Advertisement

Virtual Synthesis of Electronic Nanomaterials: Fundamentals and Prospects

  • Liudmila A. PozharEmail author
  • William C. Mitchel
Chapter
First Online:
Part of the Lecture Notes in Nanoscale Science and Technology book series (LNNST, volume 5)

Abstract

Increasingly, integrated logic-storage and quantum information-process-ing paradigms are being viewed as dominant approaches to facilitate further advances in electronics, communication, information processing, and storage technologies. Realization of these concepts is based upon understanding the formation of coherent, polarized, and especially entangled (CPE) electron spin states, ability to control their dynamics and their contributions to quantum spin–charge transport properties of small, few-atomic systems at realistic conditions at interfaces and in quantum confinement.

This chapter is focused on novel, first-principle, synergetic theoretical and computational methods designed to predict the electron spin–charge transport properties of small atomic clusters (quantum dots, or QDs) and molecules that may be used as sources of CPE electron spin states. Theoretical methods are derived from a many-body quantum theory formalism – a projection operator method by Zubarev and Tserkovnikov (ZT) – based on equilibrium, commutatorial two-time temperature Green functions (or TTGFs). The ZT approach has been widely used to predict thermodynamic and charge transport properties of bulk systems, including metals, semi- and superconductors, etc. In this chapter, the linearized version of the ZT method is generalized to include strongly spatially inhomogeneous systems, such as a single molecule or QD.

There are several significant advantages of this approach, as compared to the traditional nonequilibrium two-time thermodynamic and field-theoretical Green function (NGF) methods that are used to study electron transport at nanoscale. In particular, the TTGF method does not require introduction of the distribution functions to link the GFs to the transport coefficients (in contrast to the existing NGF-based methods), thus avoiding effects of this major uncontrolled approximation, while also significantly reducing the use of controlled approximations and calculation efforts related to derivation of a kinetic theory. Further on, the TTGFs are susceptibilities, and thus are directly related to experimentally assessable microscopic charge, spin and microcurrent densities. In their turn, the latter quantities are directly related to the spin states of contributing electrons. Thus, measurements of these quantities provide direct experimental information on the contributing electron spin states. It is also important that the equilibrium TTGFs have to be calculated only once for a considered system, while NGFs must be calculated for the same system every time when process conditions change. The theoretical TTGF-based formulae for the electron transport coefficients directly related to experimental data are crucial to identify propagating (or dynamic) CPE electron spin states.

Practical significance of the fundamental insights into electron spin–charge transport provided by analytical theoretical means is limited without accurate data on the equilibrium electronic structure of small systems, because specific predictions are very sensitive to details of the electron spin–charge density distributions of the small systems and their quantum confinement. These data can be obtained using virtual (i.e., many-body quantum theory-based computational) synthesis and evaluation of the corresponding model molecules and QDs. Such computational results used in theoretical formulae provide reliable predictions, and thus a valuable guideline for experimental synthesis of small systems with predesigned electron CPE spin states and spin–charge transport properties. In this work, GAMESS software package has been used to synthesize computationally several artificial molecules composed of semiconductor compound atoms. The data so obtained contain detailed information on the molecular structure, composition, chemistry, electron energies, spin and charge distributions, and electron wave functions (molecular orbits) necessary to identify electron spin states of interest (such as entangled spin states where electrons share the spatial portion of their wave function while localized on or propagating to different QDs: spin-based qubits), and can be further used in the ZT-based theoretical formulae to calculate the TTGFs, and thus electron spin–charge transport properties of the studied systems.

Keywords

Quantum Confinement Covalent Radius Occupied Orbit Inhomogeneous System Spin Density Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

Support of the National Science Foundation through the grants DMR No. 0340613 and No. 0647356 is appreciated.

References

  1. 1.
    P. Zoller P, T. Beth, D. Binosi, R. Blatt, H. Briegel, D. Bruss, T. Calarco, J.I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassi, S. Haroche, A. Imamoglu, A. Karison, J. Kempe, L. Kouwenhoven, S. Kroll, G. Leuchs, M. Lewenstein, D. Loss, N. Lutkenhouse, S. Massar, J.E. Mooij, M.B. Plenio, E. Polzik, S. Popescu, G. Rempe, A. Sergienko, D. Suter, J. Twamley, G. Wendin, R. Werner, A. Winter, J. Wrachtrup, and A. Zellinger, Euro. Phys. J. D 36, 203 (2005).Google Scholar
  2. 2.
    G. Chen, Z.J. Diao, J.U. Kim, A. Neogi, K. Urtekin, and Z.G. Zhang, Int. J. Quant. Inform. 4, 233 (2006).Google Scholar
  3. 3.
    S. Bandyopadhyay, Superlattices and Microstructures, 37, 77 (2005).Google Scholar
  4. 4.
    T. Radtke and S. Fritzsche, Comp. Phys. Commun. 173, 91 (2005).Google Scholar
  5. 5.
    R.G. Mani, W.B. Johnson, V. Narayanamutri, V. Privman, and Y.-H. Zhang, Physica E 12, 152 (2002).Google Scholar
  6. 6.
    G. Burkard and D. Loss, Phys. Rev. B 59, 2070 (1998); D.P. DiVincenzo, Phys. Rev. A 51, 1015 (1994).Google Scholar
  7. 7.
    D. Loss and D.P. DiVincenzo, Phys. Rev. A V. 57(1), 120–126 (1998).Google Scholar
  8. 8.
    G. Prinz, Phys. Today 48, 58 (1995); G. Prinz, Science 282, 1660 (1998).Google Scholar
  9. 9.
    T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J.R. Rabeau, N. Stavrias, A.D. Greentree, S. Praver, J. Meijer, J. Twamley, P.R. Hemmer, and J. Wrachtrup, Nature (Physics) 2, 408 (2006).Google Scholar
  10. 10.
    D.D. Awschalom and J.M. Kikkawa, Phys. Today 52, 33 (1999); J.M. Kikkawa and D.D. Awschalom, Phys. Rev. Lett. 80, 4313 (1998); J.M. Kikkawa and D.D. Awschalom, Nature (London) 397, 139 (1999).Google Scholar
  11. 11.
    R. Fiederling, M. Kelm, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L.M. Molenkamp, Nature (London) 402, 787 (1999).Google Scholar
  12. 12.
    Y. Ohno, D.K. Young, B. Beschoten, F. Motsukura, H. Ohno, and D.D. Awschalom, Nature (London) 402, 790 (1999).Google Scholar
  13. 13.
    F.G. Monson and M.L. Roukes, J. Magn. Magn. Mater. 198, 632 (1999).Google Scholar
  14. 14.
    D.P. DiVincenzo, Science 270, 255 (1995).Google Scholar
  15. 15.
    D.P. DiVincenzo and D. Loss, J. Magnet. Magnet. Mater. 200, 202 (1999).Google Scholar
  16. 16.
    F.H.L. Koppens, C. Buizert, K.J. Tielrooij, I.T. Vink, K.C. Nowack, T. Meunier, L.P. Kouwenhoven, and L.M.K. Vandersypen, Nature 442, 766 (2006); D. Kitchens, A. Richardella, J.-M. Tang, M.E. Flatte, and A. Yazdani, Nature 442, 436 (2006).Google Scholar
  17. 17.
    L.J. Sham and J. Magnet. Magnet. Mater. 200, 219 (1999).Google Scholar
  18. 18.
    G.M. Jones, B.H. Hu, and C.H. Young, Appl. Phys. Lett. 88, 192102(3) (2006); G.M. Jones, B.H. Hu, and C.H. Young, Appl. Phys. Lett. 89, 073106 (3) (2006).Google Scholar
  19. 19.
    R. Skomsky, J. Zhou, A.Y. Istomin, A.F. Starace, and D.J. Sellmyer, J. Appl. Phys. 97, 10R511(3) (2005).Google Scholar
  20. 20.
    R. Skomsky, A.Y. Istomin, A.F. Starace, and D.J. Sellmyer, Phys. Rev. A 70, 062307(4) (2004).Google Scholar
  21. 21.
    X. Hu and S. Das Sarma, Phys. Rev. A 61, 062301 (19) (2000).Google Scholar
  22. 22.
    A. Mizel and D.A. Lidar, Phys. Rev. B 70, 115310 (13) (2004).Google Scholar
  23. 23.
    V.W. Scarola and S. Das Sarma, Phys. Rev. A 71, 032340 (12) (2005).Google Scholar
  24. 24.
    B. Zhou, R. Tao, S.-Q. Shen, and J.-Q. Liang, Phys. Rev. A 66, 010301 (R) (2002).Google Scholar
  25. 25.
    M. Wagner, U. Merkt, and A.V. Chaplik, Phys. Rev. B 45, 1951 (1992).Google Scholar
  26. 26.
    T. Fujizawa, D.G. Austing, Y. Tokura, Y. Hirayama, and S. Tarucha, Nature 419, 278 (2002).Google Scholar
  27. 27.
    R. Hanson, B. Witkamp, L.M.K. Vandersypen, L.H. Willems van Beveren, J.M. Elzerman, and L.P. Kouwenhoven, Phys. Rev. Lett. 91, 196802 (4) (2003).Google Scholar
  28. 28.
    J.M. Eizerman, R. Hanson, L.H. Willems van Beveren, B. Witkamp, L.M.K. Vandersypen, and L.P. Kouwenhoven, Nature 430, 431 (2004).Google Scholar
  29. 29.
    J.M. Eizerman, R. Hanson, J.S. Greidanus, L.H. Willems van Beveren, S. De Franceschi, L.M.K. Vandersypen, S. Tarucha, and L.P. Kouwenhoven, Phys. Rev. B 67, 161308 (R) (2003).Google Scholar
  30. 30.
    M. Bauer, P. Hawrylak, K. Hinzer, S. Fafard, M. Korkusinski, Z.K. Wasilewski, O. Stern, and A. Forchel, Science 291, 451 (2001).Google Scholar
  31. 31.
    M. Atatűre, J. Dreiser, A. Badolato, A. Högele, K. Karrai, and A. Imamoglu, Science 312, 551 (2006).Google Scholar
  32. 32.
    R. Schleser, E. Ruh, T. Ihn, K. Ensslin, D.C. Driscoll, and A.C. Gossard, Appl. Phys. Lett. 85, 2005 (2004).Google Scholar
  33. 33.
    R. Hanson, L.H. Willems van Beveren, I.T. Vink, J.M. Elzerman, W.J.M. Naber, F.H.L. Koppens, L.P. Kouwenhoven, and L.M.K. Vandersypen, Phys. Rev. Lett. 94, 196802 (4) (2005).Google Scholar
  34. 34.
    W. Lu, Z.Q. Li, L. Pfeiffer, K.W. West, and A.J. Rimberg, Nature 423, 422 (2003).Google Scholar
  35. 35.
    L.M.K. Vandersypen, J.M. Elzerman, R.H. Schouten, L.H. Willems van Beveren, R. Hanson, and L.P. Kouwenhoven, Appl. Phys. Lett. 85, 4394 (2004).Google Scholar
  36. 36.
    P. Recher, E.V. Sukhorukov, and D. Loss, Phys. Rev. Lett. 85, 1962 (2000).Google Scholar
  37. 37.
    C.P. Poole, Electron Spin Resonance, 2nd edn., Wiley, New York (1983).Google Scholar
  38. 38.
    M. Xiao, I. Martin, E. Yablonovich, and H.W. Jiang, Nature (London) 430, 435 (2004).Google Scholar
  39. 39.
    F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, Phys. Rev. Lett. 92, 076401(4) (2004).Google Scholar
  40. 40.
    D. Rugar, R. Badakian, H.J. Mamin, and B.W. Chui, Nature (Londin) 430, 329 (2004).Google Scholar
  41. 41.
    A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).Google Scholar
  42. 42.
    Y. Kato, R.C. Myers, A.C. Gossard, and D.D. Awschalom, Nature 427, 50 (2004).Google Scholar
  43. 43.
    V.N Golovach, M. Borhani, and D. Loss, www.arXiv.org/con-mat/0601674 (2006).
  44. 44.
    Y. Tokura, W.G. Van der Wiel, T. Obata, and S. Tarucha, Phys. Rev. Lett. 96, 047202 (4) (2006).Google Scholar
  45. 45.
    R. Hanson, L.H. Willems van Beveren, I.T. Vink, J.M. Elzerman, W.J.M. Naber, F.H.L. Koppens, L.P. Kouwenhoven, and L.M.K. Vandersypen, Physica E 34, 1 (2006).Google Scholar
  46. 46.
    J. Nogues, J. Sort, V. Langlais, V. Skumryev, S. Sarinach, J.S. Munoz, M.D. Baro, Phys. Reports 422, 65 (2005).Google Scholar
  47. 47.
    J. Stangl, V. Holý, and G. Bauer, Rev. Mod. Phys. 76, 725 (2004).Google Scholar
  48. 48.
    I.N. Stranski and L. Krastanow, Sitzungsbericht d. Akad. d. Wissenschaften in Wien, Abt. IIb, Band 146, 797 (1937).Google Scholar
  49. 49.
    Q. Xie, A. Madhukar, P. Chen, and N. P. Kobayashi, Phys. Rev. Lett. 75, 2542 (1995).Google Scholar
  50. 50.
    G. Bester, A. Zunger, Z. Wu, and D. Vanderbilt, Phys. Rev. B 74, 081305R (2006).Google Scholar
  51. 51.
    C. B. Murray, C. R. Kagan, and M. G. Bawendi, Annu. Rev. Mater. Sci. 30, 545 (2000).Google Scholar
  52. 52.
    J. E. Bowen Katari, V. L. Colvin, and A. P. Alivisatos, J. Phys. Chem. 98, 4109 (1994).Google Scholar
  53. 53.
    O. I. Mićić and A. J. Nozik, J. Lumin. 70, 95 (1996).Google Scholar
  54. 54.
    M. A. Reed, R. T. Bate, K. Bradshaw, W. M. Duncan, W. R. Frensley, J. W. Lee, and H. D. Shih, J. Vac. Sci. Technol. B 4, 358 (1986).Google Scholar
  55. 55.
    A. B. Fowler, A. Hartstein, and R. A. Webb, Phys. Rev. Lett. 48, 196 (1982); T. J. Thornton, M. Pepper, H. Ahmed, D. Andrews, and G. J. Davies, Phys. Rev. Lett. 56, 1198 (1986).Google Scholar
  56. 56.
    H. Ishikuro and T. Hiramoto, Appl. Phys. Lett. 71, 3691 (1997); A. Aassime, G. Johansson, G. Wendin, R. J. Schoelkopf, and P. Delsing, Phys. Rev. Lett. 86, 3376 (2001).Google Scholar
  57. 57.
    B. E. Kane, N. S. McAlpine, A. S. Dzurak, R. G. Clark, G. J. Milburn, H. B. Sun, and H. Wiseman, Phys. Rev. B 61, 2961 (2000).Google Scholar
  58. 58.
    M. A. Kastner, Rev. Mod. Phys. 64, 849 (1992).Google Scholar
  59. 59.
    K. K. Likharev, Proc. IEEE 87, 606 (1999).Google Scholar
  60. 60.
    L. Guo, E. Leobandung, S. Y. Chou, Science 275, 649 (1997).Google Scholar
  61. 61.
    B. E. Kane, N. S. McAlpine, A. S. Dzurak, R. G. Clark, G. J. Milburn, H. B. Sun, and H. Wiseman, Phys. Rev. B 61, 2961 (2000).Google Scholar
  62. 62.
    S. K. Su, S. J. Chang, L. W. Ji, C. S. Chang, L. W. Wu, W. C. Lai, T. H. Fang, and K. T. Lam, Semicond. Sci. Technol. 19, 389 (2003); D. Damilano, N. Grandjean, J. Massies, S. Dalmasso, J. L. Reverchon, M. Calligaro, J. Y. Duboz, L. Siozade, and J. Leymarie, Phys. Stat. Sol. A 180, 363 (2000).Google Scholar
  63. 63.
    M. Shamsa, W. Liu, A. A. Balandin, and J. Liu, Appl. Phys. Lett. 87, 202105 (2005).Google Scholar
  64. 64.
    T. C. Harmon, R. E. Reeder, M. P. Walsh, B. E. LaForge, C. D. Hoyt, and G. W. Turner, Appl. Phys. Lett. 88, 243504 (2006).Google Scholar
  65. 65.
    J. M. Zide, D. O. Klenov, S. Stemmer, A. C. Gossard, G. Zeng, J. E. Bowers, D. Vashaee, and A. Shakouri, Appl. Phys. Lett. 87, 1121102 (2005).Google Scholar
  66. 66.
    J.R. Chelikowsky, J. Phys. D 33, R33 (2000).Google Scholar
  67. 67.
    Y. Alhassid, Rev. Mod. Phys. 72, 895 (2000).Google Scholar
  68. 68.
    D.L. Smith and C. Mailhiot, Rev. Mod. Phys. 62, 173 (1990).Google Scholar
  69. 69.
    E. Landsberg (ed). Quantum Theory of Real Materials, Kluwer, Boston, MA (1996).Google Scholar
  70. 70.
    A.J. Freeman, Ann. Rev. Mat. Sci. 25, 1 (1995).Google Scholar
  71. 71.
    N.M. Ashkroft and N.D. Mermin, Solid State Physics, Holt, Rinehart&Winston, New York (1976).Google Scholar
  72. 72.
    E.L. Ivchenko and G.E. Pikus, Superlattices and Other Heterostructures, 2nd edn., Springer-Verlag, Berlin, New York (1997).Google Scholar
  73. 73.
    J.M. Tang and M.E. Flatte, Phys.Rev. Lett. 92, 047201 (2004).Google Scholar
  74. 74.
  75. 75.
  76. 76.
  77. 77.
    F. Meier, J. Levy, and D. Loss, Phys. Rev. B 68, 134417 (15) (2003).Google Scholar
  78. 78.
    V.W. Scrola and S. Das Sarma, Phys. Rev. A 71, 032340 (12) (2005).Google Scholar
  79. 79.
    A. Mizel and D.A. Lidar, Phys. Rev. B 70, 115310 (13) (2004).Google Scholar
  80. 80.
    F. Meier, V. Carletti, O. Gywat, D. Loss, and D.D. Awschalom, Phys. Rev. B 69, 195315 (12) (2004).Google Scholar
  81. 81.
    J. Lehmann and D. Loss, Phys. Rev. B 73, 045328 (10) (2006).Google Scholar
  82. 82.
    G.D. Mahan, Many Particles Physics, 2nd edn, Plenum, New York (1993).Google Scholar
  83. 83.
    C.W. Miller, Z.-P. Li, I.K. Schuller, R.W. Dave, J.M. Slaughter, and J. Akerman, Phys. Rev. B 74, 212404 (4) (2006).Google Scholar
  84. 84.
    B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, Reading, MA (1972).Google Scholar
  85. 85.
    M.I. Dykman, L.F. Santos, and M. Shapiro, J. Optics B 7, Special Issue SI, S363 (2005).Google Scholar
  86. 86.
    J. Rammer, Rev. Mod. Phys. 63, 781 (1991), and references therein.Google Scholar
  87. 87.
    S. Fujita, Introduction to Non-Equilibrium Quantum Statistical Mechanics, W.B. Saunders, Philadelphia (1986), etc.Google Scholar
  88. 88.
    S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University, Cambridge, England (1995).Google Scholar
  89. 89.
    D.K. Ferry and S.M. Goodnick, Transport in Nanostructures, Cambridge University, Cambridge, England (1997).Google Scholar
  90. 90.
    Y. Imry and R. Landauer, Rev. Mod. Phys. 71, S306 (1999).Google Scholar
  91. 91.
    C.W.J. Beenakker, Phys. Rev. B 44, 1646 (1991).Google Scholar
  92. 92.
    Y. Imry, Directions in Condensed Matter Physics, Vol. 1, World Scientific, Singapore (1986).Google Scholar
  93. 93.
    Mesoscopic Phenomena in Solids, B.L. Altshuler, P.A. Lee and R.A. Webb (eds). North-Holland, Amsterdam (1991).Google Scholar
  94. 94.
    Y. Meir and N.S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992).Google Scholar
  95. 95.
    D.V. Averin and K.K. Likharev, Phys. Rev. B 44, 6199 (1991).Google Scholar
  96. 96.
    Nanotechnology, G. Timp (ed.), AIP, New York (1998).Google Scholar
  97. 97.
    C.W.J. Beenakker, Phys. Rev. B 44, 1646 (1991).Google Scholar
  98. 98.
    S.N. Datta, J. Phys. Chem. A 109, 11417 (2005).Google Scholar
  99. 99.
    D.V. Averin and Yu. N. Nazarov, Phys. Rev. Lett. 65, 2446 (1990); L.I. Glazman and K.A. Matveev, JETP Lett. 51, 484 (1990).Google Scholar
  100. 100.
    A. Wacker, Phys. Reports 357, 1 (2002)Google Scholar
  101. 101.
    G.B. Arnold, J. Low Temp. Phys. 68, 1 (1987).Google Scholar
  102. 102.
    R.A. Jalabert, A.D. Stone, and Y. Alhassid, Phys. Rev. Lett. 68, 3468 (1992); J.C. Cuevas, A. Martin-Rodero, and A.L. Yeyati, Phys. Rev. B 54, 7366 (1996).Google Scholar
  103. 103.
    Y. Alhassid, Rev. Mod. Phys. 72, 895 (2000).Google Scholar
  104. 104.
    Y.V. Fyodorov and H.J. Sommers, J. Math. Phys. 38, 1918 (1997).Google Scholar
  105. 105.
    O. Bohigas and M.-J. Giannoni, Mathematical and Computational methods in Nuclear Physics. Lecture Notes in Physics, Vol. 209, J.S. Dehesa, J.M.G. Gomez, and A. Polls (eds). Springer, Berlin (1984).Google Scholar
  106. 106.
    B.L. Altshuler, D.E. Khmelnitskii, A.I. Larkin, and P.A. Lee, Phys. Rev. B 22, 5142 (1980).Google Scholar
  107. 107.
    P.A. Lee and A.D. Stone, Phys. Rev. Lett. 55, 1622 (1985); E.A. Yuzbashyan, W. Happer, B.L. Altshuler, and S.B. Shastry, J. Phys. A 36, 2577 (2003).Google Scholar
  108. 108.
    K.B. Efetov, Adv. Phys. 32, 53 (1983).Google Scholar
  109. 109.
    T.N. Todorov, J. Phys: Condens. Matter. 12, 8995 (2000); M. Buttiker, Pramana J. Phys. 58, 241 (2002); M. Brandbyge, J. Taylor, K. Stokbro, J.-L Moroz, and P. Ordejon, Phys. Rev. B 65, 165401 (2002).Google Scholar
  110. 110.
    M. Buttiker, Phys. Rev. B 33, 3020 (1986); J.L. D’Amato and H. Pastawski, Phys. Rev. B 41, 7411 (1990).Google Scholar
  111. 111.
    H. van Hauten, C.W.J. Beenakker, and A.A.M. Starring, in: Single Electron Tunneling, H. Grabert, M.H. Devoret (Eds.), Plenum Press, New York, 167 (1991).Google Scholar
  112. 112.
    E.V. Sukhorukov and D. Loss, Phys. Rev. B 59, 13054 (1999); B. Qiao, H.E. Ruda, and M.S. Zhan, Phys. Rev. A 65, 042325(11) (2002); X.-Q. Li, W.-K. Zhang, P. Cui, J. Shao, Z. Ma, and Y. Yan, Phys. Rev. B 69, 085315(9) (2004); H. Moya-Cessa, Phys. Reports 432, 1 (2006).Google Scholar
  113. 113.
    B. Qiao, X.S. Xing, and H.E. Ruda, Physica A 355, 319 (2005); B. Qiao and H.E. Ruda, Physica A 334, 459 (2004); B. Qiao and H.E. Ruda, Physica A 333, 197 (2004); B. Qiao and H.E. Ruda, Physica A 327, 425 (2003).Google Scholar
  114. 114.
    E.N. Economou, Green’s Functions in Quantum Physics, Springer, Berlin (1983), and references therein; possible simplifications of some of these methods and their use are discussed in S. Mukamel, Phys. Rev. E 68, 021111(14) (2003).Google Scholar
  115. 115.
    I. G. Lang, L. I. Korovin, J. A. de la Cruz and S. T. Pavlov, Sov. Phys.–JETP 96, 268 (2003).Google Scholar
  116. 116.
    H.U. Baranger and A.D. Stone, Phys. Rev. B 40, 8169 (1989).Google Scholar
  117. 117.
    L.A. Pozhar, cond-mat/0502476, http://www.arXiv.org (2005); L.A. Pozhar, Mat. Res. Soc. Proc. 789, 49 (2004); L.A. Pozhar, Mater. Res. Soc. Proc. 900E, O03-02.1 (2006); L.A. Pozhar, Mat. Res. Soc. Proc. 789, 49 (2004).
  118. 118.
    Note that these interactions have also been neglected in [115]. This makes the approach developed in [115] not applicable to systems in strong magnetic fields and to systems with significant magnetization, despite an inclusion of the corresponding vector potential term into the particle momentum operator in [115].Google Scholar
  119. 119.
    A. I. Akhieser and S. V. Peletminskii, Methods of Statistical Physics, Nauka, Moscow (1977).Google Scholar
  120. 120.
    D. N. Zubarev, Soviet Phys. Uspekhi 3, 320 (1960/61); D.N. Zubarev, Nonlinear Statistical Thermodynamics, Plenum Press, New York (1974).Google Scholar
  121. 121.
    P. P. Ewald, Ann. de Phys. 54, 519 (1917); P. P. Ewald, Ann. de Phys. 66, 253 (1921); V. M. Agranovich and V. L. Ginzburg, Optical Properties of Crystalline Solids, Space Dispersion and the Theory of Excitons, Glavnaya Redaktsiya Fiz-Mat. Literatury, Moscow, (1965) (in Russian); Yu. L. Klimontovich, Statistical Theory of Non-Equilibrium Processes in Plasma, Glavnaya Redaktsiya Fiz-Mat. Literatury, Moscow, (1964) (in Russian).Google Scholar
  122. 122.
    D. N. Zubarev and Yu. A. Tserkovnikov, Trudy Matematicheskogo Instituta im. Steklova 175, 139 (1986); Proceedings of the Steklov Institute of Mathematics 2, 139 (1988), and references therein.Google Scholar
  123. 123.
    S. V. Tyablikov, Methods in the Quantum Theory of Magnetism, Plenum Press, New York (1967); N. N. Bogolyubov, Introduction to Quantum Statistical Mechanics, World Scientific, NJ, (1982); N. N. Bogolyubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, General Principles of Quantum Field Theory, Nauka, Moscow (1987); N.N. Bogolubov, Selected Works, N. N. Bogolubov, Jr. and A. M. Kurbatov (Eds.), Gordon and Breach, New York (1991).Google Scholar
  124. 124.
    Yu. A. Tserkovnikov, Dokl. Acad. Nauk SSSR 143, 832 (1962); Soviet Phys. Dokl. 7, (1962/1963); G. F. Mazenko, Phys. Rev. A 7, 209 (1973); 7, 222 (1973); 9, 360 (1974).Google Scholar
  125. 125.
    Yu. A. Tserkovnikov, Teoreticheskaya I Matematicheskaya Fizika, 7, 250 (1971); English translation in Theor. Math. Phys. 7 (1971); 23, 221 (1975); English translation in Theor. Math. Phys. 23 (1975); 26, 77 (1976); English translation in Theor. Math. Phys. 26 (1976); 50, 261 (1982); English translation in Theor. Math. Phys. 50 (1982); 52, 147 (1982); English translation in Theor. Math. Phys. 52 (1982); N.N. Bogolyubov, V.V. Tolmachev, and D.V. Shirkov, New Methods in the Theory of Superconductivity, Chapman and Hall, London (1959); N.M. Plakida, in Statistical Physics and Quantum Field Theory, N.N. Bogolyubov (Ed.), Nauka, Moscow, p. 205 (1973), etc.Google Scholar
  126. 126.
    L.A. Pozhar, V.F. de Almeida, and M.Z.-C. Hu, Ceramics Transactions 137, 101 (2003); L.A. Pozhar, E.V. Kontar, and M. Z.-C. Hu, J. Nanosci. Nanotech. 2, 209 (2002); L.A. Pozhar, Phys. Rev. E 61, 1432 (2000); L.A. Pozhar and K.E. Gubbins, Int. J. Thermophys. 20, 805 (1999); L.A. Pozhar and K.E. Gubbins, Phys. Rev . E 56, 5367 (1997); E. Akhmatskaya, B.D. Todd, P.J. Daivis, D.L. Evans, K.E. Gubbins, L.A. Pozhar, J. Chem. Phys. 106, 4684 (1997); J.K. Percus, L.A. Pozhar, and K.E. Gubbins, Phys. Rev . E 51, 261 (1995); L.A. Pozhar and K.E. Gubbins, J. Chem. Phys. 99, 8970 (1993), etc. [Wider list of relevant publications is available on http://bama.ua.edu/lpozhar].Google Scholar
  127. 127.
    A.K. Singh et al., Phys. Rev. Lett. 91, 146802 (2003); V. Kumar and Y. Kawazoe, Phys. Rev. Lett. 90, 055502 (2003), etc.Google Scholar
  128. 128.
    P.S. Fodor, G.M. Tsoi, and L.E. Wenger, J. Appl. Phys. 91, 8186 (2002).Google Scholar
  129. 129.
    These and other aspects of such virtual synthesis of small artificial molecules with predesigned electronic properties are a subject of intensive research, and have been discussed in numerous publications, including L.A. Pozhar, A.T. Yeates, F. Szmulowicz and W.C. Mitchel, Phys. Rev. B 74, 085306 (2006); J. Virtual Nanoscale Sci. Technol. 14, No. 8 (2006): http://www.vjnano.org; L.A. Pozhar, A.T. Yeates, F. Szmulowicz and W.C. Mitchel, EuroPhys. Lett. 71, 380 (2005); Mat. Res. Soc. Proc. 829, 49 (2005), etc.
  130. 130.
    M.W. Schmidt et al., J. Comput. Chem. 14, 1347 (1993).Google Scholar
  131. 131.
    G.W. Bryant and W. Jaskolski, Mat. Res. Soc. Proc. 789, N13.2 (2004).Google Scholar
  132. 132.
    L.A. Pozhar and G. Brown, Mater. Res. Soc. Proc. 957, 0957-K10-04 (2007); L.A. Pozhar, G. Brown and W.C. Mitchel, Mater. Res. Soc. Proc. 959E, 0959-M05-02 (2007); L.A. Pozhar, A.T. Yeates, F. Szmulowicz and W.C. Mitchel, Mater. Res. Soc. Proc . 891, EE02-04.1 (2006); Ibid., 906E, HH01-05.1 (2006).Google Scholar
  133. 133.
    E.F. Archibong, A. St-Amant, S.K. Goh, and D.S. Marynick, Chem.Phys. Lett. 361, 411 (2002); S. Katircioğlu and H. Kökten, J. Mol. Struct.: Theochem 712, 67 (2004); E.-L. Li, X.-M. Luo, W. Shi, and X.-W. Wang, J. Mol. Struct.: Theochem 723, 79 (2005).Google Scholar
  134. 134.
    A.I. Boldyrev and L.-S. Wang, J. Phys. Chem. A 105, 10759 (2001).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of IdahoMoscowUSA
  2. 2.Air Force Research Laboratory, Materials and Manufacturing DirectorateWright-Patterson Air Force BaseUSA

Personalised recommendations

Cite chapter

Buy options