Narrow Band and Localization

Abstract

Clearly the concept of energy bands is one of the most fundamental ingredients in the theory of condensed matter. It is now well established that energy band calculations are very useful in order to develop a microscopic understanding of materials. During the last 10–15 years there has been a very strong development of both computational techniques and computers so that now even bulk properties can be calculated from just a knowledge of the atomic constitution of the material (at least for moderately complex systems). The crystal structures of the elemental metals have also been successfully treated by means of energy band calculations. However, when we proceed to materials possessing so-called narrow bands the situation is less clear as regards the appropriateness of band structure calculations. When we go even further, namely to systems containing localized atomic-like configurations, then the conventional band theory approach fails to provide a proper description of the electronic properties. A well-known example of this is the CoO compound, which is a very good insulator, although normal band theory would predict it to be a metal. Thus it appears that the d-electrons in this system do not form extended Bloch states but rather are localized. This problem about locatization versus itineracy was recognized long ago and especially Mott has stressed the difficulties involved.