Topic

# Filling factor

About: Filling factor is a research topic. Over the lifetime, 2069 publications have been published within this topic receiving 35760 citations.

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Bell Labs

^{1}, Harvard University^{2}, Massachusetts Institute of Technology^{3}, Yale University^{4}TL;DR: In this article, a two-dimensional electron system in an external magnetic field, with Landau-level filling factor \ensuremath{
u}=1/2, can be transformed to a mathematically equivalent system of fermions interacting with a Chern-Simons gauge field such that the average effective magnetic field acting on the fermion is zero.

Abstract: A two-dimensional electron system in an external magnetic field, with Landau-level filling factor \ensuremath{
u}=1/2, can be transformed to a mathematically equivalent system of fermions interacting with a Chern-Simons gauge field such that the average effective magnetic field acting on the fermions is zero. If one ignores fluctuations in the gauge field, this implies that for a system with no impurity scattering, there should be a well-defined Fermi surface for the fermions. When gauge fluctuations are taken into account, we find that there can be infrared divergent corrections to the quasiparticle propagator, which we interpret as a divergence in the effective mass ${\mathit{m}}^{\mathrm{*}}$, whose form depends on the nature of the assumed electron-electron interaction v(r). For long-range interactions that fall off slower than 1/r at large separation r, we find no infrared divergences; for short-range repulsive interactions, we find power-law divergences; while for Coulomb interactions, we find logarithmic corrections to ${\mathit{m}}^{\mathrm{*}}$. Nevertheless, we argue that many features of the Fermi surface are likely to exist in all these cases. In the presence of a weak impurity-scattering potential, we predict a finite resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$ at low temperatures, whose value we can estimate. We compute an anomaly in surface acoustic wave propagation that agrees qualitatively with recent experiments. We also make predictions for the size of the energy gap in the fractional quantized Hall state at \ensuremath{
u}=p/(2p+1), where p is an integer. Finally, we discuss the implications of our picture for the electronic specific heat and various other physical properties at \ensuremath{
u}=1/2, we discuss the generalization to other filling fractions with even denominators, and we discuss the overall phase diagram that results from combining our picture with previous theories that apply to the regime where impurity scattering is dominant.

1,014 citations

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TL;DR: In this paper, the existence of fractional charges carrying current is experimentally demonstrated using a 2D electron system in a high perpendicular magnetic field, and the shot noise associated with tunneling in the fractional quantum Hall regime at Landau level filling factor 1/3.

Abstract: The existence of fractional charges carrying current is experimentally demonstrated. Using a 2D electron system in a high perpendicular magnetic field we measure the shot noise associated with tunneling in the fractional quantum Hall regime at Landau level filling factor 1/3. The noise gives a direct determination of the quasiparticle charge, which is found to be ${e}^{*}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}e/3$ as predicted by Laughlin. The existence of $e/3$ Laughlin quasiparticles is unambiguously confirmed by the shot noise to Johnson-Nyquist noise crossover found for temperature $\ensuremath{\Theta}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}e}^{*}{V}_{\mathrm{ds}}/{2k}_{B}$.

648 citations

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TL;DR: It is found that the two-dimensional electron gas in a high magnetic field at filling factor ν=1 for an arbitrary ratio of the Zeeman energy gμ B B to the typical interaction energy always has a gap, even when the one-particle gap vanishes.

Abstract: We study the two-dimensional electron gas in a high magnetic field at filling factor \ensuremath{
u}=1 for an arbitrary ratio of the Zeeman energy g${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$B to the typical interaction energy. We find that the system always has a gap, even when the one-particle gap vanishes, i.e., when g=0. When g is sufficiently large, the quasiparticles are perturbatively related to those in the noninteracting limit; we compute their energies to second order in the Coulomb interaction. For g smaller than a critical value ${\mathit{g}}_{\mathit{c}}$ the quasiparticles change character; in the limit of g\ensuremath{\rightarrow}0, they are skyrmions---spatially unbounded objects with infinite spin. In GaAs heterojunctions, the gap is unambiguously predominantly due to correlation effects; indeed, we tentatively conclude that g is always smaller than ${\mathit{g}}_{\mathit{c}}$, so the relevant quasiparticles are the skyrmions. The generalization to other odd-integer filling factors, and to \ensuremath{
u}=1/3 and 1/5, is discussed.

641 citations

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TL;DR: This is the first time that a three-dimensional itinerant-electron system is proved to exhibit ferromagnetism in a finite range of the electron filling factor.

Abstract: We study a class of Hubbard models in which the corresponding single-electron ground states have bulk degeneracy. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to ${\mathrm{\ensuremath{\rho}}}_{0}$=\ensuremath{\Vert}V\ensuremath{\Vert}/2\ensuremath{\Vert}\ensuremath{\Lambda}\ensuremath{\Vert} (where \ensuremath{\Vert}V\ensuremath{\Vert} is the dimension of degeneracy and \ensuremath{\Vert}\ensuremath{\Lambda}\ensuremath{\Vert} is the number of sites), and exhibit paramagnetism when the filling factor is sufficiently small. This is the first time that a three-dimensional itinerant-electron system is proved to exhibit ferromagnetism in a finite range of the electron filling factor.

427 citations

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TL;DR: Demonstration de l'existence d'un nouveau type d'ordre a longue distance non diagonal dans l'etat fondamental of l'effet Hall quantique fractionnaire, basee sur l'application de la transformation de jauge de Wilczek.

Abstract: We demonstrate the existence of a novel type of off-diagonal long-range order in the fractional-quantum-Hall-effect (FQHE) ground state. This is revealed for the case of fractional filling factor \ensuremath{
u}=1/m by application of Wilczek's ``anyon'' gauge transformation to attach m quantized flux tubes to each particle. The binding of the zeros of the wave function to the particles in the FQHE is a (2+1)-dimensional analog of oblique confinement in which a condensation occurs, not of ordinary particles, but rather of composite objects consisting of particles and gauge flux tubes.

344 citations