Abstract
We consider single-channel transmission through a double quantum dot that consists of two identical single dots coupled by a wire. The numerical solution for the scattering wave function shows that the resonance width of a few of the states may vanish when the width (or length) of the wire and the energy of the incident particle each take a certain value. In such a case, a particle is trapped inside the wire as the numerical visualization of the scattering wave function shows. To understand these numerical results, we explore a simple model with a small number of states, which allows us to consider the problem analytically. If the eigenenergies of the closed system cross the energies of the transmission zeroes, the wire effectively decouples from the rest of the system and traps the particle.
Similar content being viewed by others
References
P. Kleinwächter and I. Rotter, Phys. Rev. C 32, 1742 (1985); I. Rotter, Rep. Prog. Phys. 54, 635 (1991).
J. Okołowicz, M. Płoszajczak, and I. Rotter, Phys. Rep. 374, 271 (2003).
A. I. Magunov, I. Rotter, and S. I. Strakhova, J. Phys. B 32, 1669 (1999); J. Phys. B 34, 29 (2001).
E. Persson, K. Pichugin, I. Rotter, and P. Seba, Phys. Rev. E 58, 8001 (1998); P. Seba, I. Rotter, M. Müller, et al., Phys. Rev. E 61, 66 (2000); I. Rotter, E. Persson, K. Pichugin, and P. Seba, Phys. Rev. E 62, 450 (2000).
E. Persson, I. Rotter, H. J. Stöckmann, and M. Barth, Phys. Rev. Lett. 85, 2478 (2000); H. J. Stöckmann et al., Phys. Rev. E 65, 066211 (2002).
I. Rotter and A. F. Sadreev, Phys. Rev. E 71, 036227 (2005).
R. G. Nazmitdinov, K. N. Pichugin, I. Rotter, and P. Seba, Phys. Rev. E 64, 056214 (2001); Phys. Rev. B 66, 085322 (2002).
I. Rotter and A. F. Sadreev, Phys. Rev. E 71, 046204 (2005).
V. Shahbazyan and M. E. Raikh, Phys. Rev. B 49, 17123 (1994).
M. L. Ladron de Guevara, F. Claro, and P. A. Orellana, Phys. Rev. B 67, 195335 (2003).
C. S. Kim and A. M. Satanin, Phys. Rev. B 58, 15 389 (1998).
N. C. van der Vaart et al., Phys. Rev. Lett. 74, 4702 (1995).
F. R. Waugh et al., Phys. Rev. Lett. 75, 705 (1995).
J. C. Chen, A. M. Chang, and M. R. Melloch, Phys. Rev. Lett. 92, 176801 (2004).
H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge Univ. Press, Cambridge, 1999).
K.-F. Berggren and Zh.-L. Ji, Phys. Rev. B 47, 6390 (1993).
K. Vacek, A. Okiji, and H. Kasai, Phys. Rev. B 47, 3695 (1993).
J. P. Carini et al., Phys. Rev. B 55, 9842 (1997).
H. Feshbach, Ann. Phys. (N.Y.) 5, 357 (1958); Ann. Phys. (N.Y.) 19, 287 (1962).
M. S. Livshits, Sov. Phys. JETP 4, 91 (1957).
I. Rotter, Rep. Prog. Phys. 54, 635 (1991).
S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge Univ. Press, Cambridge, 1995).
A. F. Sadreev and I. Rotter, J. Phys. A 36, 11413 (2003).
M. N. Kiselev, K. A. Kikoin, and L. W. Molenkamp, JETP Lett. 77, 366 (2003).
T.-S. Kim and S. Hershfield, Phys. Rev. B 67, 235330 (2003).
F. M. Dittes, Phys. Rep. 339, 215 (2000).
Author information
Authors and Affiliations
Additional information
From Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 82, No. 8, 2005, pp. 556–561.
Original English Text Copyright © 2005 by Sadreev, Bulgakov, Rotter.
The text was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Sadreev, A.F., Bulgakov, E.N. & Rotter, I. Trapping of an electron in the transmission through two quantum dots coupled by a wire. Jetp Lett. 82, 498–503 (2005). https://doi.org/10.1134/1.2150869
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.2150869