GW approach to Anderson model out of equilibrium: Coulomb blockade and false hysteresis in the I-V characteristics

TL;DR

This paper uses the GW approximation to study the non-equilibrium Anderson model, revealing Coulomb blockade and false hysteresis in I-V characteristics, and discusses the limitations of GW in capturing quantum fluctuations.

Contribution

It develops a non-equilibrium GW approach to analyze Coulomb blockade and hysteresis in the Anderson model, highlighting artifacts of the approximation.

Findings

GW captures Coulomb blockade in I-V characteristics.

Multiple steady states can occur depending on parameters.

Hysteresis observed is an artifact of the GW approximation.

Abstract

The Anderson model for a single impurity coupled to two leads is studied using the $GW$ approximation in the strong electron-electron interaction regime as a function of the alignment of the impurity level relative to the chemical potentials in the leads. We employ a non-equilibrium Green's function technique to calculate the electron self-energy, the spin density and the current as a function of bias across the junction. In addition we develop an expression for the change in the expectation value of the energy of the system that results when the impurity is coupled to the leads, including the role of Coulomb interactions through the electron self energy in the region of the junction. The current-voltage characteristics calculated within the GW approximation exhibit Coulomb blockade. Depending on the gate voltage and applied bias, we find that there can be more than one steady-state solution for the system, which may give rise to a hysteresis in the I-V characteristics. We show that the hysteresis is an artifact of the $GW$ approximation and would not survive if quantum fluctuations beyond the $GW$ approximation are included.