THE EXISTENCE OF EXTENDED STATES IN QUANTUM HALL TYPE SYSTEMS
RESEARCHER: WILLIAM C. HALL
DEPARTMENT: UALR DEPARTMENT OF PHYSICS
MENTOR: PROFESSOR LENORE HORNER
PROGRAM: REUP-FOM/SIUE
PRESENTATION OUTLINE
INTRODUCTION
METHODS
RESULTS
SUMMARY
BIBLIOGRAPHY
ACKNOWLEDGEMENTS
TWO MEASURES OF EXTENSION
ROOT-MEAN-SQUARE RADIUS 
PARTICIPATION NUMBER 
WHEREIS THE SINGLE-ELECTRON WAVEFUNCTION AND
SPECIAL CASES / EXAMPLES
UNIFORM DISK OF RADIUS RUNIFORM RING OF RADIUS R AND THICKNESSGIVEN BY
GIVEN BY
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DISK
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RING
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R |
P |
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SUMMARY
WE ARE INTERESTED IN THE ENERGY AND SIZE DEPENDENCE OF EXTENDED STATES IN QUANTUM HALL TYPE SYSTEMS
WE HAVE COMPUTED THE ROOT-MEAN-SQUARE RADIUS (
) AND THE PARTICIPATION NUMBER (P)
AS A FUNCTION OF ENERGY, FOR A FEW SYSTEM SIZES
OUR NEXT STEP IS TO ANALYZE THE PEAK VALUES OF
AND P AS A FUNCTION OF “IMPURITY”
DISTRIBUTION, SHAPE, AND NUMBER RELATIVE TO THE STRENGTH OF THE MAGNETIC
FIELD
BIBLIOGRAPHY
Stormer, Horst L., Daniel C. Tsui and Arthur S. Gossard, The fractional Hall effect, Reviews of Modern Physics, vol. 71 no. 2 (1999) pp. S298-S305.
Gedik, Z. and Bayindir, Disorder and localization in the lowest Landau level in the presence of dilute point scatterers, Solid State Communications vol. 112 (1999) pp. 157-160.
Jain, Jainendra K., The Composite Fermion: A Quantum particle and its quantum Fluids, Physics Today, vol. 53 no. 4 (April 2000) pp. 39-45.
Thouless, D.J., Electrons in disordered systems and the theory of Localization, Physics Reports, vol. 13 no. 3 (1974) pp. 93-142.
Aoki, H., Computer simulation of two-dimensional disordered electron systems in strong magnetic fields, J. Phys. C: Solid State Phys., vol. 10(1977) pp. 2583-2593.
Press Release: The Nobel Prize in Physics 1998. Web site: http://sunsite.iisc.ernet.in/nobel98/physics98.html