Last edited by Voodoolabar
Saturday, February 15, 2020 | History

6 edition of The Quantum Hall Effect found in the catalog.

The Quantum Hall Effect

Poincaré Seminar 2004 (Progress in Mathematical Physics)

by

  • 318 Want to read
  • 26 Currently reading

Published by Birkhäuser Basel .
Written in English

    Subjects:
  • Theoretical methods,
  • Quantum Hall effect,
  • Congresses,
  • Science,
  • Science/Mathematics,
  • Quantum Theory,
  • Mathematical Physics,
  • Optics,
  • Science / Quantum Theory

  • Edition Notes

    ContributionsBenoît Douçot (Editor), Bertrand Duplantier (Editor), Vincent Pasquier (Editor), Vincent Rivasseau (Editor)
    The Physical Object
    FormatHardcover
    Number of Pages197
    ID Numbers
    Open LibraryOL9091009M
    ISBN 103764373008
    ISBN 109783764373009

    References A. So the energy spectrum really looks like that of a harmonic oscillator. At relatively high density, the Hall conductance of this system behaves itself accordingly and scales linearly with gate voltage, which is tuned to control the density. However, my point is that for FQHE we have even less.

    Baumgartner, M. Qi, Taylor L. In general we expect the electric and magnetic fields present in our Hall bar to apply a force to the electrons, and increase their velocity. Nevertheless, most people are far happier to accept that interactions may be neglected entirely, than somehow incorporating part of the interaction into a topological order, and neglecting the rest.

    The simplest explanation of this phenomenon was based on an independent electron picture. A prominent example is the two-dimensional 2D integer quantum Hall effect 1 : it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field 2. So let us try to do this for the simplest case of electrons in a magnetic field. 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 two-dimensional electron systems.


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The Quantum Hall Effect book

The Laughlin argument breaks down because it assumes specific values of the magnetic field. The key difference there is that such a longitudinal current breaks time-reversal through energy dissipation, which turns into heat that breaks time-reversal by the second law of thermodynamics.

But the large field needed for the quantum Hall effect would destroy most superconducting states. It will still be important to understand the quantum Hall effect in a bit more detail. In particular, we take the following geometry, which is called a Hall bar and is routinely used in experiments: The electron gas is contacted by six electrodes, numbered in the figure.

Originally the quantum Hall effect QHE was a term coined to describe the unexpected observation of a fundamental electrical resistance, with a value independent of the microscopic details of the semiconductor device.

We can drive a Hall current without wasting any energy because the current flows perpendicular to the voltage gradient. Tremendous theoretical and experimental developments are still being made in this sphere. The coverage also includes the recent development of the unconventional QHE in graphene a single atomic layer graphitewhere the electron dynamics can be treated as relativistic Dirac fermions and even the supersymmetric quantum mechanics plays a key role.

A superconducting quantum Hall system is predicted to be a chiral topological superconductor [8]which can be used to realize topological quantum computing—a quantum computing approach that is naturally robust against quantum decoherence.

Therefore Landau levels have a huge degeneracy, proportional to the area of the sample. The easiest way to do this is to apply a time-dependent magnetic field in the centre of the disc and use the Faraday effect.

At relatively high density, the Hall conductance of this system behaves itself accordingly and scales linearly with gate voltage, which is tuned to control the density. Mellor, New J. The microscopic theory of the QHE is formulated based on noncommutative geometry, the underlying mathematical structure.

Wu, and S. You can put many electrons in the same Landau level: one for every flux quantum of the magnetic flux passing through the system. The integer here is equal to the Chern number which arises out of topological properties of the material band structure.

Fantastic phenomena associated with the interlayer phase coherence and SU 4 quantum Hall ferromagnets in the bilayer system are extensively reviewed. In practise, one could level the same criticism at IQHE, which relies on Fermi liquid arguments, which are also foundationally not really rigorous.

The Quantum Hall Effect

We can use this Hall bar geometry set-up to measure the transport characteristics of the gas, as follows. Finite and proportional to density but independent of magnetic field.

These plateaus are incredibly sample independent and occur at the same value in many other materials. In condensed matter this is not always a problem many things are really just guesses which work exceptionally well.

The Hall conductance is not a topological invariant since it changes. It is the "quantum" version of the anomalous Hall effect. Infinity since there are no impurities in the system. An English reference is Pruisken, Nucl. Shi, and S.

Lectures on the Quantum Hall Effect

By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect 56.

But other than that small problem everything works just the same.would also not be possible to observe the quantum Hall effect in a perfect probe. The von Klitzing constant h=e2 can be so precisely defined through the quan-tum Hall effect measurement, that it is nowadays used worldwide as a resistance standard.

Another application of the quantum Hall effect is in determining the fine. The quantum Hall effect, discovered in the s, is an important fundamental effect in condensed matter physics that links topological states with electronic properties in two-dimensional atlasbowling.com by: An example of the quantum Hall effect in a band theory is provided by a simple model of graphene in a periodic magnetic field introduced by Haldane [34].

This model is important because it provides a simple 2 band description of the quantum Hall effect. It also provides a. The Quantum Hall effect.

Quantum Hall effect

Publication date Topics Hall effect, Quantum theory Publisher New York: Springer-Verlag Collection Borrow this book to access EPUB and PDF files. IN COLLECTIONS.

Books to Borrow. Books for People with Print Disabilities. Trent University Library Donation. The Quantum Hall Effect (Graduate Texts in Contemporary Physics) and a great selection of related books, art and collectibles available now at atlasbowling.com The Hall effect¶ We now move on to the quantum Hall effect, the mother of all topological effects in condensed matter physics.

But let's start from the classical Hall effect, the famous phenomenon by which a current flows perpendicular to an applied voltage, or .