Abstract
We provide an introduction to the nonequilibrium physics encountered in quantum dots. A brief summary of the relevant Coulomb blockade physics and a concise account of the Keldysh functional integral method is followed by a derivation of the Keldysh Ambegaokar-Eckern-Schön action, which represents a prototypical model for charge transport through quantum dots. We show that the nonequilibrium current fluctuations cause a dephasing that can be probed via the tunneling density of states. We provide analytical and numerical estimates for the corresponding dephasing rates.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The time-ordering operator is defined as \({\mathcal T} [A(t_1) B(t_2)]= \Uptheta(t_1-t_2) A(t_1) B(t_2) + \Uptheta(t_2-t_1) B(t_2) A(t_1).\)
- 2.
The value of \(\Uptheta(0)\) follows from the discrete version (finite N). Consistent results follow, e.g., with \(\Uptheta(0)=1/2.\)
- 3.
We can extend the lower limit for the integral to \(-\infty,\) since we could have started with the interval \([-t_f/2,t_f/2].\)
References
Nazarov, Y.V., Blanter, Y.M.: Quantum Transport: Introduction to Nanoscience. Cambridge University Press, Cambridge (2009)
Esposito, M., Harbola, U., Mukamel, S.: Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems. Rev. Mod. Phys. 81, 1665 (2009)
Weiss, S., Eckel, J., Thorwart, M., Egger, R.: Iterative real-time path integral approach to nonequilibrium quantum transport. Phys. Rev. B 77, 195316 (2008)
Anders, F.B.: Steady-state currents through nanodevices: a scattering-states numerical renormalization-group approach to open quantum systems. Phys. Rev. Lett. 101, 066804 (2008)
Boulat, E., Saleur, H., Schmitteckert, P.: Twofold advance in the theoretical understanding of far-from-equilibrium properties of interacting nanostructures. Phys. Rev. Lett. 101, 140601 (2008)
Metha, P., Andrei, N.: Nonequilibrium transport in quantum impurity models: the Bethe ansatz for open systems. Phys. Rev. Lett. 96, 216802 (2006)
Alhassid, Y.: The statistical theory of quantum dots. Rev. Mod. Phys. 72, 895 (2000)
Aleiner, I.L., Brouwer, P.W., Glazman, L.I.: Quantum effects in Coulomb blockade. Phys. Rep. 358, 309 (2002)
Kamenev, A., Levchenko, A.: Keldysh technique and non-linear \(\sigma\)-model: basic principles and applications. Adv. Phys. 58, 197 (2009)
Kamenev, A., Andreev, A.: Electron–electron interactions in disordered metals: Keldysh formalism. Phys. Rev. B 60, 2218 (1999)
Altland, A., Simons, B.D.: Condensed Matter Field Theory, 2nd edn. Cambridge University Press, Cambridge (2010)
Altland, A., Egger, R.: Nonequilibrium dephasing in coulomb blockaded quantum dots. Phys. Rev. Lett. 102, 026805 (2009)
Kaminski, A., Nazarov, Yu.V., Glazman, L.I.: Suppression of the Kondo effect in a quantum dot by external irradiation. Phys. Rev. Lett. 83, 384 (1999)
Rosch, A., Paaske, J., Kroha, J., Wölfle, P.: Nonequilibrium transport through a Kondo dot in a magnetic field: perturbation theory and poor man’s scaling. Phys. Rev. Lett. 90, 076804 (2003)
Kehrein, S.: Scaling and decoherence in the nonequilibrium Kondo model. Phys. Rev. Lett. 95, 056602 (2005)
Muzykantskii, B., d’Ambrumenil, N., Braunecker, B.: Fermi-edge singularity in a nonequilibrium system. Phys. Rev. Lett. 91, 266602 (2003)
Mitra, A., Millis, A.J.: Coulomb gas on the Keldysh contour: Anderson–Yuval–Hamann representation of the nonequilibrium two-level system. Phys. Rev. B 76, 085342 (2007)
Gutman, D.B., Gefen, Y., Mirlin, A.D.: Nonequilibrium Luttinger liquid: zero-bias anomaly and dephasing. Phys. Rev. Lett. 101, 126802 (2008)
Neder, I., Marquardt, F.: Coherence oscillations in dephasing by non-Gaussian shot noise. New J. Phys. 9, 112 (2007)
Gutman, D.B., Gefen, Y., Mirlin, A.D.: Nonequilibrium zero-bias anomaly in disordered metals. Phys. Rev. Lett. 100, 086801 (2008)
König, J., Schoeller, H.: Strong tunneling in the single-electron box. Phys. Rev. Lett. 81, 3511 (1998)
Göppert, G., Grabert, H., Prokof’ev, N.V., Svistunov, B.: Effect of tunneling conductance on the coulomb staircase. Phys. Rev. Lett. 81, 2324 (1998)
Schön, G., Zaikin, A.D.: Quantum coherent effects, phase transitions, and the dissipative dynamics of ultra small tunnel junctions. Phys. Rep. 198, 237 (1990)
Pothier, H., Guéron, S., Birge, N.O., Esteve, D., Devoret, M.H.: Energy distribution function of quasiparticles in mesoscopic wires. Phys. Rev. Lett. 79, 3490 (1997)
Anthore, A., Pierre, F., Pothier, H., Esteve, D.: Magnetic-field-dependent quasiparticle energy relaxation in mesoscopic wires. Phys. Rev. Lett. 90, 076806 (2003)
Kamenev, A., Gefen, Y.: Zero-bias anomaly in finite-size systems. Phys. Rev. B 54, 5428 (1996)
Sedlmayr, N., Yurkevich, I.V., Lerner, I.V.: Tunnelling density of states at Coulomb-blockade peaks. Europhys. Lett. 76, 109 (2006)
Nazarov, Yu.V.: Coulomb blockade without tunnel junctions. Phys. Rev. Lett. 82, 1245 (1999)
Golubev, D.S., Zaikin, A.D.: Coulomb interaction and quantum transport through a coherent scatterer. Phys. Rev. Lett. 86, 4887 (2001)
Golubev, D.S., Zaikin, A.D.: Electron transport through interacting quantum dots in the metallic regime. Phys. Rev. B 69, 075318 (2004)
Blanter, Ya.M., Büttiker, M.: Shot noise in mesoscopic conductors. Phys. Rep. 336, 1 (2000)
Acknowledgments
We acknowledge support by the SFB Transregio 12 by the Deutsche Forschungsgemeinschaft.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Altland, A., Egger, R. (2012). Nonequilibrium Transport and Dephasing in Coulomb-Blockaded Quantum Dots. In: Cabra, D., Honecker, A., Pujol, P. (eds) Modern Theories of Many-Particle Systems in Condensed Matter Physics. Lecture Notes in Physics, vol 843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10449-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-10449-7_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10448-0
Online ISBN: 978-3-642-10449-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)