Spatial Correlation of Conduction Electrons in Metal with Complicated Geometry Of The Fermi Surface

TL;DR

This paper investigates how the shape and local geometry of the Fermi surface in metals influence the asymptotic behavior of conduction electron correlations, affecting phenomena like Friedel oscillations and RKKY interactions.

Contribution

It provides a detailed analysis of the density-density correlation function's dependence on Fermi surface geometry, including the damping of Friedel oscillations and applications to electron transitions and exchange interactions.

Findings

Exponent of Friedel oscillations depends on local Fermi surface geometry

Asymptotic behavior of correlation functions varies with Fermi surface shape

Results applicable to electron topological transitions and RKKY interactions

Abstract

The "density-density" correlation function of conduction electrons in metal is investigated. It is shown, that the asymptotic behaviour of the CF depends on the shape and the local geometry of the Fermi surface. In particular, the exponent of power law which describes the damping of Friedel oscillations at large r (-4 for an isotropic Fermi gas) is determined by local geometry of the FS. The applications of the obtained results to calculations of the CF in a metal near the electron topological transition and of the RKKY exchange integral are considered as well.