Abstract.
The density of the transmission eigenvalues of Pb nano-contacts has been estimated recently in mechanically controllable break-junction experiments. Motivated by these experimental analyses, here we study the evolution of the density of the transmission eigenvalues with the disorder strength and the number of channels supported by the ballistic constriction of a quantum point contact in the framework of the Dorokhov-Mello-Pereyra-Kumar equation. We find that the transmission density evolves rapidly into the density in the diffusive metallic regime as the number of channels Nc of the constriction increase. Therefore, the transmission density distribution for a few Nc channels comes close to the known bimodal density distribution in the metallic limit. This is in agreement with the experimental statistical-studies in Pb nano-contacts. For the two analyzed cases, we show that the experimental densities are seen to be well described by the corresponding theoretical results.
Similar content being viewed by others
References
B.J. van Wees, H. van Houten, C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel, 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, G.A.C. Jones, J. Phys. C 21, L209 (1988)
N. Agraït, A. Levy Yeyati, Jan M. van Ruitenbeek, Phys. Rep. 377, 81 (2003)
C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997)
D.L. Maslov, C. Barnes, G. Kirczenow, Phys. Rev. Lett. 70, 1984 (1993)
C.W.J. Beenakker, J.A. Melsen, Phys. Rev. B 50, 2450 (1994)
G. Campaganano, O.N. Jouravlev, Ya.M. Blanter, Yu.V. Nazarov, Phys. Rev. B 69, 235319 (2004)
E. Scheer et al., Nature 394, 154 (1998)
R.H.M. Smit, C. Untiedt, G. Rubio-Bollinger, R.C. Segers, J.M. van Ruitenbeek, Phys. Rev. Lett. 91, 076805-1 (2003)
J.J. Riquelme, L. de la Vega, A. Levy Yeyati, N. Agraït, A. Martin-Rodero, G. Rubio-Bollinger, Europhys. Lett. 70, 663 (2005)
J.J. Riquelme, Memoria de Investigación, Universidad Autónoma de Madrid
P.A. Mello, N. Kumar, Quantum Transport in Mesoscopic Systems. Complexity and statistical fluctuations (Oxford University Press, Oxford, 2004)
O. N. Dorokhov, JETP Lett. 36, 318 (1982)
C.W.J. Beenakker, B. Rejaei, Phys. Rev. Lett. 71, 3689 (1993)
V.A. Gopar, K.A. Muttalib, P. Wölfle, Phys. Rev. B 66, 174204 (2002)
K.A. Muttalib, P. Wölfle, V.A. Gopar, Ann. Phys. 308, 156 (2003)
A.A. Abrikosov, Solid State Commun. 37, 997 (1981)
M. Caselle, Phys. Rev. Lett. 74, 2776 (1995)
P.A. Mello, J.-L. Pichard, Phys. Rev. B 40, 5276 (1989)
The data points to produce Figure 2 have been extracted from Figure 2 in reference riquelme and Figure 8 in reference memory
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gopar, V. Statistical analysis of the transmission based on the DMPK equation: an application to Pb nano-contacts. Eur. Phys. J. B 62, 299–304 (2008). https://doi.org/10.1140/epjb/e2008-00169-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2008-00169-x