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Composite-particles (Boson, Fermion) Theory of Fractional Quantum Hall Effect
- Publication Year :
- 2013
- Publisher :
- arXiv, 2013.
-
Abstract
- A quantum statistical theory is developed for a fractional quantum Hall effects in terms of composite bosons (fermions) each of which contains a conduction electron and an odd (even) number of fluxons. The cause of the QHE is by assumption the phonon exchange attraction between the conduction electron ("electron", "hole") and fluxons (quanta of magnetic fluxes). We postulate that c-fermions with \emph{any} even number of fluxons have an effective charge (magnitude) equal to the electron charge $e$. The density of c-fermions with $m$ fluxons, $n_\phi^{(m)}$, is connected with the electron density $n_{\mathrm e}$ by $n_\phi^{(m)}=n_{\mathrm e}/m$, which implies a more difficult formation for higher $m$, generating correct values $me^2/h$ for the Hall conductivity $\sigma_{\mathrm H}\equiv j/E_{\mathrm H}$. For condensed c-bosons the density of c-bosons-with-$m$ fluxons, $n_\phi^{(m)}$, is connected with the boson density $n_0$ by $n_\phi^{(m)}=n_0/m$. This yields $\sigma_{\mathrm H}=m\,e^2/h$ for the magnetoconductivity, the value observed of the QHE at filling factor $\nu=1/m$ ($m=$odd numbers). Laughlin's theory and results about the fractional charge are not borrowed in the present work.<br />Comment: 11 pages, 1 figure
- Subjects :
- Physics
Condensed Matter::Quantum Gases
Electron density
Condensed Matter - Mesoscale and Nanoscale Physics
Physics and Astronomy (miscellaneous)
Condensed matter physics
General Mathematics
FOS: Physical sciences
Charge (physics)
02 engineering and technology
Fermion
Electron
Quantum Hall effect
021001 nanoscience & nanotechnology
Condensed Matter::Mesoscopic Systems and Quantum Hall Effect
01 natural sciences
0103 physical sciences
Fractional quantum Hall effect
Composite fermion
Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
010306 general physics
0210 nano-technology
Boson
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....9e61f906f6548054a19572f15cb825bd
- Full Text :
- https://doi.org/10.48550/arxiv.1304.7631