Inelastic quantum transport: the self-consistent Born approximation and correlated electron-ion dynamics

TL;DR

This paper compares a dynamical method and a steady-state Green's function approach for inelastic quantum transport in nanostructures, showing they agree well under many conditions but differ at high vibrational excitations.

Contribution

It introduces a simplified dynamical method for inelastic transport that aligns with steady-state results in the weak-coupling limit and compares their effectiveness.

Findings

Both methods accurately capture current-induced heating and inelastic effects.

Good agreement between methods over a wide range of conditions.

Differences emerge at very high vibrational excitations.

Abstract

A dynamical method for inelastic transport simulations in nanostructures is compared with a steady-state method based on non-equilibrium Green's functions. A simplified form of the dynamical method produces, in the steady state in the weak-coupling limit, effective self-energies analogous to those in the Born Approximation due to electron-phonon coupling. The two methods are then compared numerically on a resonant system consisting of a linear trimer weakly embedded between metal electrodes. This system exhibits enhanced heating at high biases and long phonon equilibration times. Despite the differences in their formulation, the static and dynamical methods capture local current-induced heating and inelastic corrections to the current with good agreement over a wide range of conditions, except in the limit of very high vibrational excitations, where differences begin to emerge.