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Electron Conductance and Lifetimes in a Ballistic Electron Waveguide

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Abstract

Ballistic electron waveguides are open quantum systems that can be formed at very low temperatures at a GaAs/AlGaAs interface. Dissipation due to electron–phonon and electron–electron interactions in these systems is negligible. Although the electrons only interact with the walls of the waveguide, they can have a complicated spectrum including both positive energy bound states and quasibound states which appear as complex energy poles of the scattering S-matrix or energy Green's function. The quasibound states can give rise to zeros in the waveguide conductance as the energy of the electrons is varied. The width of the conduction zeros is determined by the lifetimes of the quasibound states. The “complex energy spectrum” associated with the quasibound states also governs the survival probability of electrons placed in the waveguide cavities.

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REFERENCES

  1. C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Phys. Rev. Lett. 69:506 (1992).

    Google Scholar 

  2. M. A. Eriksson, R. G. Beck, M. Topinka, J. A. Katine, R. M. Westervelt, K. L. Campman, and A. C. Gossard, Appl. Phys. Lett. 69:671 (1996).

    Google Scholar 

  3. S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1995).

    Google Scholar 

  4. F. Sols and M. Macucci, Phys. Rev. B 41:11887 (1990); J. Martorell, S. Klarsfeld, D. W. L. Sprung and H. Wu, Solid State Commun. 78:13 (1991); H. Wu, D. W. L. Sprung, and J. Martorell, Phys. Rev. B 45:11960 (1992); Y. B. Gaididei and O. O. Vakhnenko, J. Phys. Condens. Matter 6:3229 (1994); C.-K. Wang and K.-F. Berggren, and Z.-l. Ji, J. Appl. Phys. 77:2564 (1995); K. Lin and R. L. Jaffe, Phys. Rev. B 54:5750 (1996).

    Google Scholar 

  5. K. Vacek, A. Okiji, and H. Kasai, Phys. Rev. B 47:3695 (1993); K. Vacek, H. Kasai, and A. Okiji, J. Phys. Soc. Japan 61:27 (1992).

    Google Scholar 

  6. A. Okiji, H. Kasai, and A. Nakamura, Prog. Theor. Phys. Suppl. 106:209 (1991).

    Google Scholar 

  7. K.-F. Berggren and Z.-L. Ji, Phys. Rev. B 43:4760 (1991).

    Google Scholar 

  8. T. Itoh, N. Sano, and A. Yoshii, Phys. Rev. B 45:14131 (1992).

    Google Scholar 

  9. C. S. Lent, Appl. Phys. Lett. 57:1678 (1990).

    Google Scholar 

  10. Y. Avishai and Y. B. Band, Phys. Rev. B 41:3253 (1990); Y. Avishai, M. Kaveh, and Y. B. Band, Phys. Rev. B 42:5867 (1990); H. U. Baranger, Phys. Rev. B 42:11479 (1990); H. Ishio and K. Nakamura, J. Phys. Soc. Japan 61:2649 (1992); I. Y. Popov, S. L. Popova, Phys. Lett. A 173:484 (1993); P. Exner, P. Seba, M. Tater, and D. Vanek, J. Math. Phys. 37:4867 (1996).

    Google Scholar 

  11. C. S. Lent and S. Sivaprakasam, Proc. Int. Soc. Opt. Eng. SPIE 1284:31 (1990).

    Google Scholar 

  12. R. Landauer, Phil. Mag. 21:863 (1970); R. Landauer, J. Phys. Condens. Matter 1:8099 (1989); M. Buttiker, Phys. Rev. Lett. 57:1761 (1986).

    Google Scholar 

  13. R. Kubo, Can. J. Phys. 34:1274 (1956).

    Google Scholar 

  14. D. S. Fisher and P. A. Lee, Phys. Rev. B 23:6851 (1981).

    Google Scholar 

  15. H. U. Baranger and A. D. Stone, Phys. Rev. B 40:8169 (1989).

    Google Scholar 

  16. G. Garcia-Calderon, A. Rubio, and R. Romo, J. Appl. Phys. 69:3612 (1991).

    Google Scholar 

  17. F. R. Frohne, M. J. McLennan, and S. Datta, J. Appl. Phys. 66:2699 (1989).

    Google Scholar 

  18. C. M. Marcus, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Chaos 3:643 (1993).

    Google Scholar 

  19. K. Nakazato and R. J. Blaikie, J. Phys. Condens. Matter 3:5729 (1991).

    Google Scholar 

  20. P. F. Bagwell, Phys. Rev. B 41:10354 (1990).

    Google Scholar 

  21. P. F. Bagwell and R. K. Lake, Phys. Rev. B 46:15329 (1992).

    Google Scholar 

  22. Z. Shao, W. Porod, and C. S. Lent, Phys. Rev. B 49:7453 (1994).

    Google Scholar 

  23. U. Fano, Phys. Rev. 124:1866 (1961).

    Google Scholar 

  24. F. Schwabl, Quantum Mechanics (Springer, New York, 1992).

    Google Scholar 

  25. P. J. Price, Appl. Phys. Lett. 62:289 (1993); P. J. Price, Phys. Rev. B 48:17301 (1993).

    Google Scholar 

  26. W. Porod, Z. Shao, and C. S. Lent, Appl. Phys. Lett. 61:1350 (1992).

    Google Scholar 

  27. R. L. Schult, D. G. Ravenhall, and H. W. Wyld, Phys. Rev. B 39:5476 (1989).

    Google Scholar 

  28. M. Andrews and C. M. Savage, Phys. Rev. A 50:4535 (1994); W. Bulla, F. Gesztesy, W. Renger, and B. Simon, Proc. AMS 125:1487 (1997).

    Google Scholar 

  29. J. Goldstone and R. L. Jaffe, Phys. Rev. B 45:14100 (1992); J. P. Carini, J. T. Londergan, K. Mullen, and D. P. Murdock, Phys. Rev. B 46:15538 (1992); 48 4503 (1993); J. P. Carini, J. T. Londergan, D. P. Murdock, D. Trinkle, and C. S. Yung, Phys. Rev. B 55:9842 (1997); J. P. Carini, J. T. Londergan, D. P. Murdock, Phys. Rev. B 55:9852 (1997); P. Exner and P. Seba, J. Math. Phys. 30:2574 (1989).

    Google Scholar 

  30. P. Duclos, P. Exner, and P. Stovicek, Ann, Inst. H. Poincare 62:81 (1995).

    Google Scholar 

  31. E. N. Economou, Green's Functions in Mathematical Physics, (Springer-Verlag, Berlin, 1983).

    Google Scholar 

  32. S. Cocke and L. E. Reichl, Phys. Rev. A 52:4515 (1995).

    Google Scholar 

  33. M. Buttiker, Phys. Rev. B 27:6178 (1983).

    Google Scholar 

  34. G. Iannaccone, Phys. Rev. B 51:4727 (1995); G. Iannaccone and G. Pellegrini, Phys. Rev. B 53:2020 (1996).

    Google Scholar 

  35. T. R. Ravuri, V. A. Mandelshtam, and H. S. Taylor, Superlattices and Microstructures 20:87 (1996).

    Google Scholar 

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Authors and Affiliations

  1. Center for Studies in Statistical Mechanics and Complex Systems, University of Texas at Austin, Austin, Texas, 78712

    Kyungsun Na & L. E. Reichl

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  1. Kyungsun Na
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  2. L. E. Reichl
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Na, K., Reichl, L.E. Electron Conductance and Lifetimes in a Ballistic Electron Waveguide. Journal of Statistical Physics 92, 519–542 (1998). https://doi.org/10.1023/A:1023032420009

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  • DOI: https://doi.org/10.1023/A:1023032420009

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