Abstract.
We show that a spin-up electron from a normal metal entering a superconductor propagates as a composite object consisting of a spin-down hole and a pair in the condensate. This leads to a factorization of the non local conductance as two local Andreev reflections at both interfaces and one propagation in the superconductor, which is tested numerically within a one dimensional toy model of reflectionless tunneling. Small area junctions are characterized by non local conductance fluctuations. A treatment ignoring weak localization leads to a Thouless energy inverse proportional to the sample size, as observed in the numerical simulations. We show that weak localization can have a strong effect, and leads to a coupling between evanescent quasiparticles and the condensate by Andreev reflections “internal” to the superconductor.
Similar content being viewed by others
References
A.F. Andreev, Sov. Phys. JETP 19, 1228 (1964)
C.J. Lambert, R. Raimondi, J. Phys.: Condens. Matter 10, 901 (1998)
F.J. Jedema et al., Phys. Rev. B 60, 16549 (1999)
M.S. Choi, C. Bruder, D. Loss, Phys. Rev. B 62, 13569 (2000); P. Recher, E.V. Sukhorukov, D. Loss Phys. Rev. B 63, 165314 (2001)
G.B. Lesovik, T. Martin, G. Blatter, Eur. Phys. J. B 24, 287 (2001); N.M. Chtchelkatchev, G. Blatter, G.B. Lesovik, T. Martin, Phys. Rev. B 66, 161320(R) (2002)
J.M. Byers, M.E. Flatté, Phys. Rev. Lett. 74, 306 (1995)
G. Deutscher, D. Feinberg, App. Phys. Lett. 76, 487 (2000)
P. Samuelsson, E.V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 91, 157002 (2003)
E. Prada, F. Sols, Eur. Phys. J. B 40, 379 (2004)
C.J. Lambert, J. Koltai, J. Cserti, Towards the Controllable Quantum States (Mesoscopic Superconductivity and Spintronics, 119, edited by H. Takayanagi, J. Nitta (World Scientific, 2003)
R. Mélin, S. Peysson, Phys. Rev. B 68, 174515 (2003); R. Mélin, Phys. Rev. B 72, 134508 (2005)
G. Falci, D. Feinberg, F.W.J. Hekking, Europhysics Lett. 54, 255 (2001)
D. Feinberg, Eur. Phys. J. B 36, 419 (2003)
N.M. Chtchelkatchev, I.S. Burmistrov, Phys. Rev. B 68, 140501 (2003)
R. Mélin, D. Feinberg, Eur. Phys. J. B 26, 101 (2002)
R. Mélin, D. Feinberg, Phys. Rev. B 70, 174509 (2004)
F. Taddei, R. Fazio, Phys. Rev. B 65, 134522 (2002)
G. Bignon, M. Houzet, F. Pistolesi, F.W.J. Hekking, Europhys. Lett. 67, 110 (2004)
R. Mélin, Phys. Rev. B 73, 174512 (2006)
D. Beckmann, H.B. Weber, H.V. Löhneysen, Phys. Rev. Lett. 93, 197003 (2004); D. Beckmann, H. v. Löhneysen, LT 24 Conference Proceedings, arXiv:cond-mat/0512445 (2005)
S. Russo, M. Kroug, T.M. Klapwijk, A.F. Morpugo, Phys. Rev. Lett. 95, 027002 (2005)
G.E. Blonder, M. Tinkham, T.M. Klapwijk, Phys. Rev. B 25, 4515 (1982)
J.A. Melsen, C.W.J. Beenakker, Physica B (Amsterdam) 203, 219 (1994)
T. Yamashita, S. Takahashi, S. Maekawa, Phys. Rev. B 68, 174504 (2003); S. Maekawa, Phys. Rev. B 67, 094515 (2003)
R.A. Smith, V. Ambegaokar, Phys. Rev. B 45, 2463 (1992)
Normal state universal conductance fluctuations were obtained with the same parameters and with a recursive method, A. Levy Yeyati, Phys. Rev. B 45, 14189 (1992)
P.W. Anderson, Phys. Rev. 110, 827 (1958); P.W. Anderson, Phys. Rev. 112, 1900 (1958)
N.N. Bogoliubov, J. Exptl. Theoret. Phys. U.S.S.R. 34, 73 (1958); [Soviet Phys. JETP 34(7), 51 (1958)]
I.O. Kulik, O. Entin-Wohlman, R. Orbach, Jour. Low Temp. Phys. 43, 591 (1981)
L.P. Gorkov, A. Larkin, D.E. Khmelnitskii, Pis'ma Zh. Eksp. Teor. Fiz 30, 248 (1979); [JETP Lett. 30, 228 (1979)]
S. Hikami, Phys. Rev. B 24, 2671 (1981)
E. Akkermans, G. Montambaux, Physique mésoscopique des électrons et des photons (CNRS Editions, EDP Sciences, 2004)
J.P. Morten, A. Brataas, W. Belzig, arXiv:cond-mat/0606561
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Duhot, S., Mélin, R. Thouless energy of a superconductor from non local conductance fluctuations. Eur. Phys. J. B 53, 257–266 (2006). https://doi.org/10.1140/epjb/e2006-00372-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2006-00372-9