### Abstract

A central long standing prediction of the theory of fractional quantum Hall (FQH) states that it is a topological fluid whose elementary excitations are vortices with fractional charge and fractional statistics. Yet, the unambiguous experimental detection of this fundamental property, that the vortices have fractional statistics, has remained an open challenge. Here we propose a three-terminal " T junction" as an experimental setup for the direct and independent measurement of the fractional charge and statistics of fractional quantum Hall quasiparticles via cross current noise measurements. We present a nonequilibrium calculation of the quantum noise in the T -junction setup for FQH Jain states. We show that the cross current correlation (noise) can be written in a simple form, a sum of two terms, which reflects the braiding properties of the quasiparticles: the statistics dependence captured in a factor of cos θ in one of two contributions. Through analyzing these two contributions for different parameter ranges that are experimentally relevant, we demonstrate that the noise at finite temperature reveals signatures of generalized exclusion principles, fractional exchange statistics and fractional charge. We also predict that the vortices of Laughlin states exhibit a "bunching" effect, while higher states in the Jain sequences exhibit an "antibunching" effect.

Original language | English (US) |
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Article number | 155324 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 74 |

Issue number | 15 |

DOIs | |

State | Published - Nov 6 2006 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

**Measuring fractional charge and statistics in fractional quantum Hall fluids through noise experiments.** / Kim, Eun Ah; Lawler, Michael J.; Vishveshwara, Smitha; Fradkin, Eduardo.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 74, no. 15, 155324. https://doi.org/10.1103/PhysRevB.74.155324

}

TY - JOUR

T1 - Measuring fractional charge and statistics in fractional quantum Hall fluids through noise experiments

AU - Kim, Eun Ah

AU - Lawler, Michael J.

AU - Vishveshwara, Smitha

AU - Fradkin, Eduardo

PY - 2006/11/6

Y1 - 2006/11/6

N2 - A central long standing prediction of the theory of fractional quantum Hall (FQH) states that it is a topological fluid whose elementary excitations are vortices with fractional charge and fractional statistics. Yet, the unambiguous experimental detection of this fundamental property, that the vortices have fractional statistics, has remained an open challenge. Here we propose a three-terminal " T junction" as an experimental setup for the direct and independent measurement of the fractional charge and statistics of fractional quantum Hall quasiparticles via cross current noise measurements. We present a nonequilibrium calculation of the quantum noise in the T -junction setup for FQH Jain states. We show that the cross current correlation (noise) can be written in a simple form, a sum of two terms, which reflects the braiding properties of the quasiparticles: the statistics dependence captured in a factor of cos θ in one of two contributions. Through analyzing these two contributions for different parameter ranges that are experimentally relevant, we demonstrate that the noise at finite temperature reveals signatures of generalized exclusion principles, fractional exchange statistics and fractional charge. We also predict that the vortices of Laughlin states exhibit a "bunching" effect, while higher states in the Jain sequences exhibit an "antibunching" effect.

AB - A central long standing prediction of the theory of fractional quantum Hall (FQH) states that it is a topological fluid whose elementary excitations are vortices with fractional charge and fractional statistics. Yet, the unambiguous experimental detection of this fundamental property, that the vortices have fractional statistics, has remained an open challenge. Here we propose a three-terminal " T junction" as an experimental setup for the direct and independent measurement of the fractional charge and statistics of fractional quantum Hall quasiparticles via cross current noise measurements. We present a nonequilibrium calculation of the quantum noise in the T -junction setup for FQH Jain states. We show that the cross current correlation (noise) can be written in a simple form, a sum of two terms, which reflects the braiding properties of the quasiparticles: the statistics dependence captured in a factor of cos θ in one of two contributions. Through analyzing these two contributions for different parameter ranges that are experimentally relevant, we demonstrate that the noise at finite temperature reveals signatures of generalized exclusion principles, fractional exchange statistics and fractional charge. We also predict that the vortices of Laughlin states exhibit a "bunching" effect, while higher states in the Jain sequences exhibit an "antibunching" effect.

UR - http://www.scopus.com/inward/record.url?scp=33750434296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750434296&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.74.155324

DO - 10.1103/PhysRevB.74.155324

M3 - Article

AN - SCOPUS:33750434296

VL - 74

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 15

M1 - 155324

ER -