Validity criteria for Fermi's golden rule scattering rates applied to metallic nanowires

TL;DR

This paper develops a framework to assess when Fermi's golden rule provides reliable scattering rates for electrons in metallic nanowires, considering their statistical properties and various scattering mechanisms.

Contribution

It introduces general validity criteria for Fermi's golden rule in metallic nanowires, accounting for different elastic scattering mechanisms and system properties.

Findings

Derived concrete validity criteria for impurity scattering

Established criteria for grain boundary scattering

Assessed surface roughness scattering validity

Abstract

Fermi's golden rule underpins the investigation of mobile carriers propagating through various solids, being a standard tool to calculate their scattering rates. As such, it provides a perturbative estimate under the implicit assumption that the effect of the interaction Hamiltonian which causes the scattering events is sufficiently small. To check the validity of this assumption, we present a general framework to derive simple validity criteria in order to assess whether the scattering rates can be trusted for the system under consideration, given its statistical properties such as average size, electron density, impurity density et cetera. We derive concrete validity criteria for metallic nanowires with conduction electrons populating a single parabolic band subjected to different elastic scattering mechanisms: impurities, grain boundaries and surface roughness.