Dynamical quantum hall effect in the parameter space pnas. The fractional quantum hall effect, in particular, has opened up a new paradigm in the study of strongly correlated electrons, and it has been shown that new concepts, such as fractional statistics, anyon, chiral luttinger liquid and composite particles, are realized in twodimensional electron systems. Steven girvin quantum hall effect institute for quantum computing. But in a magnetic eld, a system of charged particles e. The hall resistance in the classical hall effect changes continuously with applied magnetic field. Originally associated with effects in classical physics it has fascinating extensions to quantum physics. Left the quantum hall effect qhe occurs in a twodimensional electron system under a large applied magnetic field. Right the quantum anomalous hall effect has quantum hall features without an applied field. Theory of the integer and fractional quantum hall effects shosuke sasaki. Quantum hall effect 55 skipping cyclotron orbits fourterminal sample configuration to measure the hall and longitudinal resistivities quantum hall effect 56 for a given plateau not a perfect conductor. The interaction physics in the extreme quantum limit which is responsible for the fractional quantum hall effect is discussed at length and from an elementary point. This is a course on the quantum hall effect, given in tifr, mumbai. The freeelectron quantum gas model still predicts a hall coe. Introduction to the physics of the quantum hall regime.
Two prominent ones are prange and girvin, the quantum hall e. Introduction to the quantum hall effect and topological phases mark o. Tremendous theoretical and experimental developments are still being made in this sphere. Quantum hall effects an introduction 1 quantum hall effects an introduction m. The first four chapters require only basic quantum mechanics. The quantum hall effect or integer quantum hall effect is a quantummechanical version of the hall effect, observed in twodimensional electron systems subjected to low temperatures and strong magnetic fields, in which the hall conductance.
The quantum hall effect qhe is one of the most remark able condensedmatter. The discovery of the quantized and fractional quantum hall effect phenomena is among the most important physics findings in the latter half of this century. Topological aspects of the quantum hall effect y hatsugaiy department of applied physics, university of tokyo, 731 hongo, bunkyoku, tokyo 1, japan received 12 august 1996, in. Introduction to the quantum hall effect and topological phases. Semiclassical view of skipping orbits at the fermi level at the two. Later also plateaus at intermediate values of hall voltages were measured 2. The vonklitzing constant depends only on the planck constant h and the charge of the electron e. Quantum hall transitions are the quantum phase transitions that occur between different robustly quantized electronic phases of the quantum hall effect.
Aug 01, 2002 this book describes the classical electromagnetics, atoms in a magnetic field, spinorbit coupling, semiconductors, insulatormetal transition by doping, heterostructures, landau levels, response function, quantum hall effect, combination of gvalues, halffilled landau levels, spinorbit interaction with 1c coupling, flux tunnelling goldstone mode, experimental as well as theoretical. Ppt quantum hall effects an introduction powerpoint. Lecture note on quantum hall effect solid state physics. A test of the quantum hall effect as a resistance standard. Local investigation of the classical and quantum hall effect article pdf available in aip conference proceedings 772. A smooth transition from the classical to the quantum hall effect as 2 a decreases. There are surprisingly few dedicated books on the quantum hall e. Parameswaran slightly edited version of the introductory chapter from quixotic order and broken symmetry in the. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum hall effect. Correlated 2d electron aspects of the quantum hall effect. This will provide a useful background for our discussion of the quantum hall e.
Pdf lecture note on quantum hall effect solid state physics. With this small detour into classical mechanics we are now in the position to tackle the quantum mechanical problem of a particle in a magnetic field. Electrons are restricted to move in the 2d x,yplane while a constant magnetic eld points in the zdirection. Transition from the classical to the quantum hall effect in a system. A test of the quantum hall effect as a resistance standard author. Ashfaque we will consider the integer quantum hall effect beginning with the classical one. For low temperatures and strong magnetic elds, however, r r 0. Pdf study material of classical and quantum hall effect. Classical and quantum simulations describe well most of our. Introduction to the fractional quantum hall e ect steven m. Pdf this is class notes made by student and teacher on quantum hall effect, taught in iit bhilai on nov, 2019 by sabyasachi ghosh find. It is a simple consequence of the motion of charged particles in a magnetic. Theory of the integer and fractional quantum hall effects. Quantum hall e ect and electromechanics in graphene a thesis submitted to the tata institute of fundamental research, mumbai for the degree of doctor of philosophy in physics by vibhor singh department of condensed matter physics and materials science tata institute of fundamental research mumbai march, 2012.
It bears the name of the american edwin hall who discovered it in 1879. The integer quantum hall effect iqhe explaining the existence of plateaus 5. Classical magnetotransport resistivity and lowfield hall effect measurements have been performed in the temperatures between 1. Definition hall effect classical hall effect quantum. Since its discovery in 1980, the quantum hall effect became the fertible. Quantum hall e ect and electromechanics in graphene. Exploring 4d quantum hall physics with a 2d topological. The classical hall e ect was discovered by edwin hall in 1879. Parameswaran slightly edited version of the introductory chapter from quixotic order and broken symmetry in the quantum hall e. Quantum hall effects and related topics international symposium. Classical and quantum hall effect measurements in galnnas. The quantum hall e ect seminar talk by tobias witt given on may 24, 2017 abstract when exposed to a magnetic eld belectrons will move in a direction perpendicular to the drop of voltage. The hall current does not increase continuously with hall voltage but in steps.
We assume that the chemical potential is in between two landau levels at positive energies, shown by the dashed line in fig. Localization and the integer quantum hall e ect the aim of this lecture is to explain how disorder which creates a random potential for electrons, thereby destroying translational symmetry is a necessary and su cient condition for the observed plateaus, for noninteracting electrons. The quantum spin hall effect is a fundamental property of. The landau level structure shows two zeroenergy modes.
Girvin yale university sloane physics laboratory new haven, ct 06520 usa 1 introduction the quantum hall e ect qhe is one of the most remarkable condensedmatter phenomena discovered in the second half of the 20th century. The basics are described well but theres nothing about chernsimons theories or the importance of the edge modes. This proposal has been at the center of active discussions over the last twenty years. The robust quantization of these electronic phases is due to strong localization of electrons in their disordered, twodimensional potential.
The quantum hall effect, discovered in the 1980s, is an important fundamental effect in condensed matter physics that links topological states with electronic properties in twodimensional systems. The quantum hall effect like all others has its root in the classical hall effect, which we have linked to the physical explanations based on the lorentz force. Jun 06, 2011 the quantum hall effect qhe is the remarkable observation of quantized transport in two dimensional electron gases placed in a transverse magnetic field. The hall conductivity a, does not depend on the parameters of the scatterers. Quantum coherence in mesoscopic systems created date. The quantum hall effect is a typical realization of topological effects in condensed matter physics. Quantum hall effect an overview sciencedirect topics. History of the quantum hall effect 9 function, where strong correlations prevent the simultaneous occupation of any site by two electrons. In 1980 the measurements have revealed the quantization of the hall conductance at low temperatures 1. It is shown that an increase in the strength of the coulomb interaction. The quantum spin hall effect for electrons allows for the existence of an unusual type of materialcalled a topological insulatorwhich conducts electricity on the surface but not through the.
These lecture notes attempt to explain the main ideas of the theory of the quantum hall effect. The hall effect is a well known phenomenon in the field of material electromagnetism. We report on the properties of a system of interacting electrons in a narrow channel in the quantum hall effect regime. The conventional quantum hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. These results can be interpreted as a dynamical quantum hall effect in a parameter space. Local investigation of the classical and quantum hall effect. The quantum hall effect qhe is one of the most fascinating and beautiful phenomena in all branches of physics. The quantum hall effect or integer quantum hall effect is a quantum mechanical version of the hall effect, observed in twodimensional electron systems subjected to low temperatures and strong magnetic fields, in which the hall conductance. Center for advanced high magnetic field science, graduate school of science, osaka university, 11 machikaneyama, toyonaka, osaka 5600043, japan.