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Spin-Flip Scattering at Quantum Hall Transition
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Journal of Modern Physics·Volume 02 (2011)·Pages 970–976·Published 19 September 2011·DOI10.4236/jmp.2011.29117
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Abstract
We formulate a generalized Chalker-Coddington network model that describes the effect of nuclear spins on the two-dimensional electron gas in the quantum Hall regime. We find exact analytical expression for spin-dependent transmission coefficients of a charged particle through a saddle point potential in a perpendicular magnetic field. Spin-flip scattering creates a metallic state in a finite range around the critical energy of quantum Hall transition. As a result we find that the usual insulating phases with Hall conductance σ<sub>xy</sub>=0,1,2 are separated by novel metallic phases.
KeywordsPACS 73.43.Nq72.25.Mk73.20.Jc
- K. V. Klitzing, G. Dorda and M. Pepper, “New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance,” Physical Review Letters, Vol. 45, No. 6, 1980, pp. 494-497. doi:10.1103/PhysRevLett.45.494
- R. B. Laughlin, “The Quantized Hall Conductivity in Two Dimensions,” Physical Review B, Vol. 23, No.10, 1981, pp. 5632-5633. doi:10.1103/PhysRevB.23.5632
- B. I. Halperin, “Quantized Hall Conductance, Cur-rent-Carrying Edge States, and the Existence of Extended States in a Two-Dimensional Disordered Potential,” Physical Review B, Vol. 25, No. 4, 1982, pp. 2185-2190. doi:10.1103/PhysRevB.25.2185
- H. Levine, S. B. Libby and A. M. M. Pruisken, “Electron Delocalization by a Magnetic Field in Two Dimensions,” Physical Review Letters, Vol. 51, No. 20, 1983, pp. 1915-1918. doi:10.1103/PhysRevLett.51.1915
- D. E. Khmel’nitskii, “Quantization of Hall Conductivity,” Journal of Experimental and Theoretical Physics Letters, Vol. 38, No. 9, 1983, pp. 552-556.
- J. T. Chalker and P. D. Coddington, “Percolation, Quan-tum Tunnelling and the Integer Quantum Hall Effect,” Journal of Physics C, Vol. 21, No. 14, 1988, pp. 2665- 2679.
- D. K. K. Lee and J. T. Chalker, “A Unified Model for Two Localisation Problems: Electron States in Spin-Degenerate Landau Levels, and in a Random Mag-netic Field,” Physical Review Letters, Vo. 72, No. 10, 1994, pp. 1510-1513.
- V. Kagalovsky, B. Horovitz, Y. Avishai and J. T. Chalker, “Quantum Hall Plateau Transitions in Disordered Super-conductors,” Physical Review Letters, Vol. 82, No. 17, 1999, pp. 3516-3519. doi:10.1103/PhysRevLett.82.3516
- J. T. Chalker, N. Read, V. Kagalovsky, B. Horovitz, Y. Avishai and A. W. W. Ludwig, “Thermal Metal in Net-work Models of a Disordered Two-Dimensional Super-conductor,” Physical Review B, Vol. 65, No.1 , 2001, Ar-ticle ID: 012506.
- A. Berg, M. Dobers, R. R. Gerhardts and K. V. Klitzing, “Magnetoquantum Oscillations of the Nuclear-Spin-Lat- tice Relaxation near a Two-Dimensional Electron Gas,” Physical Review Letters, Vol. 64, No. 21. 1990. pp. 2563-2566. doi:10.1103/PhysRevLett.64.2563
- I. D. Vagner and T. Maniv, “Nuclear Spin-Lattice Relax-ation: A Microscopic Local Probe for Systems Exhibiting the Quantum Hall Effect,” Physical Review Letters, Vol. 61, No. 12, 1988, pp. 1400-1403. doi:10.1103/PhysRevLett.61.1400
- V. Kagalovsky and I. Vagner, “Hyperfine Interaction Induced Critical Exponents in the Quantum Hall Effect,” Physical Review B, Vol. 75, No. 11, 2007, Article ID: 113304. doi:10.1103/PhysRevB.75.113304