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Quantum Hall Effect

Quantum Hall Effect. Jesse Noffsinger Group Meeting Talk (As required by the Governor of the State of California) April 17, 2007. Classical Hall Effect. Experimental Values *. B. +++++++++++++++++++. E x , j x. V H. E y. - - - - - - - - - - - - - - - - - - . *Ashcroft and Mermin.

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Quantum Hall Effect

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  1. Quantum Hall Effect Jesse Noffsinger Group Meeting Talk (As required by the Governor of the State of California) April 17, 2007

  2. Classical Hall Effect Experimental Values* B +++++++++++++++++++ Ex, jx VH Ey - - - - - - - - - - - - - - - - - - *Ashcroft and Mermin

  3. Integer QHE Discovered in 1980, Nobel Prize awarded to von Klitzing in 1985 aa SEM image of a Hall bar* *Georgia Tech physics website

  4. Quantum Mechanical Description Landau Gauge:

  5. Degeneracy of Landau Levels Each wavefunction is centered at Energy DOS: Increasing B

  6. Impurity Effects Isolated -fn potential localizes one extended state Only extended states carry current! Extended States E Localized States DOS

  7. The Laughlin Argument for the Integer Hall effect Form a closed loop w/ Hall bar Change the flux through the loop by one quanta: No change can take place in the bulk – move one electron to the other edge p must be an integer

  8. Fractional QHE Filling factor is a rational fraction Cannot be explained in terms of free electrons

  9. Composite Fermion Picture ElectronsIQHE Composite FermionsFQHE Fractional Hall effect encompasses states with filling factors: Composite fermions can be viewed as electrons with attached flux quanta is screened to

  10. Lowest Landau level splitting for composite fermions Energy v=1 lowest Landau Level splits into levels separated by The fractional filling of electrons is really the integral filling of composite fermions

  11. Conclusion • Integral Quantum Hall effect can be accurately modeled as • a non-interacting electron gas in a magnetic field • The Fractional Quantum Hall effect involves composite fermion • quasi-particles which are electrons with attached flux quanta

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