Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport
Abstract
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. Furthermore, we also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport.
- Authors:
-
- National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States). Center for Nanoscale Science and Technology; Univ. of Maryland, College Park, MD (United States). Maryland Nanocenter; Oregon State Univ., Corvallis, OR (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
- National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States). Center for Nanoscale Science and Technology
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1259467
- Alternate Identifier(s):
- OSTI ID: 1304838
- Report Number(s):
- LA-UR-16-22311
Journal ID: ISSN 2045-2322; srep24514
- Grant/Contract Number:
- 70NANB10H193; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Volume: 6; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; transport; fermions; Green's function
Citation Formats
Gruss, Daniel, Velizhanin, Kirill A., and Zwolak, Michael. Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport. United States: N. p., 2016.
Web. doi:10.1038/srep24514.
Gruss, Daniel, Velizhanin, Kirill A., & Zwolak, Michael. Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport. United States. https://doi.org/10.1038/srep24514
Gruss, Daniel, Velizhanin, Kirill A., and Zwolak, Michael. Wed .
"Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport". United States. https://doi.org/10.1038/srep24514. https://www.osti.gov/servlets/purl/1259467.
@article{osti_1259467,
title = {Landauer’s formula with finite-time relaxation: Kramers’ crossover in electronic transport},
author = {Gruss, Daniel and Velizhanin, Kirill A. and Zwolak, Michael},
abstractNote = {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. Furthermore, we also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport.},
doi = {10.1038/srep24514},
journal = {Scientific Reports},
number = ,
volume = 6,
place = {United States},
year = {Wed Apr 20 00:00:00 EDT 2016},
month = {Wed Apr 20 00:00:00 EDT 2016}
}
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