7 Nov 2016 Introductory idea of integral & fractional quantum hall effect and by imposing the idea of composite fermions showing the existence of fractional

The unexpected discovery of the quantum Hall effect was the result of basic research on silicon field-effect transistors combined with my experience in metrology, the science of measurements. This personal review demonstrates that condensed matter physics is full of surprises and that access to excellent crystals and materials is a crucial ingredient of the success of experimentalists in

It is used to determine the concentration of electrons. The Quantum Hall effect has been discovered by von Klitzing in Germany and by The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. The quantum Hall effect (QHE), a quantized version of the Hall effect (), was observed in two-dimensional (2D) electron systems more than 30 years ago (2, 3).In QHE, the Hall resistance, which is the voltage across the transverse direction of a conductor divided by the longitudinal current, is quantized into plateaus of height h/νe 2, with h being Planck’s constant, e the electron's charge On the other hand, at high magnetic fields the Hall resistance has been observed to be quantized in units of (h/2e 2) with an accuracy that is specified in parts per million. Indeed the accuracy of the quantum Hall effect is so impressive that the National Institute of Standards and Technology is interested in utilizing it as a resistance standard.

In the so-called integer quantum Hall e ect (IQHE) discovered by von Klitzing in 1980, the quantum number is a simple integer with a precision of about 10 10 and an absolute accuracy of about 10 8 (both being limited by our ability to do resistance metrology). The quantum Hall effect was discovered on about the hundredth anniversary of Hall's original work, and the finding was announced in 1980 by von Klitzing, Dorda and Pepper. Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery. Current advances: The fine-structure constant and quantum Hall effect The fine-structure constant α is of dimension 1 (i.e., it is simply a number) and very nearly equal to 1/137. It is the "coupling constant" or measure of the strength of the electromagnetic force that governs how electrically charged elementary particles (e.g., electron, muon) and light (photons) interact. This effect is called integer quantum Hall effect. Interestingly, the values of the Hall resistance are independent on the materials chosen in the measurements.

The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. 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.

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The 1980 discovery of the quantum Hall effect kicked off the study of topological orders, electronic states with "protected" patterns of long-range quantum entanglement that are remarkably robust.

The full lecture notes are around 230 pages.

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This effect is called integer quantum Hall effect. Interestingly, the values of the Hall resistance are independent on the materials chosen in the measurements.

= −. 1 ne. Hall coefficient. 51.
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Nobel Lecture: The fractional quantum Hall effect* Horst L. Stormer Department of Physics and Department of Applied Physics, Columbia University, New York, New York 10023 and Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974 [S0034-6861(99)00704-7] INTRODUCTION The fractional quantum Hall effect is a very counter-

I. Introduction: materials, transport, Hall effects In this 3D quantum Hall effect, the edge states are located at only one edge on the top surface and at the opposite edge on the bottom surface (green and orange arrowed lines in Fig. 1d and e), which can be probed by scanning tunneling microscopy. The 3D quantum Hall effect may be realized in other systems with novel surface states. The Quantum Hall Effect Could someone help me understand the Quantum Hall effect qualitatively or provide good resources that do this? I know how the classical Hall effect works but I haven't learnt quantum mechanics to understand QHE and would really love a intuitive explanation.