Resistance saturation in semi-conducting polyacetylene molecular wires

Abstract

Realizing the promises of molecular electronic devices requires an understanding of transport on the nanoscale. Here, we consider a Su-Schrieffer-Heeger model for semi-conducting trans-polyacetylene molecular wires in which we endow charge carriers with a finite lifetime. The aim of this exercise is two-fold: (i) the simplicity of the model allows an insightful numerical and analytical comparison of the Landauer and Kubo linear-response formalism; (ii) we distill the prototypical characteristics of charge transport through gapped mesoscopic systems and compare these to bulk semiconductors. We find that both techniques yield a residual differential conductance at low temperatures for contacted polyacetylene chains of arbitrary length—in line with the resistivity saturation in some correlated narrow-gap semiconductors. Quantitative agreement, however, is limited to not too long molecules. Indeed, while the Landauer transmission is suppressed exponentially with the system size, the Kubo response only decays hyperbolically. Our findings inform the choice of transport methodologies for the ab initio modelling of molecular devices.

LinReTraCe: The linear response transport centre

“…If the same quasi-particle renormalization is applied to all states, a partial cancellation of the pre-factors in Eqs. (38)(39)(40)(41)(42)(43) occurs due to renormalization of the scattering rate Γ = ZΓ 0 . The Boltzmann response kernels then verify…”

“…[2] for details and Ref. [40] for a discussion of saturation from inter-band transitions. Further, entropy transport is thermodynamically consistent, as S ∝ T and ν ∝ T towards absolute zero.…”