After a brief historical overview in chapter 1, we discuss in detail the kineticenergy quantisation of nonrelativistic and the relativistic. The calculations and the explanations are terse, but provide a. Theory of the integer and fractional quantum hall effects arxiv. Dynamical quantum hall effect in the parameter space pnas. The emphasis is on the localization and interaction physics in the extreme quantum limit which. This proposal has been at the center of active discussions over the last twenty years. 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. History of the quantum hall effect 9 function, where strong correlations prevent the simultaneous occupation of any site by two electrons. This phenomenon is known as the hall e ect and associated with a resistance r.
Introduction to the quantum hall effect and topological phases. 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. Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. Jain, composite fermions, cambridge university press 2007 introduction in a magnetic eld, a system of charged particles e. Pdf introduction to quantum hall effects researchgate. Topological insulators generic form of a twoband hamiltonian. 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. Quantized hall plateaus have been found corresponding to a few even denominator fractions.
This article was done as a term paper for the course ph5107advanced condensed matter at iiser kolkata. These lecture notes attempt to explain the main ideas of the theory of the quantum hall effect. 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 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. This can be included phenomenologically by introducing an impulse. References home university of waterloo university of. Universal introduction to the quantum hall effect international. The quantum hall effect as an electrical resistance standard. The quantum hall effects remains one of the most important subjects to have emerged in condensed matter physics over the past 20 years. Hall effect measurements in materials characterization. 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. Integer and fractional quantum hall transport data showing the plateau regions in the. Quantum hall effects an introduction 1 quantum hall effects an introduction m.
This is a simple classical model, and many of its concepts extend to the quantum case. 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. The nature of this plateau is still a matter of debate, and active current research. Correlated 2d electron aspects of the quantum hall effect. 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. Quantum hall effect an overview sciencedirect topics. Fortunately, our understanding of this menagerie is based almost entirely on many body wavefunctions of a. The common feature of these systems is that the bulk has a. Laughlin introduced a quasiparticle with fractional charge and its wave. Pdf quantum hall effect a brief introduction researchgate.
These phenomena are known collectively as the quantum hall e. Hall effect measurements can also be used for characterizing novel storage devices that employ quantized hall effect, magnetoresistance profiling, etc. The freeelectron quantum gas model still predicts a hall coe. Before introducing quantum hall effect, one may take a look at the classical hall.
The ordinary hall effect was discovered by edwin hall 1 in 1879. International centre for theoretical sciences 3,262 views. This simple setup provides the setting for some of the most wonderful and surprising results in physics. The calculations and the explanations are terse, but provide a basic understanding to a first time reader. This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum hall effect. 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. Introduction to integer quantum hall effect by ganpathy murthy duration. 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. Landau levels, cyclotron frequency, degeneracy strength, flux quantum.
For clarity, the original effect is sometimes called the ordinary hall effect to distinguish it from other hall effects. Ppt quantum hall effects an introduction powerpoint. 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 quantum hall effect as an electrical resistance standard 1605 1.
Readers are referred to chapter 4 for the basic concepts of quantum hall effects in semiconductors, e. The integer quantum hall effect iqhe was discovered by k. It gives a brief introduction to both integer and 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. 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. 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.
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. Generally speaking, the iqhe in graphene has the same underlying mechanism as that in the semiconductor 2deg. Introduction to integer quantum hall effect by ganpathy. Introduction to the physics of the quantum hall regime. The fractional quantum hall effect is one of the most remarkable phenomena in all of condensed matter physics. Another factor driving the growing interest in the hall effect is related to. The quantum hall effect in a periodic potential 14 e. Hall effect experiment utk department of physics and. In 1930, landau showed that the orbital motion of the electron gives magnetic susceptibility. Similar to the iqhe, this is the result of gaps in the density of states, unlike the iqhe, however, it is not. One of the best known examples is the berry phase m. We have developed the theory of the quantum hall effect by using the theory of. To do so we will use the drude theory of conductors.
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