Abstract
Theory and experiment are reviewed of the classical and quantum mechanical focusing by a magnetic field of ballistic electrons injected through a point contact in a two-dimensional electron gas. Two alternative points of view are emphasized. On the one hand, the experiment is a realization of electron optics in the solid state. The three basic building blocks are a coherent and monochromatic point source/detector, an electrostatic mirror with little diffuse scattering, and a magnetic lens. On the other hand, coherent electron focusing is a resistance measurement in the quantum ballistic transport regime, which exhibits the characteristic features of this regime in a most extreme way. For example, large magnetoresistance oscillations occur (up to 95% amplitude modulation is observed), with a periodicity which is non-locally determined by the separation between current and voltage point contacts. A WKB calculation of the transmission probabilities shows that this effect is the result of the interference of coherently excited magnetic edge states at the electron gas boundary. Another example is the absence of local equilibirium: The measurements show that the point contacts can selectively populate (and detect) specific Landau levels, and that this highly non-equilibrium population is maintained over distances of microns.
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References
yu. V. Sharvin, Zh.Eksp.Teor. Fiz. 48, 984 (1965) [Sov. Phys. JETP 21, 655 (1965)]
V. S. Tsoi, Pis'ma Zh. Exp.Teor. Fiz. 19, 114 (1974) [JETP Lett. 19, 70 (1974)].
P. C. van Son, H. van Kempen, and P. Wyder, Phys. Rev. Lett. 58, 1567 (1987)
Physics and Technology of Submicron Structures, ed. by H. Heinrich, G. Bauer, and F. Kuchar (Springer, Berlin 1988); Nanostructure Physics and Fabrication, ed. be M. Reed and W. P. Kirk (Academic Press, New York, to be published)
H. van Houten, B. J. van Wees, J. E. Mooij, C. W. J. Beenakker, J. G. Williamson, and C. T. Foxon, Europhys. Lett. 5, 721 (1988).
C. W. J. Beenakker, H. van Houten, and B. J. van Wees, Europhys. Lett. 7, 359 (1988).
B. J. van Wees, E. M. M. Willems, C. J. P. M. Harmans, C. W. J. Beenakker, H. van Houten, J. G. Williamson, C. J. Foxon, and J. J. Harris, Phys. Rev. Lett. 62, 1181 (1989).
H. van Houten, C. W. J. Beenakker, J. G. Williamson, M. E. I. Broekaart, P. H. M. van Loosdrecht, B. J. van Wees, J. E. Mooji, C. T. Foxon, and J. J. Harris, Phys. Rev. B (April 15, 1989).
T. J. Thornton, M. Pepper, H. Ahmed, D. Andrews, and G. J. Davies, Phys. Rev. Lett. 56, 1198 (1986); H. Z. Zheng, H. P. Wei, D. C. Tsui, and G. Weimann, Phys. Rev. B34, 5635 (1986).
B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, and C. T. Foxon, Phys. Rev.Lett. 60, 848 (1988)
D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, J. Phys. C21, L209 (1988)
H van Houten and C. W. J. Beenakker, in: Analogies in Optics and Microelectronics, ed. by W. van Haeringen and D. Lenstra (Kluwer, Deventer, to be published)
G. Timp, A. M. Chang, P. Mankiewich, R. Behringer, J. E. Cunningham, T. Y. Chang, and R. E. Howard, Phys. Rev. Lett. 59, 732 (1987); M. L. Roukes, A. Scherer, S. J. Allen, jr., H. G. Craighead, R. M. Ruthen, E. D. Beebe, and J. P. Harbison Phys. Rev. Lett. 59, 3011 (1987); C. J. B. Ford, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, D. C. Peacock, D. A. Ritchie, J. E. F. Frost, and G. A. C. Jones, Phys. Rev. B38, 8518 (1988); G. Timp, in: Mesoscopic Phenomena in Solids, ed. by P. A. Lee, R. A. Webb, and B. L. Al'tshuler (Elsevier, New York, to be published)
G. Timp, H. U. Baranger, P. de Vegvar, J. E. Cunningham, R. E. Howard, R. Behringer, and P. M. Mankiewich, Phys. Rev. Lett. 60, 2081 (1988); Y. Takagaki, K. Gamo, S. Namba, S. Ishida, S. Takaoka, K. Murase, K. Ishibashi, and Y. Aoyagi, Solid State Comm. 68, 1051 (1988)
R. Landauer, IBM J. Res. Dev. 1, 223 (1957); 32, 306 (1988); Z. Phys. B68, 217 (1987)
M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986); IBM J. Res. Dev. 32, 317 (1988); See also: A. D. Stone and A. Szafer, IBM J. Res. Dev. 32, 384 (1988)
P. A. M. Benistant, G. F. A. van de Walle, H. van Kempen, and P. Wyder, Phys. Rev. B3, 690 (1986).
M. Büttiker, Phys. Rev. B38, 12724 (1988)
R. E. Prange and T.-W. Nee, Phys. Rev. 168 779 (1968).
M. S. Khaikin, Adv. Phys. 18, 1 (1969)
A. M. Kosevich and I. M. Lifshitz, Zh. Eksp.Teor. Fiz. 29, 743 (1955) [Sov. Phys. JETP 2, 646 (1956)]
L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford 1987) § 54
A. H. MacDonald and P. Streda, Phys. Rev. B29, 1616 (1984).
B. J. van Wees, L. P. Kouwenhoven, H. van Houten, C. W. J. Beenakker, J. E. Mooij, C. T. Foxon, and J. J. Harris, Phys. Rev. B38, 3625 (1988)
M. Büttiker, Phys. Rev. B38, 9375 (1988)
S. Komiyama, H. Hirai, S. Sasa, and S. Hiyamizu (prenprint)
B. J. van Wees, E. M. M. Willems, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. T. Foxon, and J. J. Harris, Phys. Rev. B (April 15, 1989)
P. C. van Son, H. van Kempen, and P. Harris, J. Phys. F17, 1471 (1987)
J. G. Williamson et al. (unpublished)
L. P. Kouwenhoven, B. J. van Wees, C. J. P. M. Harmans, J. G. Williamson, H. van Houten, C. W. J. Beenakker, C. T. Foxon, and J. J. Harris, Phys. Rev B (April 15, 1989).
A. Palevski, M. Heiblum, C. P. Umbach, C. M. Knoedler, A. N. Broers, and R. H. Koch (preprint)
C. W. J. Beenakker and H. van Houten, Phys. Rev. B (to be published)
D. A. Wharam, M. Pepper, H. Ahmed, J. E. F., Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones J. Phys. C21, L87 (1988)
H. U. Baranger and A. D. Stone (preiprint): A. M. Chang and T. Y. Chang (preprint); C. J. B. Ford, S. Washburn, M Büttiker, C. M. Knoedler, and J. M. Hong (preprint)
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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH
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Beenakker, C.W.J., van Houten, H., van Wees, B.J. (1989). Coherent electron focusing. In: Rössler, U. (eds) Festkörperprobleme 29. Advances in Solid State Physics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0108019
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DOI: https://doi.org/10.1007/BFb0108019
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