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Anyons in the FQHE

Anyons in the FQHE. Aut.: Jernej Mravlje Adv.: Anton Ramsak. Fermions, bosons, and … anyons. fermions bosons 2D: anyons Crucial for understanding the properties of the FQHE!. Spin…. Spin is quantized in half integers. But …. 2D – any spin.

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Anyons in the FQHE

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  1. Anyons in the FQHE Aut.: Jernej Mravlje Adv.: Anton Ramsak

  2. Fermions, bosons, and … anyons • fermions • bosons • 2D: anyons • Crucial for understanding the properties of the FQHE!

  3. Spin… Spin is quantized in half integers. But … 2D – any spin Spin-statistics theorem Pauli (1940)] 2D: any spin -> any statistics?

  4. … and statistics leads to statistics if the wave-function is single-valued

  5. 2D vs. 3D

  6. Configurational space Redundancy in notation Leinaas & Myrheim (1977) Configurational space of identical particles ex.: 1D

  7. Anyons in 1D x z Boundary conditions:

  8. Model for anyon Addition of is equal to a boost for in angular momentum of our model particle. Boson to fermion and vice-versa! Arbitrary flux -> anyon.

  9. Two particle anyonic wavefunction anyonic!

  10. HE and QHE • HE: Hall (1879) • charge and density of carriers • QHE: Von Klitzing et al. (1980) • standard for resistance • (Von Klitzing const. ) • measurement of fine structure constant

  11. IQHE: explanation Landau levels Filling factor:

  12. FQHE discovered in 1982 (Tsui et al. ) Stormer (1992)

  13. Laughlin ground state noninteracting filled Landau level Laughlin ground state at filling: Laughlin(1983) • a guess • shows excellent overlap with numerical results

  14. Fractional charge and fractional statistics of Laughlin excitations excitation of ground state fractionally charged anyonic!

  15. Measurements of frac. charge and frac. statistics • Shot noise measurements • Resonant tunneling experiments Saminadayar & Glattli (1997)

  16. Quantum computation Averin & Goldman (2001)

  17. Conclusion • Anyons in 2D • Fractional charge of excitations of FQHE ground-state • Fractional statistics -> anyons • Possible use for quantum computation which is robust against decoherence

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