Effective mass of the composite fermions and energy gaps of quantum Hall states

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dc.creatorPraz, Antoine
dc.date2006-12-22
dc.date2007-05-30
dc.date.accessioned2026-07-07T08:05:42Z
dc.date.available2026-07-07T08:05:42Z
dc.descriptionThe effective mass of the quasi-particles in the fermion-Chern-Simons description of the quantum Hall state at half-filling is computed for electron-electron interactions $V(r)\sim r^{x-2}$, for $0<x<3/2$, following the previous work of Stern and Halperin, Phys. Rev. B {\bf 52}, 5890 (1995). The energy gap of quantum Hall states with filling factors $ν=\frac{p}{2p+1}$ for $p\gg 1$ can then be obtained either from the effective mass at half-filling, as proposed by Halperin, Lee and Read, Phys. Rev. B {\bf 47}, 7312 (1993), or evaluated directly from the self-energy of the system in presence of the residual magnetic field; both results are shown to agree as $p\to \infty$. The energy gap is then given by a self-consistent equation, which asymptotic solution for $p\gg 1$ and short-range interactions is $E_g(p)\sim (2p+1)^{-\frac{3-x}{2}}$, in agreement with previous results by Kim, Lee and Wen, Phys. Rev. B {\bf 52}, 17275 (1995). The power law for the energy gap seems to be {\it exact} to all orders in the perturbative expansion. Moreover, the energy gap for systems with Coulomb interaction is recovered in the limit $x\to 1$.
dc.description13 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0612591
dc.identifierhttp://arxiv.org/abs/cond-mat/0612591
dc.identifierPhysical Review B 75, 205342 (2007)
dc.identifierdoi:10.1103/PhysRevB.75.205342
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130361
dc.subjectMesoscale and Nanoscale Physics
dc.subjectStrongly Correlated Electrons
dc.titleEffective mass of the composite fermions and energy gaps of quantum Hall states
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