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Nonlinear dynamics and the nano-mechanical control of electrons in crystalline solids

Nano-mechanical control of electrons

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Abstract

Under the umbrella of nano-mechanical control of electrons in crystalline solids, provided here are i) a discussion of aspects of the influence of static piezoelectricity on semiconductors, ii) a description of electron surfing on traveling piezopotentials/surface acoustic waves, iii) comments on the role of solitons in (dopable) polymer conductors/synthetic metals, and iv) the major component of these notes, a discussion of basic aspects of lattice solitons and discrete breathers permitting to understand genuine electron surfing on nanosolitons. This surfing offers a form of long range, fast and robust transport process in crystalline solids. The particular case of the undopable highly crystalline polydiacetylene polymer serves to illustrate the invention of a novel solectron field effect transistor (SFET).

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References

  1. M.G. Velarde, J. Computat. App. Math. 233, 1432 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  2. M.J. Hoskins, H. Morko, B.J. Hunsinger, Appl. Phys. Lett. 41, 332 (1982)

    Article  ADS  Google Scholar 

  3. W.J. Tanski, S.W. Merritt, R.N. Sacks, D.E. Cullen, E.J. Branciforte, R.D. Caroll, T.C. Eschrich, Appl. Phys. Lett. 52, 18 (1988)

    Article  ADS  Google Scholar 

  4. A.O. Govorov, A.V. Kalameitsev, M. Rotter, A. Wixforth, J.P. Kotthaus, K.-H. Hoffmann, N. Botkin, Phys. Rev. B 62, 2659 (2000)

    Article  ADS  Google Scholar 

  5. A. Wixforth, J.P. Kotthaus, G. Weimann, Phys. Rev. Lett. 56, 2104 (1986)

    Article  ADS  Google Scholar 

  6. M. Rotter, A.V. Kalameitsev, A.O. Govorov, W. Ruile, A. Wixforth, Phys. Rev. Lett. 82, 2171 (1999)

    Article  ADS  Google Scholar 

  7. M. Streibl, A. Wixforth, J.P. Kotthaus, A.O. Govorov, C. Kadow, A.C. Gossard, Appl. Phys. Lett. 75, 4139 (1999)

    Article  ADS  Google Scholar 

  8. S. Völk, F.J.R. Schülein, F. Knall, D. Reuter, A.D. Wieck, T.A. Truong, H. Kim, P.M. Petroff, A. Wixforth, H.J. Krenner, Nano Lett. 10, 3399 (2010)

    Article  ADS  Google Scholar 

  9. F.J.R. Schülein, K. Müller, M. Bichler, G. Koblmüller, J.J. Finley, A. Wixforth, H.J. Krenner, Phys. Rev B 88, 085307 (2013)

    Article  ADS  Google Scholar 

  10. S. Hermelin, S. Takada, M. Yamamoto, S. Tarucha, A.D. Wieck, L. Saminadayar, C. Bäuerle, T. Meunier, Nature 477, 435 (2011)

    Article  ADS  Google Scholar 

  11. R.P.G. McNeil, M. Kataoka, C.J.B. Ford, C.H.W. Barnes, D. Anderson, G.A.C. Jones, I. Farrer, D.A. Ritchie, Nature 477, 439 (2011)

    Article  ADS  Google Scholar 

  12. B. Bertrand, S. Hermelin, P.A. Mortemousque, S. Tanaka, M. Yamamoto, S. Tarucha, A. Ludwig, A.D. Wieck, C. Bäuerle, T. Meunier [arXiv:1601.02485] [cond-mat.mes-hall]

  13. A. Oliner (ed.), Acoustic Surface Waves (Springer, Berlin, 1978)

  14. A.P. Mayer, Phys. Reports 256, 237 (1995)

    Article  ADS  Google Scholar 

  15. V.I. Nayanov, JETP Lett. 44, 314 (1986)

    ADS  Google Scholar 

  16. P. Hess, Phys. Today 55, 42 (2002)

    Article  Google Scholar 

  17. A.M. Lomonosov, P. Hess, A.P. Mayer, Phys. Rev. Lett. 88, 076104 (2002)

    Article  ADS  Google Scholar 

  18. A. Kolomenskii, V.A. Lioubimov, S.N. Jerebtsov, H.A. Schuessler, Rev. Sci. Instr. 74, 448 (2003)

    Article  ADS  Google Scholar 

  19. C. Eckl, A.S. Kovalev, A.P. Mayer, A.M. Lomonosov, P. Hess, Phys. Rev. E 70, 046604 (2004)

    Article  ADS  Google Scholar 

  20. A. Ranciaro Neto, M.O. Sales, F.A.B.F. de Moura, Solid State Commun. 229, 22 (2016)

    Article  ADS  Google Scholar 

  21. Z.L. Wang, Piezotronics and Piezo-Phototronics (Springer, Berlin, 2012)

  22. Y. Hu, Z.L. Wang, Nano Energy 14, 3 (2015)

    Article  Google Scholar 

  23. Y. Liu, Y. Zhang, Q. Yang, S. Niu, Z.L. Wang, Nano Energy 14, 257 (2015)

    Article  Google Scholar 

  24. X. Wen, W. Wu, C. Pan, Y. Hu, Q. Yang, Z.L. Wang, Nano Energy 14, 276 (2015)

    Article  Google Scholar 

  25. S.V. Dmitriev, E.A. Korzinova, Yu.A. Baimova, M.G. Velarde, Phys. Uspekhi 59, 446 (2016)

    Article  ADS  Google Scholar 

  26. M.A. Migliorato, J. Pal, R. Garg, G. Tse, H.Y.S. Al-Zahrani, U. Monteverde, S. Tomic, C.-K. Li, Y.-R. Wu, B.G. Crutchley, I.P. Marko, S.J. Sweeney, AIP Conf. Procs. 1590, 32 (2014)

    Article  ADS  Google Scholar 

  27. R. Gausmann, W. Seemann, PAMM Proc. Appl. Math. Mech. 2, 64 (2003)

    Article  Google Scholar 

  28. G. Bester, X. Wu, D. Vanderbilt, A. Zunger, Phys. Rev. Lett. 96, 187602 (2006)

    Article  ADS  Google Scholar 

  29. G. Bester, A. Zunger, X. Wu, D. Vanderbilt, Phys. Rev. B 74, 081305 (2006)

    Article  ADS  Google Scholar 

  30. R. Tao, G. Ardila, L. Montes, M. Mouis, Nano Energy 14, 62 (2015)

    Article  Google Scholar 

  31. S.C. Stanton, A. Erturk, B.P. Mann, D.J. Inman, J. Appl. Phys. 108, 074903 (2010)

    Article  ADS  Google Scholar 

  32. S.C. Stanton, C.C. McGehee, B.P. Mann, Physica D 239, 640 (2010)

    Article  ADS  Google Scholar 

  33. M.A. Migliorato, D. Powell, A.G. Cullis, T. Hammerschmidt, G.P. Srivastava, Phys. Rev. B 74, 245332 (2006)

    Article  ADS  Google Scholar 

  34. R. Garg, A. Hüe, V. Haxha, T. Hammerschmidt, G.P. Srivastava, Appl. Phys. Lett. 95, 041912 (2009)

    Article  ADS  Google Scholar 

  35. J. Pal, G. Tse, V. Haxha, Phys. Rev. B 84, 085211 (2011)

    Article  ADS  Google Scholar 

  36. H.Y.S. Al-Zahrani, J. Pal, M.A. Migliorato, Nano Energy 2, 1214 (2013)

    Article  Google Scholar 

  37. J. Pal, M.A. Migliorato, C.-K. Li, Y.-R. Wu, B.G. Crutchley, I.P. Marko, S.J. Sweeney, J. Appl. Phys. 114, 073104 (2013)

    Article  ADS  Google Scholar 

  38. G. Tse, J. Pal, U. Monteverde, R. Gang, V. Haxha, M.A. Migliorato, S. Tomic, J. Appl. Phys. 114, 073515 (2013)

    Article  ADS  Google Scholar 

  39. Y. Fan, X. Ji, X. Liu, P. Cai, Wave Motion 51, 798 (2014)

    Article  MathSciNet  Google Scholar 

  40. F. Xue, L. Zhang, X. Feng, G. Hu, F.R. Fan, X. Wen, L. Zheng, Z.L. Wang, Nano Res. 8, 2390 (2015)

    Article  Google Scholar 

  41. A.R. Hutson, J.H. McFee, D.L. White, Phys. Rev. Lett. 7, 237 (1961)

    Article  ADS  Google Scholar 

  42. R.W. Smith, Phys. Rev. Lett. 9, 87 (1962)

    Article  ADS  Google Scholar 

  43. J.H. McFee, J. Appl. Phys. 34, 1548 (1963)

    Article  ADS  Google Scholar 

  44. R. Abe, Prog. Theor. Phys. 31, 957 (1964)

    Article  ADS  Google Scholar 

  45. M. Toda, Theory of Nonlinear Lattices, 2nd. edn. (Springer, Berlin, 1989)

  46. V.I. Nekorkin, M.G. Velarde, Synergetic Phenomena in Active Lattices. Patterns, Waves, Solitons, Chaos (Springer, Berlin, 2002)

  47. T. Dauxois, M. Peyrard, Physics of solitons (Cambridge University Press, Cambridge, 2006)

  48. R.M. White, F.W. Volmer, Appl. Phys. Lett. 7, 314 (1965)

    Article  ADS  Google Scholar 

  49. H. Shirakawa, in I. Grethe (ed.), Nobel Lectures, Chemistry 1996–2000 (World Scientific, Singapore, 2003)

  50. A.G. MacDiarmid, edited by I. Grethe, Nobel Lectures, Chemistry 1996–2000 (World Scientific, Singapore, 2003)

  51. A.J. Heeger, edited by I. Grethe, Nobel Lectures, Chemistry 1996–2000 (World Scientific, Singapore, 2003)

  52. A.J. Heeger, S. Kivelson, J.R. Schrieffer, W.P. Su, Rev. Mod. Phys. 60, 781 (1988) (and references therein)

    Article  ADS  Google Scholar 

  53. S. Roth, H. Bleier, Adv. Phys. 36, 385 (1987)

    Article  ADS  Google Scholar 

  54. L. Yu (Ed.), Solitons & Polarons in Conducting Polymers (World Scientific, Singapore, 1988)

  55. N. Greenhamy R.H. Friend, edited by H. Ehrereich, F. Spaepen, Solid State Physics, Vol. 49, 1 (Academic Press, San Diego, 1995)

  56. H.S. Nalwa (ed.), Handbook of Nanostrutured Materials and Nanotechnology, Vol. 5: Organics, polymers, and biological materials (Academic Press, San Diego, 2000)

  57. N. Tessler, Y. Preezant, N. Rappaport, Y. Roichman, Adv. Mater. 21, 2741 (2009)

    Article  Google Scholar 

  58. J.-L. Bredas, S.R. Marder (ed.), The WSPC Reference on Organic Electronics: Organic Semiconductors, vol. 1 Basic concepts, Vol. 2 Fundamental aspects of materials and applications (World Scientific, Singapore, 2015)

  59. S. Kivelson, D.E. Heim, Phys. Rev. B 26, 4278 (1982)

    Article  ADS  Google Scholar 

  60. C.K. Chiang, C.R. Fincher Jr., Y.W. Park, A.J. Heeger, H. Shirakawa, E.J. Louis, S.C. Gau, A.G. MacDiarmid, Phys. Rev. Lett. 39, 1098 (1977)

    Article  ADS  Google Scholar 

  61. J. Tsukamoto, A. Takahashi, K. Kawasaki, Japan J. Appl. Phys. 29, 125 (1990)

    Article  ADS  Google Scholar 

  62. N.F. Mott, Metal-Insulator Transitions, 2nd. edn. (Taylor & Francis, London, 1990), p. 50

  63. B.I. Shklovskii, A.L. Efros, Electronic Properties of Doped Semiconductors (Springer, Berlin, 1984), ch. 9

  64. A.P. Chetverikov, W. Ebeling, M.G. Velarde, Eur. Phys. J. B 88, 202 (2015)

    Article  ADS  Google Scholar 

  65. M.G. Velarde, W. Ebeling, A.P. Chetverikov, Int. J. Bifurcation Chaos 15, 245 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  66. A.P. Chetverikov, W. Ebeling, M.G. Velarde, Int. J. Bifurcation Chaos 16, 1613 (2006)

    Article  MathSciNet  Google Scholar 

  67. A. Ovchinnikov, Soviet Phys. JETP 30, 147 (1970)

    ADS  Google Scholar 

  68. S. Barisic, Phys. Rev. B 5, 932 (1972)

    Article  ADS  Google Scholar 

  69. A.S. Dolgov, Sov. Phys. Solid State 28, 907 (1986)

    Google Scholar 

  70. A. Sievers, S. Takeno, Phys. Rev. Lett. 61, 970 (1988)

    Article  ADS  Google Scholar 

  71. J.B. Page, Phys. Rev. B 41, 7835 (1990)

    Article  ADS  Google Scholar 

  72. S.A. Kiselev, S.R. Bickham, A.J. Sievers, Phys. Rev. B 48, 13508 (1993)

    Article  ADS  Google Scholar 

  73. G.P. Tsironis, Chaos 13, 657 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  74. D.K. Campbell, S. Flach, Yu.S. Kivshar, Phys. Today 57, 43 (2004) (and references therein)

    Article  ADS  Google Scholar 

  75. G. Iooss, G. James, Chaos 15, 015113 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  76. S. Aubry, Physica D 216, 1 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  77. S. Flach, A. Gorbach, Phys, Rep. 467, 1 (2008) (and references therein)

    Article  Google Scholar 

  78. A.A. Kistanov, S.V. Dmitriev, A.P. Chetverikov, M.G. Velarde, Eur. Phys. J B 87, 211 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  79. S. Dmitriev, A.P. Chetverikov, M.G. Velarde, Physica Status Solidi (b) 252, 1682 (2015)

    Article  ADS  Google Scholar 

  80. M.G. Velarde, A.P. Chetverikov, W. Ebeling, S.V. Dmitriev, V.D. Lakhno, Procs. Estonian Acad. Sci. 64, 396 (2015)

    Article  Google Scholar 

  81. J.C. Slater, Quantum Theory of Molecules and Solids, Vol. 4 (McGraw-Hill, New York, 1974)

  82. J.P. Launay, M. Verdaguer, Electrons in Molecules (Oxford University Press, Oxford, 2014)

  83. A.S. Davydov, Solitons in Molecular Systems, 2nd. edn (Reidel, Dordrecht, 1991)

  84. P.L. Christiansen, A.C. Scott (eds.), Davydov’s Soliton Revisited. Self-trapping of Vibrational Energy in Protein (Plenum Press, New York, 1990)

  85. A.C. Scott, Phys. Rep. 217, 1 (1992)

    Article  ADS  Google Scholar 

  86. D. Hennig, A.P. Chetverikov, M.G. Velarde, W. Ebeling, Phys. Rev. E 76, 046602 (2007)

    Article  ADS  Google Scholar 

  87. M.G. Velarde, W. Ebeling, A.P. Chetverikov, Int. J. Bifurcation Chaos 18, 3815 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  88. O.G. Cantu-Ross, L. Cruzeiro, M.G. Velarde, W. Ebeling, Eur. Phys. J. B 80, 545 (2011)

    Article  ADS  Google Scholar 

  89. A.P. Chetverikov, W. Ebeling, M.G. Velarde, Eur. Phys. J. B 85, 291 (2012)

    Article  ADS  Google Scholar 

  90. A.P. Chetverikov, W. Ebeling, G. Röpke, M.G. Velarde, Eur. Phys. J. B 87, 153 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  91. M.G. Velarde, A.P. Chetverikov, W. Ebeling, E.G. Wilson, Eur. Phys. Lett. EPL 106, 27004 (2014)

    Article  ADS  Google Scholar 

  92. K.J. Donovan, E.G. Wilson, Phil. Mag. B 44, 9 and 31 (1981)

  93. K.J. Donovan, P.D. Freeman, E.G. Wilson, J. Phys. C: Solid State Phys. 18, L275 (1985)

    Article  ADS  Google Scholar 

  94. K.J. Donovan, E.G. Wilson, J. Phys.: Condens. Matter 2, 1659 (1990)

    ADS  Google Scholar 

  95. K. Donovan, J.W.P. Elkins, E.G. Wilson, J. Phys.: Condens. Matter 3, 2075 (1991)

    ADS  Google Scholar 

  96. E.G. Wilson, J. Phys. C: Solid State Phys. 16, 6739 (1983)

    Article  ADS  Google Scholar 

  97. A.M. Kosevich, A.S. Kovalev, Soviet Phys. JETP 40, 891 (1975)

    ADS  Google Scholar 

  98. J.S. Zmuidzinas, Phys. Rev. B 17, 3919 (1978)

    Article  ADS  Google Scholar 

  99. A.V. Zolotaryuk, K.H. Spatschek, A.V. Savin, Phys. Rev. B 54, 266 (1996)

    Article  ADS  Google Scholar 

  100. M.G. Velarde, L. Brizhik, A.P. Chetverikov, L. Cruzeiro, W. Ebeling, G. Röpke, Int. J. Quantum Chem. 112, 551 and 2591 (2012)

    Article  Google Scholar 

  101. L. Brizhik, A.P. Chetverikov, W. Ebeling, G. Röpke, M.G. Velarde, Phys. Rev. B 85, 245105 (2012)

    Article  ADS  Google Scholar 

  102. R. Landauer, IBM J. Res. Dev. 5, 183 (1961) [reprinted 44, 261 (2000)]

    Article  MathSciNet  Google Scholar 

  103. J.A. Vaccaro, S.M. Barnett, Proc. Roy. Soc. A 467, 1770 (2011)

    Article  ADS  MathSciNet  Google Scholar 

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    M.G. Velarde

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Velarde, M. Nonlinear dynamics and the nano-mechanical control of electrons in crystalline solids. Eur. Phys. J. Spec. Top. 225, 921–941 (2016). https://doi.org/10.1140/epjst/e2016-02647-2

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