Abstract
In this introductory chapter several basic concepts, relevant for mesoscopic electron transport, will be described. The aim is to provide a basis for several of the following Chapters of this volume. We, therefore, describe in the first Section various aspects of electron quantum transport in twodimensional electron gases. This includes an estimate of typical material parameters as well as comments on the fabrication. We then describe the quantization of the conductance in point contacts and the edge state picture of the Quantum Hall effect. In the second Section we describe the theory of single—electron tunneling in systems with strong charging and Coulomb-blockade effects. Here we restrict ourselves to the simplest case where low order perturbation theory is sufficient. We first discuss metallic low-capacitance junction systems and then indicate the relevant extensions when dealing with transport through quantum dots with discrete levels. Many further, equally important aspects of mesoscopic transport can not be covered here. Examples are interference and weak localization effects, level statistics or the many body description of solids. Fortunately, some of those will be covered in the more specialized Chapter of this volume.
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References
Molecular Beam Epitaxy: Fundamentals and Current Status, M. A. Herman and H. Sitter, Springer-Verlag, NY (1985); Molecular Beam Epitaxy: The Technology and Physics of Molecular Beam Epitaxy, ed. E. H. C. Parker, Plenum Press, NY (1985).
H. van Houten, B. J. van Wees, M. G. J. Heijman, and J. P. Andre, Appl. Phys. Lett. 49, 1781 (1986).
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. B 34, 5635 (1986).
S. E. Laux, D. J. Frank, and F. Stern, Surf. Sci. 196, 101 (1988).
H. Ehrenreich and D. Turnbull, eds., Solid State Physics (Academic Press, New York, 1991).
Yu. V. Sharvin, Zh. Eksp. Teor. Fiz. 48, 984 (1965) [Sov. Phys. JETP 21, 655 (1965)].
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).
B. J. van Wees, L. P. Kouwenhoven, E. M. M. Willems, C. J. P. M. Harmans, J. E. Mooij, H. van Houten, J. G. Williamson, and C. T. Foxon, Phys. Rev. B 43, 12431 (1991).
L. I. Glazman, G. B. Lesovik, Khmel’nitskli, and R. I. Shekter, JETP Lett 48, 238 (1988)
L. I. Glazman, and A. V. Khaetskii, J. Phys. : Condens. Matter 1, 5005 (1989).
K. F. Berggren, T. J. Thornton, D. J. Newson, and M. Pepper, Phys. Rev. Lett. 57, 1769 (1986).
R. Landauer, IBM J. Res. Dev. 1, 223 (1957)
R. Landauer, Phys. Lett. 85A, 91 (1981);
R. Landauer, J. Phvs. Condens. Matter 1 8099 (1989).
A. Szafer and A. D. Stone, Phys. Rev. Lett. 62, 300 (1989)
E. G. Haanappel and D. van der Marel, Phys. Rev. B 39, 5484 (1989)
G. Kirczenow, Phys. Rev. B 39, 10452 (1989).
Several authors have obtained transmission resonances in the calculated conductance of narrow constrictions, see Ref. [13].
J. Nixon and J. Davies, Phys. Rev. B 41, 7929 (1990).
J. G. Williamson, C. E. Timmering, C. J. P. M. Harmans, J. J. Harris, and C. T. Foxon. Phvs. Rev. B 42, 7675 (1990).
B. I. Halperin, Phys. Rev. B 25, 2185 (1982).
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. B 38, 3625 (1988).
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 39, 8040 (1989).
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)
H. van Houten et al., Phys. Rev. B 39. 8556 (1989).
M. Büttiker, Phys. Rev. Lett. 57, 1761, (1986).
J. Spector, H. L. Stormer, K. W. Baldwin, L. N. Pfeiffer, and K. W. West, Surf. Sci. 228, 283 (1990).
P. Streda, J. Kucera, and A. H. MacDonald, Phys. Rev. Lett. 59, 1973 (1987).
J. K. Jain and S. A. Kivelson, Phys. Rev. Lett. 60, 1542 (1988).
M. Büttiker, Phys. Rev. B 38, 9375 (1988).
M. Reed, ed. , Semiconductors and Sernirnetals (Academic Press, New York, 1990).
B. J. van Wees, E. M. M. Willems, C. J. P. M. Harmans, C. W. J. Beenakker, H. van Houten, J. G. Williamson, C. T. Foxon, and J. J. Harris, Phys. Rev. Lett. 62, 1181 (1989).
G. Muiller, D. Weiss, S. Koch, K. von Klitzing, H. Nickel, W. Schlapp, and R. Lösch, Phys. Rev. B 42, 7633 (1990).
S. Komiyama, H. Hirai, S. Sasa, and S. Hiyamizu, Phys. Rev. B 40, 12566 (1989).
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 39, 8066 (1989).
B. W. Alphenaar, P. L. McEuen, R. G. Wheeler, and R. N. Sacks, Phys. Rev. Lett. 64, 677 (1990).
P. L. McEuen, A. Szafer, C. A. Richter, B. W. Alphenaar, J. K. Jain, A. D. Stone, R. G. Wheeler, and R. N. Sacks. Phvs. Rev. Lett. 64. 2062 (1990).
For a review see T. Chakraborty and P. Pietiläinen, The fractional quantum Hall effect, Springer series in Solid-State Sciences 85 (Springer-Verlag 1988).
For a review see S. C. Zhang Int. J. of Mod Phys B 6 25 (1992)
S. L. Sondhi, A. Karlhede, S. A. Kivelson, and E. H. Rezayi, Phys. Rev. B 47, 16419 (1993)
H. A. Fertig, L. Brey, R. Cote, and A. H. MacDonald, Phys. Rev. B 50, 11018 (1994).
S. E. Barrett, G. Dabbagh, L. N. Pfeiffer, K. W. West, and R. Tycko, Phys. Rev. Lett. 74 5112 (1995).
L. P. Kouwenhoven, unpublished.
G. Timp, R. Behringer, J. E. Cunningham, R. E. Howard, Phys. Rev. Lett. 63, 2268 (1989).
L. P. Kouwenhoven, B. J. van Wees, N. C. van der Vaart, C. J. P. M. Harmans
C. E. Timmering, and C. T. Foxon, Phys. Rev. Lett 64, 685 (1990).
A. M. Chang and J. E. Cunningham, Phys. Rev. Lett. 69, 2114 (1992).
C. W. J. Beenakker, Phys. Rev. Lett. 64. 216 (1990).
A. H. MacDonald Phys. Rev. Lett. 64, 220 (1990).
A. M. Chang, Solid State Commun. 74, 871 (1990).
P. L. McEuen, E. B. Foxman, J. Kinaret, U. Meirav, M. A. Kastner, N. S. Wingreen, and S. J. Wind, Phys. Rev B 45, 11419 (1992)
D. B. Chklovskii, B. I. Shklovskii, and L. I. Glazman, Phys. Rev. B 46, 4026 (1992).
I. O. Kulik and R. I. Shekhter, Zh. Eksp. Teor. Fiz. 68, 623 (1975) [Sov. Phys. JETP 41, 308 (1975)].
D. V. Averin and K. K. Likharev, J. Low Temp. Phys. 62, 345 (1986)
D. V. Averin and K. K. Likharev, in Mesoscopic Phenomena in Solids, B. L. Altshuler, P. A. Lee and R. A. Webb, eds. , p. 173 (Elsevier, Amsterdam, 1991).
T. A. Fulton and G. J. Dolan, Phys. Rev. Lett. 59, 109 (1987).
L. J. Geerligs et al., Phys. Rev. Lett. 64, 2691 (1990).
H. Pothier et al., Physica B 169, 573 (1991)
H. Pothier et al., Europhys. Lett. 17, 249 (1992)
Single Charge Tunneling, NATO ASI Series, Vol. B 294, eds. H. Grabert and M. H. Devoret, (New York, Plenum Press 1992).
Mesoscopic Superconductivity, Proceedings of the NATO ARW, edited by F. W. J. Hekking. G. Schön. and D. V. Averin. Physica B 203 (1994).
G. Schön and A. D. Zaikin, Phys. Rep. 198, 237 (1990).
L. I. Glazman and K. A. Matveev, Sov. Phys. JETP. 71, 1031 (1990)
K. A. Matveev, Sov. Phvs. JETP 72. 892 (1991).
J. König, H. Schoeller, G. Schön, and R. Fazio, in Quantum Dynamics of Submicron Structures, NATO ASI Series B 291, edited by H. Cerdeira et al. (Kluwer 1995), p. 221
J. König, H. Schoeller, and G. Schön, Europhvs. Letters 31. 31 (1995).
K. Mullen, E. Ben-Jacob, R. C. Jaklevic, and Z. Schuss, Phys. Rev. B 37, 98 (1988).
J. König H. Schoeller and G. Schön, Phys. Rev. Lett. 78, 4482 (1997).
P. Joyez, V. Bouchiat, D. Estève, C. Urbina, and M. H. Devoret, preprint.
D. V. Averin and A. N. Korotkov, Zh. Eksp. Teor. Fiz. 97, 1661 (1990) [Sov. Phys. JETP 70, 937 (1990)]
D. V. Averin, A. N. Korotkov, and K. K. Likharev, Phys. Rev. B 44, 6199 (1991).
C. W. J. Beenakker, Phys. Rev. B 44, 1646 (1991).
Y. Meir, N. S. Wingreen, and P. A. Lee, Phys. Rev. Lett. 66. 3048 (1991).
H. van Houten, C. W. J. Beenakker, and A. A. M. Staring, in Ref. (50].
D. Weinmann, W. Häusler, W. Pfaff, B. Kramer, and U. Weiss, Europhys. Lett. 26, 467 (1994)
D. Weinmann et al Phys. Rev. Lett. 74, 984 (1995).
K. Jauregui, W. Häusler, D. Weinmann, and B. Kramer, Phys. Rev. B 53 R1713 (1996).
D. Pfannkuche and S. E. Ulloa, Phys. Rev. Lett. 74 1194 (1995).
R. H. Blick, R. J. Haug, J. Weis, D. Pfannkuche, K. von Klitzing, and K. Eberl, Phys. Rev. B 53, 7899 (1996) .
G. Klimeck, G. Chen, and S. Datta, Phys. Rev. B 50, 2316 (1994)
G. Klimeck, G. Chen, and S. Datta, Phys. Rev. B 50, 8035 (1994).
L.P. Kouwenhoven, S. Jauhar, K. McCormick, D. Dixon, P.L. McEuen, Yu.V. Nazarov. N. C. van der Vaart and C. T. Foxon Phys Rev B 50 2019 (1994)
I. A. Devvatov and K. K. Likharev Physica B 194–196 1341 (1994)
C. Bruder and H. Schoeller, Phys. Rev. Lett. 72, 1076 (1994).
G. Ingold and Yu. V. Nazarov, in Ref. [501].
A. A. Odintsov, G. Falci, and G. Schön, Phys. Rev. B 44, 13089 (1991).
K. Flensberg, S. M. Girvin, M. Jonson, D. R. Penn, and M. D. Stiies, Phys. Scripta T 42, 189 (1992).
D. Pfannkuche, V. Gudmundssnn, and P. A Makcvm Phys Rev R 47 2244 (1993)
W. Häusler, Ann. Physik 5, 401 (1996).
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Kouwenhoven, L.P., Schön, G., Sohn, L.L. (1997). Introduction to Mesoscopic Electron Transport. In: Sohn, L.L., Kouwenhoven, L.P., Schön, G. (eds) Mesoscopic Electron Transport. NATO ASI Series, vol 345. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8839-3_1
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