Introduction to quantum hall effect pdf

The quantum hall effect is a set of phenomena observed at low temperature in a twodimensional electron gas subject to a strong perpendicular magnetic field. Fortunately, our understanding of this menagerie is based almost entirely on many body wavefunctions of a. The freeelectron quantum gas model still predicts a hall coe. This is a simple classical model, and many of its concepts extend to the quantum case. 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. Introduction to the physics of the quantum hall regime. Laughlin introduced a quasiparticle with fractional charge and its wave. This phenomenon is known as the hall e ect and associated with a resistance r. Introduction to integer quantum hall effect by ganpathy murthy. The calculations and the explanations are terse, but provide a basic understanding to a first time reader.

The emphasis is on the localization and interaction physics in the extreme quantum limit which. Generally speaking, the iqhe in graphene has the same underlying mechanism as that in the semiconductor 2deg. Dan arav and gil novik from the school of media studies of the college of management academic studies for their help in preparing the videos. Introduction to the quantum hall effect and topological phases. After a brief historical overview in chapter 1, we discuss in detail the kineticenergy quantisation of nonrelativistic and the relativistic electrons in a strong magnetic field chapter 2. Introduction to integer quantum hall effect by ganpathy. This can be included phenomenologically by introducing an impulse. Landau levels, cyclotron frequency, degeneracy strength, flux quantum. One of the best known examples is the berry phase m. This simple setup provides the setting for some of the most wonderful and surprising results in physics. Before introducing quantum hall effect, one may take a look at the classical hall. Plotting the hall resistance essentially the reciprocal of the hall conductance of a lowtemperature twodimensional electron gas against the strength of the imposed magnetic field normal to the gas plane, one finds a stairlike quantized sequence of hall conductances very precisely equal to ne 2 h, where n is the integer that characterizes. 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.

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. These phenomena are known collectively as the quantum hall e. Another factor driving the growing interest in the hall effect is related to. After a brief historical overview in chapter 1, we discuss in detail the kineticenergy quantisation of nonrelativistic and the relativistic. This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics. These lecture notes attempt to explain the main ideas of the theory of the quantum hall effect. Pdf introduction to quantum hall effects researchgate.

Readers are referred to chapter 4 for the basic concepts of quantum hall effects in semiconductors, e. Universal introduction to the quantum hall effect international. The nature of this plateau is still a matter of debate, and active current research. The integer quantum hall effect iqhe was discovered by k. Hall effect experiment utk department of physics and. The fractional quantum hall effect results in deep minima in the diagonal resistance, accompanied by exact quantization of the hall plateaux at fractional filling factors tsui et al. History of the quantum hall effect 9 function, where strong correlations prevent the simultaneous occupation of any site by two electrons. Quantized hall plateaus have been found corresponding to a few even denominator fractions. The fractional quantum hall effect is one of the most remarkable phenomena in all of condensed matter physics. The quantum hall effect as an electrical resistance standard 1605 1. Correlated 2d electron aspects of the quantum hall effect. For clarity, the original effect is sometimes called the ordinary hall effect to distinguish it from other hall effects. Theory of the integer and fractional quantum hall effects arxiv. Quantum hall effects an introduction 1 quantum hall effects an introduction m.

The ordinary hall effect was discovered by edwin hall 1 in 1879. The hall effect is the production of a voltage difference the hall voltage across an electrical conductor, transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current. Quantum hall effects in graphene 55, 56 have been studied intensively. International centre for theoretical sciences 3,262 views. Jain, composite fermions, cambridge university press 2007 introduction in a magnetic eld, a system of charged particles e. The calculations and the explanations are terse, but provide a. Pdf the quantum hall effect is a set of phenomena observed at low temperature in a twodimensional electron gas subject to a strong. The common feature of these systems is that the bulk has a. Integer and fractional quantum hall transport data showing the plateau regions in the. Advancement in nanotechnologies made possible the fabrication of nanostructures only in recent times and the 2d structures turn out to host one of the most beautiful physics known to mankind. Hall effect measurements in materials characterization. We have developed the theory of the quantum hall effect by using the theory of. Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature.

Hall effect measurements can also be used for characterizing novel storage devices that employ quantized hall effect, magnetoresistance profiling, etc. This article was done as a term paper for the course ph5107advanced condensed matter at iiser kolkata. To do so we will use the drude theory of conductors. References home university of waterloo university of. Pdf quantum hall effect a brief introduction researchgate. It gives a brief introduction to both integer and fractional quantum hall effect. The quantum hall effect in a periodic potential 14 e. The quantum hall effect as an electrical resistance standard. The unexpected discovery of the quantum hall effect was the result of basic research on silicon fieldeffect transistors combined with my experience in metrology, the science of measurements. The quantum hall effect is most representative of mesoscale systems or nanoscale devices because it exists only in twodimensional 2d systems, which do not normally exist in nature.

These lecture notes yield an introduction to quantum hall effects both for nonrelativistic electrons in conventional 2d electron gases such as in semiconductor heterostructures and relativistic electrons in graphene. Ppt quantum hall effects an introduction powerpoint. Dynamical quantum hall effect in the parameter space pnas. Topological insulators generic form of a twoband hamiltonian. In 1930, landau showed that the orbital motion of the electron gives magnetic susceptibility. These phenomena are known collectively as the quantum hall e ect. In the presence of a strong magnetic field, charged particles confined to move in the plane can form a series of new states of matter with bizarre properties. The quantum hall effects remains one of the most important subjects to have emerged in condensed matter physics over the past 20 years. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum hall effect. As a new phd student, the opportunity to undertake a short exploratory training project etp is one of the main appeals of a centre for doctoral training. The drude theory and the hall effect before considering the effect of magnetic fields on conductors, we need some model to describe the flow of currents in response to electric fields.