Projection operator approach to lifetimes of electrons in metals

TL;DR

This paper introduces a projection operator method to analytically compute electron lifetimes in metals, providing an intuitive scattering interpretation and applicable at any temperature, demonstrated on a simplified aluminium model.

Contribution

It presents a novel analytic approach using the time-convolutionless projection operator method for calculating electron lifetimes in metals, offering an alternative to self-energy formalism.

Findings

Derived an explicit decay rate expression for excited electrons.

Validated the approach with a jellium model of aluminium.

Results are comparable to existing self-energy calculations.

Abstract

We present an alternative approach to the calculation of the lifetime of a single excited electron (hole) which interacts with the Fermi sea of electrons in a metal. The metal is modelled on the level of a Hamilton operator comprising a pertinent dispersion relation and scattering term. To determine the full relaxation dynamics we employ an adequate implementation of the time-convolutionless projection operator method (TCL). This yields an analytic expression for the decay rate which allows for an intuitive interpretation in terms of scattering events. It may furthermore be efficiently evaluated by means of a Monte-Carlo integration scheme. As an example we investigate aluminium using, just for simplicity, a jellium-type model. This way we obtain data which are directly comparable to results from a self-energy formalism. Our approach applies to arbitrary temperatures.