Introduction to the theory of the integer quantum hall effect pdf

In 1930, landau showed that the orbital motion of the electron gives magnetic susceptibility. Pdf quantum hall effect a brief introduction researchgate. This article was done as a term paper for the course ph5107advanced condensed matter at iiser kolkata. We have developed the theory of the quantum hall effect by using the theory of angular momentum. The integer quantum hall effect iqhe huge interest in topological aspects of quantum matter, enhanced by the recent nobel prize to m. Southampton university, southampton so9 5nh, uk received 16 october 1987 abstract. Theory of the integer and fractional quantum hall effects arxiv. Introduction to the theory of the integer quantum hall.

Mar 03, 2015 introduction to integer quantum hall effect by ganpathy murthy duration. By contrast, the fractional quantum hall effect is a collective phenomenon for which coulomb interactions between electrons are essential. No amount of examination of newtons laws as an abstract system will lead you to quantum mechanics. The emphasis is on the localization and interaction physics in the extreme quantum limit which. Historically, the qhe has also been used to define the. Thouless d others 3 proposed various topological arguments showing why the hall conductance has to be an integer in units of e quantum conductance e 2 h. Introduction constructing a rigorous theory of the integer quantum hall effect, discovered by k. Together with a detailed introduction by the editor, this volume serves as a stimulating and valuable. In this book, only the underlying physics of the quantum hall effects are discussed and they are introduced in simple, intuitive pictures. Basic physics underlying the phenomenon is explained, along with diverse. Together with a detailed introduction by the editor, this volume serves as a.

Introduction to integer quantum hall effect by ganpathy murthy duration. There are surprisingly few dedicated books on the quantum hall e. Readings quantum physics iii physics mit opencourseware. Lecture notes on quantum hall effect a work in progress. Quantum hall effects comprise the integer quantum hall effect iqhe and the fractional quantum hall effect fqhe. Hall effect experiment utk department of physics and. This textbook on the quantum hall effect was conceived and written by four scientists who have long been active in the area. Two prominent ones are prange and girvin, the quantum hall e. Theory of the integer quantum hall effectan introductory survey. The aim of these lectures is to give an introduction to the present state of the theory of the integer quantum hall effect iqhe. Scaling theory of the integer quantum hall effect and localized states, and we shall call these states critical states. Theory of the integer quantum hall effect an introductory. A model is introduced for anderson localisation in the integer quantum hall regime. A generic theory of the integer quantum hall effect.

In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. Chapter 9 spin polarization in the fractional quantum hall states. Quantum hall effect by michael stone quantum hall effect by michael stone this book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics. The integer quantum hall e ect university of british. Introduction to the physics of the quantum hall regime.

Percolation, quantum tunnelling and the integer hall effect. The observation that an explanation of the qhe involves both extended and localized states was the more unanticipated, as the scaling theory of localization wegner, 1976, 1979. Introduction of the flux quantization immediately explains. Introduction in this chapter an overview of the integer quantum hall e ect iqhe will be provided. International centre for theoretical sciences 3,262 views. The quantum hall qh effect is one of the most remarkable phenomena discovered in the last century. Calculation of hall current due to a single filled landau level. Introduction to the theory of the integer quantum hall effect em. The integer quantum hall effect classical dynamics quantizing magnetic fields the eigenvalue problem the landau model models of confinement bloch representation. Introduction to the quantum hall effect and topological phases. The ordinary hall effect was discovered by edwin hall 1 in 1879.

Selecting this option will search all publications across the scitation platform selecting this option will search all publications for the publishersociety in context. An instructive and comprehensive overview of the qhe, this book is also suitable as an introduction to quantum field theory with vivid applications. Not intended as an exhaustive survey, it covers subjects which have turned out to have had a significant and lasting impact on our understanding of the quantum hall effect. Homotopy approach to fractional quantum hall effect. 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. Pdf introduction to quantum hall effects researchgate. E gives the relationship between the applied electric eld and the induced current density at the level of linear response theory, where the conductivity.

The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum hall effect. Girvin yale university sloane physics laboratory new haven, ct 06520 usa. Quantum mechanical problem of a particle in crossed magnetic and electric fields. Provides an introduction to the ways of using the various models that try to explain diverse aspects of the quantum hall effect qhe, an effect that is still not properly understood. Read introduction to the theory of the integer quantum hall effect. The fractional quantum hall effect fqhe is a collective behaviour in a twodimensional system of electrons. 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. The qualitative explanation of the iqhe due to the localization of electrons in a random.

More recently, examples of topological phases that do not require external magnetic. One constructs a two dimensional electron gas from a semiconductor heterostructure, for example a gaas structure sandwiched in between two alas semiconductors. The quantum hall effects remains one of the most important subjects to have emerged in condensed matter physics over the past 20 years. Pdf this article was done as a term paper for the course ph5107advanced condensed. The fundamental quantum of hall resistance is he2 25,8 in this lab we will only be concerned with the hall coefficient. Microscopic approach people from condensed matter and effective. The structure of fractional quantum hall effect data is similar to that for the integer effect, and can be understood according to a. The quantum hall effect in a periodic potential 14 e. Quantum hall effect an overview sciencedirect topics.

In the model oftwodimensional noninteracting electrons in strong magnetic fields, the transitions are disorderinduced localization. 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. As in the integer quantum hall effect, the hall resistance undergoes. These lecture notes attempt to explain the main ideas of the theory of the quantum hall effect. Introduction in a 2dimensional electron system 2des, ohms law j. The full text of this article is available in pdf format. Quantum phase transitions, as we shall see, are present in a number of quantum hall e. The following article is intended to provide a introduction to the iqhe from this viewpoint, as a supplement to the broader. The integer quantum hall effect is a singleparticle phenomenon. Percolation, quantum tunnelling and the integer hall effect j t chalker and p d coddington physics department.

This will provide a useful background for our discussion of the quantum hall e ect. The calculations and the explanations are terse, but provide a basic understanding to a first time reader. The noncommutative geometry of the quantum hall effect. The elementary theory of the hall effect and the quantum mechanics of free electrons in a strong magnetic field are recalled. Fqhe revisted shortly after discovery of the integer quantum hall effect iqhe in two dimensional electron system 2deg. 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.

Topological insulators generic form of a twoband hamiltonian. Thouless d others 3 proposed various topological arguments showing why the hall conductance. The original, classical hall e ect was discovered in 1879 by edwin hall. The phenomena are typically divided into two classes, the integer quantum hall effect iqhe. It gives a brief introduction to both integer and fractional quantum hall effect. The basics are described well but theres nothing about chernsimons theories or the importance of the edge modes. This option allows users to search by publication, volume and page selecting this option will search the current publication in context. The quantum hall e ect qhe is one of the most remarkable condensedmatter phenomena dis covered in the second half of the 20th century. Lecture 12 the integer quantum hall effect continued. Subsequent work in my laboratory in wiirzburg using a super conducting solenoid confirmed the constancy of the hall resistance both in dordas samples and in samples. Introduction to the theory of the integer quantum hall effect. Integer quantum hall effect, which is the hall effect quantized into integer times e 2 h e. The quantum world forced itself upon us when physicists tried and failed to explain the results of experiments using the tools of classical.