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Landauer's formula with finite-time relaxation: Kramers' crossover in electronic transport

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https://ir.library.oregonstate.edu/concern/articles/s1784n35d

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  • Landauer’s formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of behavior: weak relaxation gives a contact-limited current; strong relaxation localizes electrons, distorting their natural dynamics and reducing the current; and in an intermediate regime the Landauer view of the system only is recovered. We also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport.
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  • Gruss, D., Velizhanin, K. A., & Zwolak, M. (2016). Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport. Scientific Reports, 6, 24514. doi:10.1038/srep24514
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  • 6
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  • Daniel Gruss acknowledges support under the Cooperative Research Agreement between the University of Maryland and the National Institute of Standards and Technology Center for Nanoscale Science and Technology, Award 70NANB10H193, through the University of Maryland. Kirill A. Velizhanin was supported by the U.S. Department of Energy through the LANL/LDRD Program.
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