Tunneling conduction in disordered dissipative systems

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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 - 1986
Externally publishedYes

ASJC Scopus subject areas

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

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