Download Presentation
## Quantum Hall Effect

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Hsinzon Tsai**Raymond Co University of California, Berkeley May 4th 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 • Conclusion**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**Systematic Setup**http://www.rikenresearch.riken.jp/eng/hom/5674**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**Definitions**• Fermi Level • Cyclotron Frequency • Landau Level • Density of States**Landau Levels**Landau Level**Derivation**See blackboard**Quantum Hall Effect**http://askbluey.com/Image?q=Quantum+Invariant**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**Fractional Quantum Hall EffectFQHE**http://www.ua.es/personal/jj.palacios/qhe.html**References**• From Landau levels to quantum Hall effects • http://landaucongress.itp.ac.ru/Talks/halperin.pdf