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

Abstract

We present an extension of the work of D'Amato and Pastawski 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 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 $N>>\ell$, where $\ell$ is a coherence length scale, dissipation takes place uniformly along the wire. For $N<<\ell$, 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.

21 pages, 4 figures, revised version, to appear in Phys. Rev. B

References in corpus (3)

• Inelastic scattering and local heating in atomic gold wires
• Heat transport in harmonic lattices
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs

Cited by in corpus (7)

• Heat Transport in low-dimensional systems
• Heat transport in harmonic lattices
• Crossover from ballistic to diffusive thermal transport in quantum Langevin dynamics study of a harmonic chain connected to self-consistent reservoirs
• ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs
• Electron transport in an open mesoscopic metallic ring
• Random-phase reservoir and a quantum resistor: The Lloyd model
• Decohering d-dimensional quantum resistance