Distribution of the resistance of nanowires with strong impurities

Christophe Deroulers (1)

1 Institut für Theoretische Physik [Köln]

Motivated by recent experiments on nanowires and carbon nanotubes, we study theoretically the effect of strong, point-like impurities on the linear electrical resistance R of finite length quantum wires. Charge transport is limited by Coulomb blockade and cotunneling. ln R is slowly self-averaging and non Gaussian. Its distribution is Gumbel with finite-size corrections which we compute. At low temperature, the distribution is similar to the variable range hopping (VRH) behaviour found long ago in doped semiconductors. We show that a result by Raikh and Ruzin does not apply. The finite-size corrections decay with the length L like 1/ln L. At higher temperatures, this regime is replaced by new laws and the shape of the finite-size corrections changes strongly: if the electrons interact weakly, the corrections vanish already for wires with a few tens impurities.

Mots clés: nanowires; disorder; carbon nanotubes; electrical conductivity; charge transport; gumbel distribution; extreme value statistics

Domaines: Electrons fortement corrélés [cond-mat.str-el]; Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

Christophe Deroulers. Distribution of the resistance of nanowires with strong impurities. 2007. ⟨hal-00148141⟩