13 - Interactions and diffusion

Summary

In this chapter v₀is the average density of states per spin direction and ρ₀ = v₀/Ω is the density of states per unit volume. The energy Δ = 1/(_ρ0Ω) = 1/v₀is the average level spacing per spin direction. Most results will be presented in the CGS system, in the form most commonly found in the literature. Unless specified, we take ħ = 1.

Introduction

Up to this point, electron–electron interaction has been neglected in the description of spectral properties and electronic transport. Although electrons interact through the Coulomb interaction, the free electron model is a very good approximation for the description of many physical properties. This is due to the screening of the Coulomb interaction which occurs on a length of the order of the average distance between electrons. However, the electron–electron interaction has important physical consequences which can be classified in two categories.

• Each electron is sensitive not only to the disorder potential but also to the electronic density fluctuations induced by other electrons. As a result, the energy levels are shifted and the thermodynamic and transport properties are modified, particularly the density of states and the conductivity. The change in density of states is maximum around the Fermi level, thus constituting a direct signature of the interaction. Moreover, this change is important since it affects the orbital magnetism of the electron gas and the persistent current (Chapter 14). The change in conductivity is of the same order of magnitude as the weak localization correction, but its nature is quite different. In particular, it does not depend on the magnetic field, making it more difficult to observe.

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