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A new method of calculation in the Fractional Quantum Hall Effect regime

100%
Bentalha Z., Moumen L., Ouahrani T.
Open Physics
|
2014
|
vol. 12
|
issue 7
511-516
EN
The electron-electron and electron-background interaction energies are calculated analytically for systems with up to N = 6 electrons. The method consists of describing the position vectors of electrons using complex coordinates and all the interaction energies with complex notation, whereby simplifications become possible. As is known, in this type of calculation, complicated expressions involving integrals over many variables are encountered and the trick of using complex coordinates greatly facilitates the exact calculation of various quantities. Contrary to previous analytical calculations, using complex coordinates avoids complicated trigonometric functions from appearing in the integrand, simplifying the exact evaluation of the integrals. The method we have used can be straightforwardly extended to larger systems with N > 6 electrons.
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A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

88%
Hai W., Li Z., Xiao K.
Open Physics
|
2011
|
vol. 9
|
issue 6
1509-1517
EN
It is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-AlxGa1−x As heterojunction. The results are in good agreement with the existing experimental data.
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