Physical Review B
(Condensed Matter and Materials Physics -15(II))

Phys. Rev. B 71, 125311 (2005) (4 pages)

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Quantum Hall criticality, superconductor-insulator transition, and quantum percolation

Yonatan Dubi,1 Yigal Meir,1,2 and Yshai Avishai1,2
1Physics Department, Ben-Gurion University, Beer Sheva, 84105, Israel
2The Ilse Katz Center for Meso- and Nano-scale Science and Technology, Ben-Gurion University, Beer Sheva, 84105, Israel

(Received 19 November 2004; published 15 March 2005)

A model consisting of a mixture of superconducting and quantum links is proposed to describe the integer quantum Hall transition. The quantum links correspond to tunneling of electrons between trajectories trapped in adjacent potential valleys, while the superconducting links mimic the merging of these trajectories once the Fermi energy exceeds the saddle point energy separating the two valleys. The quantum Hall transition in this model corresponds to percolation of the superconducting links. Numerical calculations and scaling analysis using two different approaches yield the critical exponent nu[approximate]2.4 and a two-peak conductance distribution at the critical point. The role of quantum coherence is discussed, allowing an interpretation of nu[approximate]1.3, found in some experiments, in terms of the percolation critical exponent. The model suggests that the critical behavior of the superconductor-insulator transition (on the insulating side) is in the same universality class as the quantum Hall transition. 2005 The American Physical Society

PACS: 73.43.Nq, 71.30.+h, 74.20.Mn

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