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

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 non-equilibrium 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 $\cos \theta$ 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 ``anti-bunching'' effect.

arXiv comment26 pages, 10 figures. A more detailed and self-contained version of Phys. Rev. Lett. vol 95, 176402 (2005), cond-mat/0507428. One reference added and the section VII revised for clarity

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• Topological vacuum bubble by anyon braiding
• Non-equilibrium Steady States of Quantum Systems on Star Graphs
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• Quantum wire junctions breaking time reversal invariance
• Theory of non-Abelian Fabry-Perot interferometry in topological insulators
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
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• Chirality and Current-Current Correlation in Fractional Quantum Hall Systems
• Off-critical Luttinger Junctions
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• Spin Hall Effect For Anyons
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• Different fractional charges from auto- and cross-correlation noise in quantum Hall states without upstream modes
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• Electrostatics of Edge States of Quantum Hall Systems with Constrictions: Metal--Insulator Transition Tuned by External Gates
• Dualities for anyons
• Tunneling current and current correlations for anyonic quasiparticles of ν = 1/2 chiral Luttinger liquid in multi-edge geometries
• Photo-assisted current in the fractional quantum Hall effect as a probe of the quasiparticle operator scaling dimension
• Real-Time Ramsey Interferometry in Fractional Quantum Hall States
• Quantum statistics and self-interference in extended colliders