Spin-Flip Scattering at Quantum Hall Transition

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_{xy}=0,1,2 are separated by novel metallic phases.

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

Cite this paper

nullV. Kagalovsky and A. Chudnovskiy, "Spin-Flip Scattering at Quantum Hall Transition,"*Journal of Modern Physics*, Vol. 2 No. 9, 2011, pp. 970-976. doi: 10.4236/jmp.2011.29117.

nullV. Kagalovsky and A. Chudnovskiy, "Spin-Flip Scattering at Quantum Hall Transition,"

References

[1] 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

[2] 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

[3] 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

[4] 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

[5] D. E. Khmel’nitskii, “Quantization of Hall Conductivity,” Journal of Experimental and Theoretical Physics Letters, Vol. 38, No. 9, 1983, pp. 552-556.

[6] 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.

[7] 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.

[8] 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

[9] 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.

[10] 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

[11] 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

[12] 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

[13] H. A. Fertig and B. I. Halperin, “Transmission Coefficient of an Electron Through a Saddle-Point Potential in a Magnetic Field,” Physical Review B, Vol. 36, No. 15, 1987, pp. 7969-7976. doi:10.1103/PhysRevB.36.7969

[14] T. Jungwirth, Jairo Sinova, J. Masek, J. Kucera and A. H. MacDonald, “Theory of Ferromagnetic (III,Mn)V Semi-conductors,” Reviews of Modern Physics, Vol. 78, No. 3, 2006, pp. 809-864. doi:10.1103/RevModPhys.78.809

[1] 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

[2] 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

[3] 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

[4] 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

[5] D. E. Khmel’nitskii, “Quantization of Hall Conductivity,” Journal of Experimental and Theoretical Physics Letters, Vol. 38, No. 9, 1983, pp. 552-556.

[6] 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.

[7] 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.

[8] 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

[9] 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.

[10] 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

[11] 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

[12] 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

[13] H. A. Fertig and B. I. Halperin, “Transmission Coefficient of an Electron Through a Saddle-Point Potential in a Magnetic Field,” Physical Review B, Vol. 36, No. 15, 1987, pp. 7969-7976. doi:10.1103/PhysRevB.36.7969

[14] T. Jungwirth, Jairo Sinova, J. Masek, J. Kucera and A. H. MacDonald, “Theory of Ferromagnetic (III,Mn)V Semi-conductors,” Reviews of Modern Physics, Vol. 78, No. 3, 2006, pp. 809-864. doi:10.1103/RevModPhys.78.809