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20 - Open Many-Fermion Systems

Published online by Cambridge University Press:  11 May 2023

Uri Peskin
Affiliation:
Technion - Israel Institute of Technology, Haifa
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Summary

We introduce a kinetic theory of electron transport on the nanoscale, formulated in terms of the Fock space of an open many-electron system, and the “second quantization” Hamiltonian. To model a thermal electron reservoir (e.g., a metal electrode), the Fermi–Dirac distribution is derived from the corresponding density operator. A nanoscale system, weakly coupled to the reservoir, is modeled as an impurity. When the Born–Markov and secular approximations are valid, quantum master equations are derived, showing that the impurity equilibrates with the reservoir. To account for charge transport through the impurity, as in atomic point contacts or single molecule junctions, the master equations are generalized for cases of an impurity coupled to different reservoirs at different chemical potentials/temperatures. In these cases, we show that the system reaches a nonequilibrium steady state, where current flows through the impurity. Analytic expressions are derived for this steady state in simple models.

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Publisher: Cambridge University Press
Print publication year: 2023

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References

Hubbard, J., “Electron correlations in narrow energy bands,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 277, 238 (1963).Google Scholar
Anderson, P. W., “Localized magnetic states in metals,” Physical Review 124, 41 (1961).CrossRefGoogle Scholar
Desjonqueres, M-C and Spanjaard, D., “Concepts in Surface Physics” (Springer, 1996).CrossRefGoogle Scholar
Cuevas, J. C. and Scheer, E., “Molecular Electronics: An Introduction to Theory and Experiment” (World Scientific, 2nd Edition 2017).CrossRefGoogle Scholar
Galperin, M., Ratner, M. A. and Nitzan, A.. “Molecular transport junctions: Vibrational effects,” Journal of Physics: Condensed Matter 19, 103201 (2007).Google Scholar
Mühlbacher, L. and Rabani, E., “Real-time path integral approach to nonequilibrium many-body quantum systems,” Physical Review Letters 100, 176403 (2008).Google Scholar
Schinabeck, C., Erpenbeck, A., Härtle, R. and Thoss, M., “Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems,” Physical Review B 94, 201407 (2016).CrossRefGoogle Scholar
Meir, Y. and Wingreen, N. S., “Landauer formula for the current through an interacting electron region,” Physical Review Letters 68, 2512 (1992).CrossRefGoogle ScholarPubMed
Härtle, R., Cohen, G., Reichman, D. R. and Millis, A. J., “Decoherence and lead-induced interdot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach,” Physical Review B 88, 235426 (2013).Google Scholar

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  • Open Many-Fermion Systems
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.021
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  • Open Many-Fermion Systems
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.021
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Open Many-Fermion Systems
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.021
Available formats
×