Microscopic tests of topological electron-vortex binding in the fractional Hall effect

Gun Sang Jeon, Michael R. Peterson, Jainendra K. Jain

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The topological binding of quantized vortices and electrons plays a crucial role in our understanding of the fractional quantum Hall effect, and is manifest in the prototypical wave functions for the fractional Hall states. However, from a microscopic point of view, the non-Pauli vortices are not strictly bound to electrons in realistic ground state wave functions. We study here the Girvin-MacDonald off-diagonal long-range order for certain bosonic wave functions at Landau level fillings ν=1m (m odd), obtained from fermionic fractional Hall wave functions by a singular gauge transformation, and find strong evidence that the exponent describing its long-distance algebraic decay has a universal value equal to m2. We interpret this to mean that the topological notion of electron-vortex binding remains generally well defined as a long-distance property.

Original languageEnglish (US)
Article number035304
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume72
Issue number3
DOIs
StatePublished - Jul 15 2005

Fingerprint

Hall effect
Wave functions
Vortex flow
wave functions
vortices
Electrons
electrons
Quantum Hall effect
quantum Hall effect
Ground state
Gages
exponents
ground state
decay

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

@article{92c4e30749ff462aacc3f049684e12a2,
title = "Microscopic tests of topological electron-vortex binding in the fractional Hall effect",
abstract = "The topological binding of quantized vortices and electrons plays a crucial role in our understanding of the fractional quantum Hall effect, and is manifest in the prototypical wave functions for the fractional Hall states. However, from a microscopic point of view, the non-Pauli vortices are not strictly bound to electrons in realistic ground state wave functions. We study here the Girvin-MacDonald off-diagonal long-range order for certain bosonic wave functions at Landau level fillings ν=1m (m odd), obtained from fermionic fractional Hall wave functions by a singular gauge transformation, and find strong evidence that the exponent describing its long-distance algebraic decay has a universal value equal to m2. We interpret this to mean that the topological notion of electron-vortex binding remains generally well defined as a long-distance property.",
author = "Jeon, {Gun Sang} and Peterson, {Michael R.} and Jain, {Jainendra K.}",
year = "2005",
month = "7",
day = "15",
doi = "10.1103/PhysRevB.72.035304",
language = "English (US)",
volume = "72",
journal = "Physical Review B-Condensed Matter",
issn = "1098-0121",
publisher = "American Physical Society",
number = "3",

}

Microscopic tests of topological electron-vortex binding in the fractional Hall effect. / Jeon, Gun Sang; Peterson, Michael R.; Jain, Jainendra K.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 72, No. 3, 035304, 15.07.2005.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Microscopic tests of topological electron-vortex binding in the fractional Hall effect

AU - Jeon, Gun Sang

AU - Peterson, Michael R.

AU - Jain, Jainendra K.

PY - 2005/7/15

Y1 - 2005/7/15

N2 - The topological binding of quantized vortices and electrons plays a crucial role in our understanding of the fractional quantum Hall effect, and is manifest in the prototypical wave functions for the fractional Hall states. However, from a microscopic point of view, the non-Pauli vortices are not strictly bound to electrons in realistic ground state wave functions. We study here the Girvin-MacDonald off-diagonal long-range order for certain bosonic wave functions at Landau level fillings ν=1m (m odd), obtained from fermionic fractional Hall wave functions by a singular gauge transformation, and find strong evidence that the exponent describing its long-distance algebraic decay has a universal value equal to m2. We interpret this to mean that the topological notion of electron-vortex binding remains generally well defined as a long-distance property.

AB - The topological binding of quantized vortices and electrons plays a crucial role in our understanding of the fractional quantum Hall effect, and is manifest in the prototypical wave functions for the fractional Hall states. However, from a microscopic point of view, the non-Pauli vortices are not strictly bound to electrons in realistic ground state wave functions. We study here the Girvin-MacDonald off-diagonal long-range order for certain bosonic wave functions at Landau level fillings ν=1m (m odd), obtained from fermionic fractional Hall wave functions by a singular gauge transformation, and find strong evidence that the exponent describing its long-distance algebraic decay has a universal value equal to m2. We interpret this to mean that the topological notion of electron-vortex binding remains generally well defined as a long-distance property.

UR - http://www.scopus.com/inward/record.url?scp=33749158877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749158877&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.72.035304

DO - 10.1103/PhysRevB.72.035304

M3 - Article

VL - 72

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 3

M1 - 035304

ER -