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Phys. Rev. B 72, 075325 (2005) [12 pages]

Mobility gap in fractional quantum Hall liquids: Effects of disorder and layer thickness

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Xin Wan1,2, D. N. Sheng3, E. H. Rezayi4, Kun Yang5, R. N. Bhatt6, and F. D. M. Haldane7
1Institut für Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany
2Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People’s Republic of China
3Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
4Physics Department California State University Los Angeles, Los Angeles, California 90032, USA
5National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahasse, Florida 32306, USA
6Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
7Department of Physics, Jadwin Hall, Princeton University, Princeton, New Jersey 08544, USA

Received 23 May 2005; published 10 August 2005

We study the behavior of two-dimensional electron gas in the fractional quantum Hall regime in the presence of finite layer thickness and correlated disordered potential. Generalizing the Chern number calculation to many-body systems, we determine the mobility gaps of fractional quantum Hall states based on the distribution of Chern numbers in a microscopic model. We find excellent agreement between experimentally measured activation gaps and our calculated mobility gaps, when combining the effects of both disordered potential and layer thickness. We clarify the difference between mobility gap and spectral gap of fractional quantum Hall states and explain the disorder-driven collapse of the gap and the subsequent transitions from the fractional quantum Hall states to the insulator.

© 2005 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevB.72.075325
DOI:
10.1103/PhysRevB.72.075325
PACS:
73.43.Lp, 73.43.Nq, 73.43.Qt
 
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