Projection operator approach to lifetimes of electrons in metals

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.Comment: 10 pages, 3 figures; Phys. Rev. B, accepted (2009

Projection-operator approach to master equations for coarse-grained occupation numbers in nonideal quantum gases

“…Thus the results presented here may be used as a basis for a range of concrete transport-theoretical investigations. The feasibility of such an approach is supported by the fact that a similar approach has been demonstrated to yield reasonable results for electronic lifetimes in aluminum [12].…”

“…In that case one is interested in describing the decay of a single electronic excitation and therefore the corresponding projector is constructed to project only onto one single occupation number as dynamical variable, whereas the projector (10) used in this paper keeps all grain occupation numbers as time dependent variables thus giving a more detailed picture of the dynamics. In so far the considerations in this paper extend the previous work from [12]. Additionally, the D j are here defined in a slightly different way which leads to a simplification of the upcoming calculations.…”

“…This turns out to be equivalent to employing a projector which keeps only the occupation number deviation within one grain as a relevant observable. Such an investigation has been performed (on the basis of a projector that structurally slightly differs from the one used in the present paper) in [12]. There reasonable lifetimes for hot electrons in aluminum have been found.…”

“…Note that a similar projector has recently been used in the context of investigations on electronic lifetimes in aluminum [12]. In that case one is interested in describing the decay of a single electronic excitation and therefore the corresponding projector is constructed to project only onto one single occupation number as dynamical variable, whereas the projector (10) used in this paper keeps all grain occupation numbers as time dependent variables thus giving a more detailed picture of the dynamics.…”