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An electronic avalanche model for metal–insulator transition in two dimensional electron gas

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Abstract

In this paper, we present an electronic avalanche model for the transport of electrons in the disordered two-dimensional (2D) electron gas which has the potential to describe the 2D metal–insulator transition (MIT) in the zero electron–electron interaction limit. The disorder is considered to be uncorrelated-Coulomb noise with a uniform distribution. In this model we sub-divide the system to some virtual cells each of which has a linear size of the order of phase coherence length of the system. Using Thomas-Fermi-Dirac theory we propose some simple energy functions for the cells and using the thermodynamics of 2DEG we develop some rules for the charge transfer between the cells. A second order transition line arises from our model with some similarities with the experiments. The compressibility of the system also diverges on this line. We characterize this (disorder-driven) phase transition which is between the non-percolating phase and the percolating phase (in which the system shows metallic behavior) and obtain some geometrical critical exponents. The fractal dimension of the exterior frontier of the electronic avalanches on the transition line is compatible with the percolation theory, whereas the other exponents are different. The exponents are robust against disorder in the low disordered 2DEGs and change considerably in the high disordered ones.

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References

  1. E. Abrahams et al., Rev. Mod. Phys. 73, 251 (2001)

    Article  ADS  Google Scholar 

  2. S.V. Kravchenko, M.P. Sarachik, Rep. Prog. Phys. 67, 1 (2004)

    Article  ADS  Google Scholar 

  3. E. Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)

    Article  ADS  Google Scholar 

  4. G.J. Dolan, D.D. Osheroff, Phys. Rev. Lett. 43, 721 (1979)

    Article  ADS  Google Scholar 

  5. S.V. Kravchenko et al., Phys. Rev. B 51, 7038 (1995)

    Article  ADS  Google Scholar 

  6. Y. Hanein et al., Phys. Rev. Lett. 80, 288 (1998)

    Article  Google Scholar 

  7. M.Y. Simmons et al., Phys. Rev. Lett. 80, 1292 (1998)

    Article  ADS  Google Scholar 

  8. A.R. Hamilton, M.Y. Simmons, M. Pepper, E.H. Linfield, D.A. Linfield, Phys. Rev. Lett. 87, 126802 (2001)

    Article  ADS  Google Scholar 

  9. J. Yoon, C.C. Li, D. Shahar, D.C. Tsui, M. Shayegan, Phys. Rev. Lett. 82, 1744 (1999)

    Article  ADS  Google Scholar 

  10. L. Li, Y.Y. Proskuryakov, A.K. Savchenko, E.H. Linfield, D.A. Ritchie, Phys. Rev. Lett. 90, 076802 (2003)

    Article  ADS  Google Scholar 

  11. H. Noh et al., Phys. Rev. B 68, 165308 (2003)

    Article  ADS  Google Scholar 

  12. V.M. Pudalov et al., Phys. Rev. Lett. 91, 126403 (2003)

    Article  ADS  Google Scholar 

  13. D. Popovic, A.B. Fowler, S. Washburn, Phys. Rev. Lett. 79, 1543 (1997)

    Article  ADS  Google Scholar 

  14. A.A. Shashkin, V.T. Dolgopolov, G.V. Kravchenko, Phys. Rev. B 49, 14486 (1994)

    Article  ADS  Google Scholar 

  15. M.Y. Simmons et al., Phys. Rev. Lett. 84, 2489 (2000)

    Article  ADS  Google Scholar 

  16. A. Gold et al., Phys. Rev. B 33, 2495 (1986)

    Article  ADS  Google Scholar 

  17. S. Sarma et al., Solid State Commun. 135, 579 (2005)

    Article  ADS  Google Scholar 

  18. B.L. Altshuler, A.G. Aronov, Electron–electron interaction in disordered conductors, inElectron–Electron Interactions in Disordered Systems, edited by A.L. Efros, M. Pollak (Elsevier, 1985), pp. 1–153

  19. D. Backes, R. Hall, M. Pepper, H. Beere, D. Ritchie, V. Narayan, Phys. Rev. B 92, 235427 (2015)

    Article  ADS  Google Scholar 

  20. H. Bruus et al.,Many-body quantum theory in condensed matter physics: an introduction (Oxford University Press, 2004)

  21. Y. Meir, Phys. Rev. Lett. 83, 3506 (1999)

    Article  ADS  Google Scholar 

  22. S. Das Sarma et al., Phys. Rev. Lett. 94, 136401 (2005)

    Article  ADS  Google Scholar 

  23. M.J. Uren, R.A. Davies, M. Kaveh, M. Pepper, J. Phys. C 14, 5737 (1981)

    Article  ADS  Google Scholar 

  24. D.J. Bishop, D.C. Tsui, R.C. Dynes, Phys. Rev. Lett. 44, 1153 (1980)

    Article  ADS  Google Scholar 

  25. S. Das Sarma et al., Rev. Mod. Phys. 83, 407 (2011)

    Article  ADS  Google Scholar 

  26. V.Y. Butko, P.W. Adams, Nature 409, 161 (2001)

    Article  ADS  Google Scholar 

  27. P.V. Lin, D. Popović, Phys. Rev. Lett. 114, 166401 (2015)

    Article  ADS  Google Scholar 

  28. S.A. Vitkalov, H. Zheng, K.M. Mertes, M.P. Sarachik, T.M. Klapwijk, Phys. Rev. Lett. 87, 086401 (2001)

    Article  ADS  Google Scholar 

  29. A.L. Efros, B.I. Shklovskii, J. Phys. C: Solid State Phys. 8, L49 (1975)

    Article  ADS  Google Scholar 

  30. M.P. Sarachik, S.V. Kravchenko, Proc. Natl. Acad. Sci. USA 96, 5900 (1999)

    Article  ADS  Google Scholar 

  31. R. Heemskerk, T.M. Klapwijk, Phys. Rev. B 58, R1754 (1998)

    Article  ADS  Google Scholar 

  32. V.M. Pudalov, G. Brunthaler, A. Prinz, G. Bauer, JETP Lett. 70, 48 (1999)

    Article  ADS  Google Scholar 

  33. J. Jaroszynski, D. Popovic, T.M. Klapwijk, Phys. Rev. Lett. 89, 276401 (2002)

    Article  ADS  Google Scholar 

  34. Y. Hanein et al., Phys. Rev. Lett. 80, 1288 (1998)

    Article  ADS  Google Scholar 

  35. Y. Hanein et al., Phys. Rev. B 58, R7520 (1998)

    Article  ADS  Google Scholar 

  36. V.M. Pudalov, G. Brunthaler, A. Prinz, G. Bauer, Effect ofthe in-plane magnetic field on conduction of the Si-inversion layer: magnetic field driven disorder, https://arXiv:cond-mat/0103087 (2001)

  37. S. Bogdanovich, D. Popovic, Phys. Rev. Lett. 88, 236401 (2002)

    Article  ADS  Google Scholar 

  38. A.A. Shashkin, S.V. Kravchenko, T.M. Klapwijk, Phys. Rev. Lett. 87, 266402 (2001)

    Article  ADS  Google Scholar 

  39. T.C. Rödel et al., Phys. Rev. B 96, 041121 (2017)

    Article  ADS  Google Scholar 

  40. S. Muff et al., Appl. Surf. Sci. 432, 41 (2018)

    Article  ADS  Google Scholar 

  41. S. McKeown Walker et al., Phys. Rev. Lett. 113, 177601 (2014)

    Article  ADS  Google Scholar 

  42. N.C. Plumb et al., Phys. Rev. Lett. 113, 086801 (2014)

    Article  ADS  Google Scholar 

  43. A.F. Santander-Syro et al., Phys. Rev. B 86, 121107 (2012)

    Article  ADS  Google Scholar 

  44. T.C. Rödel et al., Phys. Rev. Mater. 2, 051601 (2018)

    Article  Google Scholar 

  45. A. Camjayi, K. Haule, V. Dobrosavljevic, G. Kotliar, Nat. Phys. 4, 932 (2008)

    Article  Google Scholar 

  46. M.M. Radonjic, D. Tanaskovic, V. Dobrosavljevic, K. Haule, G. Kotliar, Phys. Rev. B 85, 085133 (2012)

    Article  ADS  Google Scholar 

  47. J. Vucicevic et al., Phys. Rev. B 88, 075143 (2013)

    Article  ADS  Google Scholar 

  48. K. Byczuk, W. Hofstetter, D. Vollhardt, Phys. Rev. Lett. 94, 056404 (2005)

    Article  ADS  Google Scholar 

  49. L. Hunpyo, H.O. Jeschke, R. Valentí. Phys. Rev. B 93, 224203 (2016)

    Article  ADS  Google Scholar 

  50. A. Punnoose, A.M. Finkelstein, Science 310, 289 (2005)

    Article  ADS  Google Scholar 

  51. R. Koushik, M. Baenninger, V. Narayan, S. Mukerjee, M. Pepper, I. Farrer, D.A. Ritchie, A. Ghosh, Phys. Rev. B 83, 085302 (2011)

    Article  ADS  Google Scholar 

  52. T.S. Nunner, G. Zaránd, F. Von Oppen, Phys. Rev. Lett. 100, 236602 (2008)

    Article  ADS  Google Scholar 

  53. M.V. Sadovskii,Diagrammatics (World Scientific, 2006)

  54. Y. Yaish et al., Phys. Rev. Lett. 84, 4954 (2000)

    Article  ADS  Google Scholar 

  55. Y. Hanein, U. Meirav, D. Shahar, C.C. Li, D.C. Tsui, H. Shtrikman, Phys. Rev. Lett. 80, 1288 (1998)

    Article  ADS  Google Scholar 

  56. Y. Hanein, D. Shahar, J. Yoon, C.C. Li, D.C. Tsui, H. Shtrikman, Phys. Rev. B 58, R7520 (1998)

    Article  ADS  Google Scholar 

  57. Y. Hanein et al., Phys. Rev. B 58, R13338 (1998)

    Article  ADS  Google Scholar 

  58. A.A. Shashkin et al., Phys. Rev. Lett. 73, 3141 (1994)

    Article  ADS  Google Scholar 

  59. V.T. Dolgapolov et al., JETP Lett. 62, 162 (1995)

    ADS  Google Scholar 

  60. I.V. Kukuskin et al., Phys. Rev. B 53, R13260 (1996)

    Article  ADS  Google Scholar 

  61. S. He, X.C. Xie, Phys. Rev. Lett. 80, 3324 (1998)

    Article  ADS  Google Scholar 

  62. S. Das Sarma et al., Phys. Rev. B 88, 155310 (2013)

    Article  ADS  Google Scholar 

  63. A.G. Hunt, Philos. Mag. B 81, 875 (2001)

    Article  ADS  Google Scholar 

  64. S.V. Kranchenko et al., Phys. Rev. B 50, 8039 (1994)

    Article  ADS  Google Scholar 

  65. S.V. Kranchenko et al., Phys. Rev. B 51, 7038 (1995)

    Article  ADS  Google Scholar 

  66. S.V. Kranchenko et al., Phys. Rev. Lett. 77, 4938 (1996)

    Article  ADS  Google Scholar 

  67. W.R. Clarke, C.E. Yasin, A.R. Hamilton, A.P. Micolich, M.Y. Simmons, K. Muraki, Y. Hirayama, M. Pepper, D.A. Ritchie, Nat. Phys. 4, 55 (2008)

    Article  Google Scholar 

  68. A. Gold, W. Gotze, C. Mazure, F. Koch, inProceedings of the 17th International Conference on Low-Temperature Physics, LT–17, Karlsruhe, 1984 (Elsevier, Amsterdam, 1984)

  69. R.G. Parr, inHorizons of Quantum Chemistry (Springer, Netherlands, 1980), p. 5

  70. H. Gould, J. Tobochnik,Computer Simulation Methods (Addison-Wesley, Reading, 1996)

  71. J. Hoshen, R. Kopelman, Phys. Rev. B 14, 3438 (1976)

    Article  ADS  Google Scholar 

  72. N. Goldenfeld,Lectures on phase transitions and the renormalization group (Westview Press, 1992)

  73. M.N. Najafi, S. Moghimi-Araghi, S. Rouhani, Phys. Rev. E 85, 051104 (2012)

    Article  ADS  Google Scholar 

  74. H. Dashti-Naserabadi, M.N. Najafi, Phys. Rev. E 91, 052145 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  75. M.S. Girvin, inTopological aspects of low dimensional systems (Springer, Berlin, Heidelberg, 1999), p. 53

  76. J. Cardy, Ann. Phys. 318, 81 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  77. L.A. Tracy, E.H. Hwang, K. Eng, G.A.T. Eyck, E.P. Nordberg, K. Childs, M.S. Carroll, M.P. Lilly, S. Das Sarma, Phys. Rev. B 79, 235307 (2009)

    Article  ADS  Google Scholar 

  78. M.N. Najafi, S. Moghimi-Araghi, S. Rouhani, J. Phys. A: Math. Theor. 45, 095001 (2012)

    Article  ADS  Google Scholar 

  79. M.N. Najafi, J. Stat. Mech.: Theory Exp. 2015, P05009 (2015)

    Article  Google Scholar 

  80. J. Cheraghalizadeh et al., Phys. Rev. E 97, 042128 (2018)

    Article  ADS  Google Scholar 

  81. G. Grosso, G. Pastori Parravicini,Solid state physics (Academic Press, 2014)

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  1. Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran

    Morteza Nattagh Najafi

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  1. Morteza Nattagh Najafi
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Najafi, M.N. An electronic avalanche model for metal–insulator transition in two dimensional electron gas. Eur. Phys. J. B 92, 172 (2019). https://doi.org/10.1140/epjb/e2019-100209-8

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