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Hatano-Nelson model with a periodic potential

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Abstract.

We study a generalisation of the Hatano-Nelson Hamiltonian in which a periodic modulation of the site energies is present in addition to the usual random distribution. The system can then become localized by disorder or develop a band gap, and the eigenspectrum shows a wide variety of topologies. We determine the phase diagram, and perform a finite size scaling analysis of the localization transition.

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References

  1. P.W. Anderson, Phys. Rev. 109, 1492 (1958)

    Article  ADS  Google Scholar 

  2. D.J. Thouless, Phys. Rep. 13, 93 (1974)

    Article  ADS  Google Scholar 

  3. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, A. Aspect, Nature 453, 891 (2008)

    Article  ADS  Google Scholar 

  4. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature 453, 895 (2008)

    Article  ADS  Google Scholar 

  5. N. Paris, K. Bouadim, F. Hébert, G.G. Batrouni, R.T. Scalettar, Phys. Rev. Lett. 98, 046403 (2007)

    Article  ADS  Google Scholar 

  6. K. Bouadim, N. Paris, F. Hébert, G.G. Batrouni, R.T. Scalettar, Phys. Rev. B 76, 085112 (2007)

    Article  ADS  Google Scholar 

  7. E. Abrahams, P.W. Anderson, D.C. Licciardello, T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979)

    Article  ADS  Google Scholar 

  8. P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)

    Article  ADS  Google Scholar 

  9. D. Belitz, T.R. Kirkpatrick, Rev. Mod. Phys. 66, 261 (1994)

    Article  ADS  Google Scholar 

  10. N. Hatano, D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996)

    Article  ADS  Google Scholar 

  11. N. Hatano, D.R. Nelson, Phys. Rev. B 56, 8651 (1997)

    Article  ADS  Google Scholar 

  12. N. Hatano, D.R. Nelson, Phys. Rev. B 58, 8384 (1998)

    Article  ADS  Google Scholar 

  13. J. Feinberg, A. Zee, Phys. Rev. E 59, 6433 (1999)

    Article  ADS  Google Scholar 

  14. J. Feinberg, A. Zee, Nucl. Phys. B 552, 599 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. P. Le Doussal, unpublished

  16. A. Zee, Physica A 254, 300 (1998)

    Article  Google Scholar 

  17. M.A. Stephanov, Phys. Rev. Lett. 76, 4472 (1996)

    Article  ADS  Google Scholar 

  18. M.A. Halasz, A.D. Jackson, J.J.M. Verbaarschot, Phys. Rev. D 56, 5140 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  19. L. Civale, Supercon. Sci. Technol. 10, 11 (1997)

    Article  ADS  Google Scholar 

  20. M. Baert, V.V. Metlushko, R. Jonckheere, V.V. Moshchalkov, Y. Bruynseraede, Phys. Rev. Lett. 74, 3269 (1995)

    Article  ADS  Google Scholar 

  21. E. Rosseel, M. Van Bael, M. Baert, R. Jonckheere, V.V. Moshchalkov, Y. Bruynseraede, Phys. Rev. B 53, R2983 (1996)

    Article  ADS  Google Scholar 

  22. V.V. Moshchalkov, M. Baert, V.V. Metlushko, E. Rosseel, M. Van Bael, K. Temst, R. Jonckheere, Y. Bruynseraede, Phys. Rev. B 54, 7385 (1996)

    Article  ADS  Google Scholar 

  23. J.Y. Lin, M. Gurvitch, S.K. Tolpygo, A. Bourdillon, S.Y. Hou, J.M. Phillips, Phys. Rev. B 54, R12717 (1996)

    Article  ADS  Google Scholar 

  24. K. Harada, O. Kamimura, H. Kasai, T. Matsuda, A. Tonomura, V.V. Moshchalkov, Science 274, 1167 (1996)

    Article  ADS  Google Scholar 

  25. C. Reichhardt, C.J. Olson, J. Groth, S. Field, F. Nori, Phys. Rev. B 53, R8898 (1996)

    Article  ADS  Google Scholar 

  26. C. Reichhardt, C.J. Olson, J. Groth, S. Field, F. Nori, Phys. Rev. B 54, 16108 (1996)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. INLN, Université de Nice-Sophia Antipolis, CNRS, 1361 route des Lucioles, 06560, Valbonne, France

    F. Hébert

  2. Physics Department, Massachusetts Institute of Technology, 77, Massachusetts Avenue Cambridge, 02139-4307, MA, USA

    M. Schram

  3. Physics Department, University of California, Davis, 95616, California, USA

    R. T. Scalettar

  4. School of Mathematical Sciences, Fudan University, Shanghai, 200433, P.R. China

    W. B. Chen

  5. Departments of Mathematics and Computer Science, University of California, Davis, 95616, California, USA

    Z. Bai

Authors
  1. F. Hébert
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  2. M. Schram
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  3. R. T. Scalettar
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  4. W. B. Chen
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  5. Z. Bai
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Correspondence to F. Hébert.

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Hébert, F., Schram, M., Scalettar, R. et al. Hatano-Nelson model with a periodic potential. Eur. Phys. J. B 79, 465–471 (2011). https://doi.org/10.1140/epjb/e2011-10875-9

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  • DOI: https://doi.org/10.1140/epjb/e2011-10875-9

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