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

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

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

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

Landau Gauge: Quantum Mechanical Description

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

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

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

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

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

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

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