ÏˆWà‹s1bz€kaT€Ã§þn«$9ñܞ.÷­¤q The effective non-interacting description does not really work (for example, it fails to describe the edge states and non-Abelian states). In condense matter, we don't get to have exact theories --- everything is a simplified approximation. FQHE. My understanding (based on 3.) Beyond that, I think all other effects you mentioned (e.g. The quasiparticles excitations in IQH states are always fermions. 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). HISTORY OF THE QUANTUM HALL EFFECT 9 function, where strong correlations prevent the simultaneous occupation of any site by two electrons. IQHE does not require negligible electron-electron interactions. 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 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. References I've seen (but not read): Muzykanskii and Khmelnitskii, JETP Lett. Blue. The phenomena are typically divided into two classes, the integer quantum Hall effect (IQHE) The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. If you also apply a magnetic field in the z-direction, then the electrons that make up the current will experience a Lorentz force. non-interacting fermion with no impurity, while IQHE exists even for interacting fermions. The integer quantum Hall effect is peculiar due to the zero energy Landau level. Quantum Physics for Dummies Quantum Mechanics studies the smallest stuff in the universe. Thank you. 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. Typical experimental data looks like this (taken from M.E. 5) FQHE has again something to do with topology, TQFT, Chern-Simons theory, braiding groups and lots of other stuff. Phys. The first four chapters require only basic quantum mechanics; the final two chapters need techniques from quantum field theory. By the basic physical laws, this force acts in the y-direction. @4tnemele: Fermi liquid theory has a semi-controlled expansion (viz. Abstract. The fact that this is robust is related to the topology, the Chern number and all that good stuff. Nathan Goldman, Quantum transport in lattices subjected to external gauge fields: The quantum Hall effect in optical lattices and quantum graphs. Still, that was fun to write. Tremendous theoretical and experimental developments are still being made in this sphere. safe from small disturbances. We’ll start these lectures by reviewing the underlying physics of the 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. 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. 3) IQHE requires negligible electron-electron interactions and so is dependent on the presence of impurities that shield from Coulomb force. 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. Impurities do not screen anything. When scientists look at the tiniest stuff in the universe, things begin to act really weird. Ask Question Asked 9 years, 6 months ago. 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. ÝIÜB7WË8k…A½º The quantization of the Hall effect discovered by von Klitzing et al. 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). Things become uncertain. We consider an infinite graphene sheet with weak disorder that leads to broadening of Landau levels. In the original edition of this book, composite bosons, composite fermions and fractional charged excitations (anyons) were among the distinguished ideas presented. IQHE is an example of topological order, although topological order is introduced to mainly describe Viewed 6k times 22. 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. The quantum Hall effect has led to three Nobel Prizes in Physics (1985 von Klitzing; 1998 Tsui, Stormer, Laughlin; 2016 Thouless, Haldane, Kosterlitz). It is a simple consequence of the motion of charged particles in a magnetic eld. The quasiparticles excitations in FQH states are anyons. 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. 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. 38, 552 (1985). 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. 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. Is there any accessible introductory literature into these matters? 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. ×'½ÉP´3~Šìžoœˆ¿•N‹¿:|t]{/FY†k“Ø“÷¯Ï±,zî&\ÆÆT@OºŸCyâ’ÂM:F~*¤-¦—´e¯±^¡A3XC[F­Çà͂ŰÜØ*Àc"é 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. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. 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 (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. 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 thi… 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. (max 2 MiB). The low energy effective theories of FQH states are TQFTs (such as Chern-Simons theories). 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. This can also be referred to as the talking walls effect, where it … The characterization of IQHE by Chern number of energy band only works for Usually, the quantum Hall effect takes place only in 2D systems. 62, 76 (1995), and Khmelnitskii, JETP Lett. This proposal has been at the center of active discussions over the last twenty years. 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). 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 is the striking quantization of resistance observed under a large applied magnetic field in two-dimensional electron systems like graphene. Could you elaborate (or just give a reference) a little on the scaling theory and Khmelnitskii? I am not familiar with either. The quantum Hall effect has provided an amazingly accurate method for calibrating resistance. heirarchy states), could be described as "special topics". Do IQHE and FQHE have anything (besides last three letters) in common so that e.g. 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! @Marek: my knowledge comes from my supervisor, and I suspect it is a little folklore-ish in nature. But right now I just didn't know where to start as the topic of QHE seems quite huge. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. Four numbers, called quantum numbers, were introduced to describe the characteristics of electrons and their orbitals: The Quantum Hall Effect Michael Richardson In 1985, Klaus von Klitzing was awarded the Nobel Prize for his discovery of the quantized Hall effect. Composite bosons, composite fermions and anyons were among distinguishing ideas in … Integer Quantum Hall Effect in Graphene. https://physics.stackexchange.com/questions/6153/quantum-hall-effect-for-dummies/6173#6173. Please correct any mistakes I made and/or fill in other important observations, How do explanations 1. and 2. of IQHE come together? IQHE exist even in the clean system with Coulomb force, if you control the electron density by gates. Thanks a lot! Oh boy, hard to know where to start. Quantum Hall effect for dummies. In the context of Quantum Hall … Tremendous theoretical and experimental developments are still being made in this sphere. 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 original, classical Hall e ect was discovered in 1879 by Edwin Hall. FQH states contain a new kind of order: topological order. That's also why I ask about both QHE in a single question. The only thing IQHE and FQHE have in common is the ultimate physical effect, but the mechanism is very different. […] FQHE occures because of strong interacting effects. 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 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? Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. Dr. Jain addresses this issue in his book actually. Spin Hall effect and Spin‐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. is that this is not the case but several points hint into opposite direction. Under these conditions, the Hall-conductivity exhibits plateaus at integral multiples of e 2 /h (a universal constant). 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. Randonauting for Dummies. 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. If you find this book, those introductions are very good.). Here’s the set-up. You will emerge enlightened. Incidentally, understanding this point is crucial for understanding why the longitudinal conductance displays the spikes that it does. ... Understanding Quantum Point Information. Nathan Goldman, Quantum transport and phase transitions in lattices subjected to external gauge fields. Instead, a completely unexpected result was measured for the first time by Klaus von Klitzing. Unfortunately, I am as of yet very confused by all the (seemingly disparate) stuff I learned. [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. 6) Hierarchy states are examples of FQH states. 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. B 235, 277 (1984). 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. One good source: Mike Stone has edited a collection of papers on the subject for which he provided a series of introductions. IQHE can be treated as a special case? By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy, 2021 Stack Exchange, Inc. user contributions under cc by-sa.