Abstract
We present a real-space renormalization-group study of localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the longitudinal and Hall resistivities are derived. In agreement with recent numerical studies, we find that the Hall resistivity is quantized in the metallic phase but diverges in the insulating phase. This suggests that the characteristics of a quantized Hall insulator can occur only in the presence of a strong dephasing mechanism.
Original language | English |
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Pages (from-to) | 674-677 |
Number of pages | 4 |
Journal | Physica E: Low-Dimensional Systems and Nanostructures |
Volume | 12 |
Issue number | 1-4 |
DOIs | |
State | Published - Jan 2002 |
Externally published | Yes |
Event | 14th International Conference on the - Prague, Czech Republic Duration: 30 Jul 2001 → 3 Aug 2001 |
Bibliographical note
Funding Information:We thank A. Auerbach, O. Entin-Wohlmann, F. Evers, Y. Gefen, B. Huckestein, A. MacKinnon, A. Mirlin, L. Pryadko, B. Shapiro, D. Sheng, S. Sondhi, and I. Zharekeshev for useful discussions. This work was supported by the DIP project of the German Ministry for Education and Research (BMBF), Grant No. 96–00294 from the United States–Israel Binational Science Foundation (BSF), and the Aspen Center for Physics. U.Z. thanks the Institute of Theoretical Physics at the Technion for hospitality during two visits when part of this research was performed.
Funding
We thank A. Auerbach, O. Entin-Wohlmann, F. Evers, Y. Gefen, B. Huckestein, A. MacKinnon, A. Mirlin, L. Pryadko, B. Shapiro, D. Sheng, S. Sondhi, and I. Zharekeshev for useful discussions. This work was supported by the DIP project of the German Ministry for Education and Research (BMBF), Grant No. 96–00294 from the United States–Israel Binational Science Foundation (BSF), and the Aspen Center for Physics. U.Z. thanks the Institute of Theoretical Physics at the Technion for hospitality during two visits when part of this research was performed.
Funders | Funder number |
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Aspen Center for Physics | |
United States-Israel Binational Science Foundation | |
Bundesministerium für Bildung und Forschung | 96–00294 |
Keywords
- 2D localization
- Quantized Hall insulator
- Real-space renormalization grop