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The Quantum Hall Effects

The Quantum Hall Effects. Xinyuan Lai. Outline. About the Quantum Hall Effects (QHEs): Integral, Fractional , Anomalous, Quantum Spin Hall Effect, etc. Unconventional QHE in Graphene Methods to Characterize the Effects Transport, Direct Probing (Quantum

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The Quantum Hall Effects

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  1. The Quantum Hall Effects Xinyuan Lai 601 Presentation

  2. Outline • About the Quantum Hall Effects (QHEs): Integral, Fractional, Anomalous, Quantum Spin Hall Effect, etc. • Unconventional QHE in Graphene • Methods to Characterize the Effects Transport, Direct Probing (Quantum Capacitance), STM Spectroscopy…

  3. Hall Effect (1879) B +++++++++++++++++++ Ex, jx VH Ey - - - - - - - - - - - - - - - - - -

  4. Zyun Francis Ezawa, Quantum Hall Effects: Field Theoretical Approach and Related Topics Integral QHE vs. HE Shubnikov-de Hass Oscillation

  5. Zyun Francis Ezawa, Quantum Hall Effects: Field Theoretical Approach and Related Topics Landau Quantization electron center of cyclotron motion radial vector of cyclotron motion R Generalizing to Harmonic Oscillators gives: X H = hcR²/2l²= hc( + ½ ) Link of video

  6. Zyun Francis Ezawa, Quantum Hall Effects: Field Theoretical Approach and Related Topics DC Tsui, PRL, 1982 Fractional QHE Filling Factor equals to some fractional values: Composite Particle Picture: m m Described by Laughlin Wave Function: Integral Quantization of Quasi-particles !

  7. Eva Y Andrei et al, Rep. Prog. Phys. 2012 Unconventional QHE in Graphene 2x Degeneracy in Graphene System Not equally spacing LLs: Normal: Graphene:

  8. K. S. Novoselov, Science, 2009 Transport Measurement Room Temperature QHE

  9. Eva Y Andrei et al, Rep. Prog. Phys. 2012 http://research.physics.berkeley.edu/crommie/research:stm STM Spectroscopy

  10. A. F. Young, PRB, 2012 Z. Z. Zibrov, Nature, 2017 Direct Probe Differential Capacitance within the Plate Capacitor: Capacitance reflects the compressibility v connecting to chemical potential μ, which

  11. Thank you!

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