THE EXISTENCE OF EXTENDED STATES IN QUANTUM HALL TYPE SYSTEMS

PRESENTATION OUTLINE

INTRODUCTION
METHODS
RESULTS
SUMMARY
BIBLIOGRAPHY
ACKNOWLEDGEMENTS

TWO MEASURES OF EXTENSION

ROOT-MEAN-SQUARE RADIUS
PARTICIPATION NUMBER

WHERE IS THE SINGLE-ELECTRON WAVEFUNCTION AND 
 

SPECIAL CASES / EXAMPLES

GIVEN BY      

GIVEN BY  

   
 

	DISK	RING
		R
P

           

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

ACKNOWLEDGEMENTS

UALR DEPARTMENT OF PHYSICS AND ASTRONOMY
REUP-FOM/SILL PROGRAM
SIUE DEPARTMENT OF PHYSICS
NATASHA COLLEYMORE
DAWN OLIVE
PROFESSOR JULIA THOMPSON
PROFESSOR LENORE HORNER