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 +++++++++++++++++++ - - - - - - - - - B E x, j x EyEy VHVH MetalR H (-1/nec) Li0.8 Na1.2 Rb1.0 Ag1.3 Be-0.2 Experimental Values * *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. Landau Gauge: Quantum Mechanical Description

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

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

7. Form a closed loop w/ Hall bar The Laughlin Argument for the Integer Hall effect 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 Fractional Hall effect encompasses states with filling factors: Composite fermions can be viewed as electrons with attached flux quanta Electrons IQHE Composite Fermions FQHE is screened to

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

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