Tunneling conduction in disordered dissipative systems

Research output: Contribution to journalArticle

Abstract

We consider in this paper the incoherent transport via tunneling of an electron among randomly distributed impurity centers in a heat bath. The heat bath is modeled as a collection of harmonic oscillators. A general expression is first derived using standard instanton methods for the distance dependence of the rate of tunneling between two spatially separated impurity centers coupled to a heat bath. We find that there are two leading terms in the tunneling rate: (1) the standard e-r/r0 from the wave function overlap and (2) the dissipation correction e-ηr2, η the friction of the medium. Using this rate, we solve the pair approximation to the master equation for incoherent tunneling transport among N randomly distributed impurity sites and obtain the time dependent diffusion coefficient and the site return Green function. From the long-time limit of the return Green function, we show that as a result of dissipation, there is at long times strictly no diffusion when d=1,2 at low impurity concentrations. A crossover region from nondiffusive to diffusive transport is shown to exist when d=3 that is determined by the magnitude of the friction, η. We discuss the relationship between these results and classical percolation.

Original languageEnglish (US)
Pages (from-to)976-985
Number of pages10
JournalThe Journal of chemical physics
Volume84
Issue number2
DOIs
StatePublished - Jan 1 1986
Externally publishedYes

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Impurities
conduction
baths
impurities
Green's function
heat
friction
Green's functions
dissipation
Friction
Wave functions
instantons
harmonic oscillators
crossovers
diffusion coefficient
wave functions
Electrons
approximation
Hot Temperature
electrons

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

Tunneling conduction in disordered dissipative systems. / Phillips, Philip W.

In: The Journal of chemical physics, Vol. 84, No. 2, 01.01.1986, p. 976-985.

Research output: Contribution to journalArticle

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