Cargando…

Current-induced forces in mesoscopic systems: A scattering-matrix approach

Nanoelectromechanical systems are characterized by an intimate connection between electronic and mechanical degrees of freedom. Due to the nanoscopic scale, current flowing through the system noticeably impacts upons the vibrational dynamics of the device, complementing the effect of the vibrational...

Descripción completa

Detalles Bibliográficos
Autores principales: Bode, Niels, Kusminskiy, Silvia Viola, Egger, Reinhold, von Oppen, Felix
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Beilstein-Institut 2012
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3304326/
https://www.ncbi.nlm.nih.gov/pubmed/22428105
http://dx.doi.org/10.3762/bjnano.3.15
_version_ 1782226878302519296
author Bode, Niels
Kusminskiy, Silvia Viola
Egger, Reinhold
von Oppen, Felix
author_facet Bode, Niels
Kusminskiy, Silvia Viola
Egger, Reinhold
von Oppen, Felix
author_sort Bode, Niels
collection PubMed
description Nanoelectromechanical systems are characterized by an intimate connection between electronic and mechanical degrees of freedom. Due to the nanoscopic scale, current flowing through the system noticeably impacts upons the vibrational dynamics of the device, complementing the effect of the vibrational modes on the electronic dynamics. We employ the scattering-matrix approach to quantum transport in order to develop a unified theory of nanoelectromechanical systems out of equilibrium. For a slow mechanical mode the current can be obtained from the Landauer–Büttiker formula in the strictly adiabatic limit. The leading correction to the adiabatic limit reduces to Brouwer’s formula for the current of a quantum pump in the absence of a bias voltage. The principal results of the present paper are the scattering-matrix expressions for the current-induced forces acting on the mechanical degrees of freedom. These forces control the Langevin dynamics of the mechanical modes. Specifically, we derive expressions for the (typically nonconservative) mean force, for the (possibly negative) damping force, an effective “Lorentz” force that exists even for time-reversal-invariant systems, and the fluctuating Langevin force originating from Nyquist and shot noise of the current flow. We apply our general formalism to several simple models that illustrate the peculiar nature of the current-induced forces. Specifically, we find that in out-of-equilibrium situations the current-induced forces can destabilize the mechanical vibrations and cause limit-cycle dynamics.
format Online
Article
Text
id pubmed-3304326
institution National Center for Biotechnology Information
language English
publishDate 2012
publisher Beilstein-Institut
record_format MEDLINE/PubMed
spelling pubmed-33043262012-03-16 Current-induced forces in mesoscopic systems: A scattering-matrix approach Bode, Niels Kusminskiy, Silvia Viola Egger, Reinhold von Oppen, Felix Beilstein J Nanotechnol Full Research Paper Nanoelectromechanical systems are characterized by an intimate connection between electronic and mechanical degrees of freedom. Due to the nanoscopic scale, current flowing through the system noticeably impacts upons the vibrational dynamics of the device, complementing the effect of the vibrational modes on the electronic dynamics. We employ the scattering-matrix approach to quantum transport in order to develop a unified theory of nanoelectromechanical systems out of equilibrium. For a slow mechanical mode the current can be obtained from the Landauer–Büttiker formula in the strictly adiabatic limit. The leading correction to the adiabatic limit reduces to Brouwer’s formula for the current of a quantum pump in the absence of a bias voltage. The principal results of the present paper are the scattering-matrix expressions for the current-induced forces acting on the mechanical degrees of freedom. These forces control the Langevin dynamics of the mechanical modes. Specifically, we derive expressions for the (typically nonconservative) mean force, for the (possibly negative) damping force, an effective “Lorentz” force that exists even for time-reversal-invariant systems, and the fluctuating Langevin force originating from Nyquist and shot noise of the current flow. We apply our general formalism to several simple models that illustrate the peculiar nature of the current-induced forces. Specifically, we find that in out-of-equilibrium situations the current-induced forces can destabilize the mechanical vibrations and cause limit-cycle dynamics. Beilstein-Institut 2012-02-20 /pmc/articles/PMC3304326/ /pubmed/22428105 http://dx.doi.org/10.3762/bjnano.3.15 Text en Copyright © 2012, Bode et al. https://creativecommons.org/licenses/by/2.0https://www.beilstein-journals.org/bjnano/termsThis is an Open Access article under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The license is subject to the Beilstein Journal of Nanotechnology terms and conditions: (https://www.beilstein-journals.org/bjnano/terms)
spellingShingle Full Research Paper
Bode, Niels
Kusminskiy, Silvia Viola
Egger, Reinhold
von Oppen, Felix
Current-induced forces in mesoscopic systems: A scattering-matrix approach
title Current-induced forces in mesoscopic systems: A scattering-matrix approach
title_full Current-induced forces in mesoscopic systems: A scattering-matrix approach
title_fullStr Current-induced forces in mesoscopic systems: A scattering-matrix approach
title_full_unstemmed Current-induced forces in mesoscopic systems: A scattering-matrix approach
title_short Current-induced forces in mesoscopic systems: A scattering-matrix approach
title_sort current-induced forces in mesoscopic systems: a scattering-matrix approach
topic Full Research Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3304326/
https://www.ncbi.nlm.nih.gov/pubmed/22428105
http://dx.doi.org/10.3762/bjnano.3.15
work_keys_str_mv AT bodeniels currentinducedforcesinmesoscopicsystemsascatteringmatrixapproach
AT kusminskiysilviaviola currentinducedforcesinmesoscopicsystemsascatteringmatrixapproach
AT eggerreinhold currentinducedforcesinmesoscopicsystemsascatteringmatrixapproach
AT vonoppenfelix currentinducedforcesinmesoscopicsystemsascatteringmatrixapproach