Abstract
Full Counting Statistics is the theory of quantum statistical properties of transport phenomena. It can be accessed by a modification of the standard Keldysh-Green’s function technique, and is concisely formulated in terms of a circuit theory of mesoscopic electron transport. We summarize the basics of the theoretical methods and discuss two examples: a single-channel quantum contact and a double tunnel junction. For both examples we compare the transport statistics for the cases of normal electrons and Andreev reflection.
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References
Ya. M. Blanter and M. Büttiker, Phys. Rep. 336, 1 (2000).
X. Jehl et al., Phys. Rev. Lett. 83, 1660 (1999); X. Jehl et al., Nature 405, 50 (2000); A. A. Kozhevnikov, R. J. Schoelkopf, and D. E. Prober, Phys. Rev. Lett 83, 1660 (2000); P. Dieleman et al.; Phys. Rev. Lett. 79, 3486 (1997); T. Hoss et al., Phys. Rev. B 62, 4079 (2000).
L. S. Levitov and G. B. Lesovik, JETP Lett. 58, 230 (1993).
L. S. Levitov, H. W. Lee, and G. B. Lesovik, J. Math. Phys. 37, 4845 (1996).
H. Lee, L. S. Levitov, and A. Yu. Yakovets, Phys. Rev. B 51, 4079 (1996).
Yu. V. Nazarov, Ann. Phys. (Leipzig) 8, SI-193 (1999).
W. Belzig and Yu. V. Nazarov, Phys. Rev. Lett. 87, 067006 (2001).
W. Belzig and Yu. V. Nazarov, Phys. Rev. Lett. 87, 197006 (2001).
J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986).
Yu. V. Nazarov and M. Kindermann, cond-mat/0107133.
G. Eilenberger, Z. Phys. 214, 195 (1968); A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys. JETP 26, 1200(1968); K. D. Usadel, Phys. Rev. Lett. 25, 507 (1970).
Yu. V. Nazarov, Phys. Rev. Lett. 73, 134 (1994).
Yu. V. Nazarov, Superlattices Microst. 25, 1221 (1999).
Yu. V. Nazarov and D. Bagrets, cond-mat/0112223.
J. Börlin, W. Belzig, and C. Bruder, cond-mat/0201579.
B. A. Muzykantskii and D. E. Khmelnitskii, Phys. Rev. B 50, 3982 (1994).
V. A. Khlus, Sov. Phys. JETP 66, 1243 (1987); M. J. M. de Jong and C. W. J. Beenakker, Phys. Rev. B 49, 16070 (1994); K. E. Nagaev and M. Büttiker, ibid. 63, 081301 (R) (2001).
J. Börlin, Diploma thesis (University of Basel), 2002).
M. J. M. de Jong, Phys. Rev. B 54, 8144 (1996).
F. Taddei and R. Fazio, Phys. Rev. B 65, 075317 (2002).
A. Andreev and A. Kamenev, Phys. Rev. Lett. 85, 1294 (2000); Yu. Makhlin and A. Mirlin, ibid. 87, 276803 (2001); L. S. Levitov, cond-mat/0103617. 172
C. W. J. Beenakker and H. Schomerus, Phys. Rev. Lett. 86, 700 (2001).
M. Kindermann, Yu. V. Nazarov, and C. W. J. Beenakker, Phys. Rev. Lett. 88, 063601 (2002).
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Belzig, W. (2002). Full Counting Statistics of Mesoscopic Electron Transport. In: Kramer, B. (eds) Advances in Solid State Physics. Advances in Solid State Physics, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45618-X_13
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DOI: https://doi.org/10.1007/3-540-45618-X_13
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