Abstract
Two important themes in nanoscale physics in the last two decades are correlations between electrons and mesoscopic fluctuations. Here we review our recent work on the intersection of these two themes. The setting is the Kondo effect, a paradigmatic example of correlated electron physics, in a nanoscale system with mesoscopic fluctuations; in particular, we consider a small quantum dot coupled to a finite reservoir (which itself may be a large quantum dot). We discuss three aspects of this problem. First, in the high-temperature regime, we argue that a Kondo temperature T k which takes into account the mesoscopic fluctuations is a relevant concept: for instance, physical properties are universal functions of T/T k. Secondly, when the temperature is much less than the mean level spacing due to confinement, we characterize a natural cross-over from weak to strong coupling. This strong coupling regime is itself characterized by well-defined single-particle levels, as one can see from a Nozières Fermi-liquid theory argument. Finally, using a mean-field technique, we connect the mesoscopic fluctuations of the quasiparticles in the weak coupling regime to those at strong coupling.
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References
A C Hewson, The Kondo problem to heavy fermions (Cambridge University Press, Cambridge, 1993)
Éric Akkermans and Gilles Montambaux, Mesoscopic physics of electrons and photons (Cambdrige University Press, Cambdrige, 2007)
L P Kouwenhoven, C M Marcus, P L McEuen, S Tarucha, R M Wetervelt and N S Wingreen, in: Mesoscopic electron transport edited by L L Sohn, G Schön and L P Kouwenhoven (Kluwer, Dordrecht, 1997) pp. 105–214
R K Kaul, D Ullmo, S Chandrasekharan and H U Baranger, Europhys. Lett. 71(6), 973 (2005)
J Yoo, S Chandrasekharan, R K Kaul, D Ullmo and H U Baranger, Phys. Rev . B71, 201309(R) (2005)
R K Kaul, G Zaránd, S Chandrasekharan, D Ullmo and H U Baranger, Phys. Rev . Lett. 96, 176802 (2006)
Ribhu K Kaul, Denis Ullmo, Gergely Zaránd, Shailesh Chandrasekharan and Harold U Baranger, Phys. Rev . B80(3), 035318 (2009)
Dong E Liu, Sébastien Burdin, Harold U Baranger and Denis Ullmo, arXiv:1106.5688, in preparation (2011)
M Fowler and A Zawadowzki, Solid State Commun. 9, 471 (1971)
P W Anderson, J. Phys. C: Solid State Phys. 3(12), 2436 (1970)
A A Abrikosov, Physics 2, 5 (1965)
Kenneth G Wilson, Rev . Mod. Phys. 47(4), 773 (1975)
N Andrei, Phys. Rev . Lett. 45(5), 379 (1980)
P B Wiegmann, Sov . Phys. JETP Lett. 31, 392 (1980)
P Nozières, J. Low Temp. Phys. 17, 31 (1974)
M Grobis, I G Rau, R M Potok and D Goldhaber-Gordon, in: Handbook of magnetism and adv anced magnetic materials edited by H Kronmüller and S Parkin (Wiley, 2007) Vol. 5, pp. 2703–2724, arXiv:cond-mat/0611480
A M Chang and J C Chen, Rep. Prog. Phys. 72, 096501 (2009)
L I Glazman and M E Raikh, Pis’ma Zh. Eksp. Teor. Fiz. 47, 378 (1988); JETP Lett. 47 (1988) 452
Tai Kai Ng and Patrick A Lee, Phys. Rev . Lett. 61(15), 1768 (1988)
D Goldhaber-Gordon, H Shtrikman, D Mahalu, D Abusch-Magder, U Meirav and M A Kastner, Nature 391, 156 (1998)
G Zaránd and L Udvardi, Phys. Rev . B54(11), 7606 (1996)
A Crépieux and C Lacroix, Phys. Rev . B61(10), 6785 (2000)
Stefan Kettemann and Eduardo R Mucciolo, Phys. Rev . B75(18), 184407 (2007)
A Zhuravlev, I Zharekeshev, E Gorelov, A I Lichtenstein, E R Mucciolo and S Kettemann, Phys. Rev . Lett. 99(24), 247202 (2007)
Denis Ullmo, Rep. Prog. Phys. 71, 026001 (2008)
Rainer Bedrich, Sébastien Burdin and Martina Hentschel, Phys. Rev . B81(17), 174406 (2010)
O Bohigas, in: Chaos and quantum physics edited by M J Giannoni, A Voros and J Jinn-Justin (North-Holland, Amsterdam, 1991) pp. 87–199
Madan Lal Mehta, Random matrices, 2nd edn (Academic Press, London, 1991)
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ULLMO, D., BURDIN, S., LIU, D.E. et al. Kondo effect and mesoscopic fluctuations. Pramana - J Phys 77, 769–779 (2011). https://doi.org/10.1007/s12043-011-0191-3
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DOI: https://doi.org/10.1007/s12043-011-0191-3