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Quantum Hall Effect

Hsinzon Tsai Raymond Co University of California, Berkeley May 4 th 2011. Quantum Hall Effect. Outline. The Basics of Quantum Hall Effect Systematic Setup Definitions and Terminology Classical vs. Quantum Hall Effect Integer Quantum Hall Effect Fractional Quantum Hall Effect

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Quantum Hall Effect

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  1. Hsinzon Tsai Raymond Co University of California, Berkeley May 4th 2011 Quantum Hall Effect

  2. Outline • The Basics of Quantum Hall Effect • Systematic Setup • Definitions and Terminology • Classical vs. Quantum Hall Effect • Integer Quantum Hall Effect • Fractional Quantum Hall Effect • Conclusion

  3. Discoveries • Classical Hall Effect in 1879 • By Edwin H. Hall at his 24 • Integer Quantum Hall Effect in 1980 • Nobel Prize in 1985 • By German physicist Klaus von Klitzing • Fractional Quantum Hall Effect in 1982 • Nobel Prize in 1998 • By Professor Robert B. Laughlin, Stanford University Professor Horst L. Störmer, Columbia University Professor Daniel C. Tsui, Princeton University

  4. Systematic Setup http://www.rikenresearch.riken.jp/eng/hom/5674

  5. Systematic Setup • Two-dimension electrons system • Low temperature • Strong magnetic fields (0.1 to 45 Tesla) • Typically, in semiconductor structures • Electrons in a thin layer of GaAs surrounded by AlGaAs • Recently, graphene

  6. Definitions • Fermi Level • Cyclotron Frequency • Landau Level • Density of States

  7. Landau Levels Landau Level

  8. Derivation See blackboard

  9. Landau Levels

  10. Quantum Hall Effect http://askbluey.com/Image?q=Quantum+Invariant

  11. Integer Quantum Hall EffectIQHE The Nobel Prize in Physics 1998 Robert B. Laughlin, Horst L. Störmer, Daniel C. Tsui http://nobelprize.org/nobel_prizes/physics/laureates/1998/press.html

  12. Fractional Quantum Hall EffectFQHE http://www.ua.es/personal/jj.palacios/qhe.html

  13. References • From Landau levels to quantum Hall effects • http://landaucongress.itp.ac.ru/Talks/halperin.pdf

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