publication . Preprint . 2013

Characterization of the Quantized Hall Insulator Phase in the Quantum Critical Regime

Song, Juntao; Prodan, Emil;
Open Access English
  • Published: 22 Jan 2013
Abstract
The conductivity $\sigma$ and resistivity $\rho$ tensors of the disordered Hofstadter model are mapped as functions of Fermi energy $E_F$ and temperature $T$ in the quantum critical regime of the plateau-insulator transition (PIT). The finite-size errors are eliminated by using the non-commutative Kubo-formula. The results reproduce all the key experimental characteristics of this transition in Integer Quantum Hall (IQHE) systems. In particular, the Quantized Hall Insulator (QHI) phase is detected and analyzed. The presently accepted characterization of the QHI phase in the quantum critical regime, based entirely on experimental data, is fully supported by our t...
Subjects
arxiv: Condensed Matter::Mesoscopic Systems and Quantum Hall Effect
free text keywords: Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Disordered Systems and Neural Networks
Download from
50 references, page 1 of 4

prodan@yu.edu [1] E. Abrahams, P. Anderson, D. Licciardello, and T. Ramakr-

ishnan, Phys. Rev. Lett. 42, 673 (1979) [2] P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S.

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(1998) [9] H. Schulz-Baldes and J. Bellissard, Rev. Math. Phys. 10, 1

(1998) [10] M. Hilke, D. Shahar, S. H. Song, D. C. Tsui, Y. H. Xie, and

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Pruisken, Phys. Rev. Lett. 61, 1294 (1988) [15] H. P. Wei, S.Y.Lin, and D. C.Tsui, Phys. Rev. B 45, 3926

(1992) [16] S. Kawaji and J. Wakabayashi, J. Phys. Soc. Jpn 56, 21 (1987) [17] J. Wakabayashi, M. Yamane, and S. Kamaji, J. Phys. Soc.

Jpn. 58, 1903 (1989) [18] J. Wakabayashi, A. Fukaro, S. Kawaji, Y. Koike, and

50 references, page 1 of 4
Abstract
The conductivity $\sigma$ and resistivity $\rho$ tensors of the disordered Hofstadter model are mapped as functions of Fermi energy $E_F$ and temperature $T$ in the quantum critical regime of the plateau-insulator transition (PIT). The finite-size errors are eliminated by using the non-commutative Kubo-formula. The results reproduce all the key experimental characteristics of this transition in Integer Quantum Hall (IQHE) systems. In particular, the Quantized Hall Insulator (QHI) phase is detected and analyzed. The presently accepted characterization of the QHI phase in the quantum critical regime, based entirely on experimental data, is fully supported by our t...
Subjects
arxiv: Condensed Matter::Mesoscopic Systems and Quantum Hall Effect
free text keywords: Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Disordered Systems and Neural Networks
Download from
50 references, page 1 of 4

prodan@yu.edu [1] E. Abrahams, P. Anderson, D. Licciardello, and T. Ramakr-

ishnan, Phys. Rev. Lett. 42, 673 (1979) [2] P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S.

Fisher, Phys. Rev. B 22, 3519 (1980) [3] H. Levine, S. B. Libby, and A. M. M. Pruisken, Nucl. Phys.

B 240, 30 (1984) [4] H. Levine, S. B. Libby, and A. M. M. Pruisken, Nucl. Phys.

B 240, 49 (1984) [5] H. Levine, S. B. Libby, and A. M. M. Pruisken, Nucl. Phys.

B 240, 71 (1984) [6] E. Prodan, Appl. Math. Res. Express Advance Ac-

cess(2012), doi:“bibinfo doi 10.1093/amrx/abs017 [7] J. Bellissard, A. van Elst, and H. Schulz-Baldes, J. Math.

Phys. 35, 5373 (1994) [8] H. Schulz-Baldes and J. Bellissard, J. Stat. Phys. 91, 991

(1998) [9] H. Schulz-Baldes and J. Bellissard, Rev. Math. Phys. 10, 1

(1998) [10] M. Hilke, D. Shahar, S. H. Song, D. C. Tsui, Y. H. Xie, and

D. Monroe, Nature 395, 675 (1998) [11] D. J. Thouless, Phys. Rev. Lett. 39, 1167 (1977) [12] A. Pruisken, Phys. Rev. Lett. 61, 1297 (1988) [13] H. P. Wei, D. C. Tsui, and A. M. M. Pruisken, Phys. Rev. B

33, 1488 (1985) [14] H. P. Wei, D. C. Tsui, M. A. Paalanen, and A. M. M.

Pruisken, Phys. Rev. Lett. 61, 1294 (1988) [15] H. P. Wei, S.Y.Lin, and D. C.Tsui, Phys. Rev. B 45, 3926

(1992) [16] S. Kawaji and J. Wakabayashi, J. Phys. Soc. Jpn 56, 21 (1987) [17] J. Wakabayashi, M. Yamane, and S. Kamaji, J. Phys. Soc.

Jpn. 58, 1903 (1989) [18] J. Wakabayashi, A. Fukaro, S. Kawaji, Y. Koike, and

50 references, page 1 of 4
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