Quantum Hall Effect

1
Quantum Hall Effect

• Hsinzon Tsai
• Raymond Co
• University of California, Berkeley
• May 4th 2011

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
11
Integer Quantum Hall EffectIQHE

• The Nobel Prize in Physics 1998
• Robert B. Laughlin, Horst L. Störmer, Daniel C.
  Tsui

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