Stability analysis of multiple nonequilibrium fixed points in self-consistent electron transport calculations

TL;DR

This paper introduces a method to analyze the stability of nonequilibrium fixed points in self-consistent electron transport calculations, using linearization of kinetic equations and spectral analysis within Hartree-Fock and DFT frameworks.

Contribution

It provides a novel approach to stability analysis of nonequilibrium fixed points in electron transport, including derivations within Hartree-Fock and TDDFT.

Findings

Identified stability conditions for multiple fixed points in molecular electron transport.

Demonstrated the method on a spin-degenerate single-level molecule with Coulomb interaction.

Analyzed the asymptotic behavior of fixed points through spectral properties of the stability matrix.

Abstract

We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary, nonlinear kinetic equation for single-particle density matrix. We obtain the stability matrix by linearizing the kinetic equation around the fixed points and analyze the real part of its spectrum to assess the asymptotic time behavior of the fixed points. We derive expressions for the stability matrices within Hartree-Fock and linear response adiabatic time-dependent density functional theory. The stability analysis of multiple fixed points is performed within the nonequilibrium Hartree-Fock approximation for the electron transport through a molecule with a spin-degenerate single level with local Coulomb interaction.