Abstract
A simple statistical model for the effects of dephasing on electron transport in one-dimensional quantum systems is introduced, which allows to adjust the degree of phase and momentum randomization independently. Hence, the model is able to describe the transport in an intermediate regime between classical and quantum transport. The model is based on Büttiker’s approach using fictitious reservoirs for the dephasing effects. However, in contrast to other models, at the fictitious reservoirs complete phase randomization is assumed, which effectively divides the system into smaller coherent subsystems, and an ensemble average over randomly distributed dephasing reservoirs is calculated. This approach reduces not only the computation time but allows also to gain new insight into system properties. In this way, after deriving an efficient formula for the disorder-averaged resistance of a tight-binding chain, it is shown that the dephasing-driven transition from localized-exponential to ohmic-linear behavior is not affected by the degree of momentum randomizing dephasing.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Caroli, R. Combescot, P. Nozieres, D. Saint-James, J. Phys. C: Solid State Phys. 4, 916 (1971)
S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, 1997)
S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, 2005)
R. Golizadeh-Mojarad, S. Datta, Phys. Rev. B 75, 081301 (2007)
M. Büttiker, Phys. Rev. B 33, 3020 (1986)
M. Büttiker, Quantum Coherence and Phase Randomization in Series Resistors, in Resonant Tunneling in Semiconductors – Physics and Applications, edited by L. Chang, E. Mendez, C. Tejedor (Plenum Press, 1991), pp. 213–227
J.L. D’Amato, H.M. Pastawski, Phys. Rev. B 41, 7411 (1990)
K. Maschke, M. Schreiber, Phys. Rev. B 49, 2295 (1994)
I. Knittel, F. Gagel, M. Schreiber, Phys. Rev. B 60, 916 (1999)
X.Q. Li, Y. Yan, Phys. Rev. B 65, 155326 (2002)
X.Y. Yu, H.Y. Zhang, P. Han, X.Q. Li, Y. Yan, J. Chem. Phys. 117, 2180 (2002)
D. Roy, A. Dhar, Phys. Rev. B 75, 195110 (2007)
D. Nozaki, C. Gomes da Rocha, H.M. Pastawski, G. Cuniberti, Phys. Rev. B 85, 155327 (2012)
M.J. McLennan, Y. Lee, S. Datta, Phys. Rev. B 43, 13846 (1991)
S. Hershfield, Phys. Rev. B 43, 11586 (1991)
S.K. Joshi, D. Sahoo, A.M. Jayannavar, Phys. Rev. B 62, 880 (2000)
M.G. Pala, G. Iannaccone, Phys. Rev. B 69, 235304 (2004)
H. Zheng, Z. Wang, Q. Shi, X. Wang, J. Chen, Phys. Rev. B 74, 155323 (2006)
S. Bandopadhyay, D. Chaudhuri, A.M. Jayannavar, Phys. Lett. A 374, 813 (2010)
M. Zilly, O. Ujsághy, D.E. Wolf, Eur. Phys. J. B 68, 237 (2009)
M. Zilly, Ph.D. thesis, Universität Duisburg-Essen, 2010
M. Zilly, O. Ujsághy, D.E. Wolf, Phys. Rev. B 82, 125125 (2010)
M. Zilly, O. Ujsághy, M. Woelki, D.E. Wolf, Phys. Rev. B 85, 075110 (2012)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stegmann, T., Zilly, M., Ujsághy, O. et al. Statistical model for the effects of phase and momentum randomization on electron transport. Eur. Phys. J. B 85, 264 (2012). https://doi.org/10.1140/epjb/e2012-30348-y
Received:
Published:
DOI: https://doi.org/10.1140/epjb/e2012-30348-y