Electron transport in a one dimensional conductor with inelastic scattering by self-consistent reservoirs

Dibyendu Roy and Abhishek Dhar
Phys. Rev. B 75, 195110 – Published 11 May 2007

Abstract

We present an extension of the work of D’Amato and Pastawski [Phys. Rev. B 41, 7411 (1990)] on electron transport in a one dimensional conductor modeled by the tight-binding lattice Hamiltonian and in which inelastic scattering is incorporated by connecting each site of the lattice to one dimensional leads. This model incorporates Büttiker’s [Phys. Rev. B 32, 1846 (1985); 23, 3020 (1986)] original idea of dephasing probes. Here, we consider finite temperatures and study both electrical and heat transport across a chain with applied chemical potential and temperature gradients. Our approach involves quantum Langevin equations and nonequilibrium Green’s functions. In the linear-response limit, we are able to solve the model exactly and obtain expressions for various transport coefficients. Standard linear-response relations are shown to be valid. We also explicitly compute the heat dissipation and show that for wires of length N, where is a coherence length scale, dissipation takes place uniformly along the wire. For N, when transport is ballistic, dissipation is mostly at the contacts. In the intermediate range between Ohmic and ballistic transport, we find that the chemical-potential profile is linear in the bulk with sharp jumps at the boundaries. These are explained using a simple model where the left and right moving electrons behave as persistent random walkers.

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  • Received 10 November 2006

DOI:https://doi.org/10.1103/PhysRevB.75.195110

©2007 American Physical Society

Authors & Affiliations

Dibyendu Roy* and Abhishek Dhar

  • Raman Research Institute, Bangalore 560080, India

  • *Electronic address: dibyendu@rri.res.in
  • Electronic address: dabhi@rri.res.in

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Issue

Vol. 75, Iss. 19 — 15 May 2007

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