EFFECTIVE MASS, LANDAU INTERACTION FUNCTION AND SELF-ENERGY OF AN ELECTRON LIQUID

Abstract

A review is given of the calculations of the effective mass m* for an electron liquid at metallic densities. The review will be helpful to understand that a great deal of difficulties are involved in estimating the quasi-particle dispersion in the vicinity of the Fermi level. It is emphasized that a systematic consideration of vertex corrections in accordance with the Pauli principle up to higher orders in calculating the Landau interaction function fσσ'( p , p ') or the self-energy Σ( p , ε) is indispensable for the correct evaluation of m* for rs>1. It is concluded that the mass ratio m*/m is a monotonically decreasing function of rs and remains smaller than unity throughout the whole region of metallic densities. The deviation of m*/m from unity is as small as 8% even at the lowest metallic densities. From general considerations we shall also discuss the effects of Σ( p , ε) on the overall features of the quasi-particle dispersion.