Dependence of the D.C. conductivity of a linear chain on the phonon frequency

Shlomo Marianer*, Claudio Hartzstein, Meir Weger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We investigate the disordered tight binding Hamiltonian by solving numerically the equation of motion and then evaluating the diffusion coefficient. For static disorder we obtain, in addition to the known result that the localization length is about twice the mean free path for backward scattering, Lloc  2lB that the localization time (the time it takes the wavefunction to spread over this length) is τloc {reversed tilde equals}20τB where lB and τB are the mean free path and time in first Born approximation. We then go on to study the case of dynamic disorder. Here we get a diffusive motion (i.e. finite d.c. conductivity) where the diffusion constant for low phonon frequencies follows the law D(ωph) ∝{check mark}ωph and for high phonon frequencies D(ωph) {reversed tilde equals}Do the Drude diffusion constant. We also obtain the crossover frequency ωo {reversed tilde equals}0.02τB -1 = 0.4τloc-1.

Original languageEnglish
Pages (from-to)695-699
Number of pages5
JournalSolid State Communications
Volume43
Issue number9
DOIs
StatePublished - Sep 1982

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