The history of the development of some of the key concepts discussed in this book is quite interesting and has some rather unexpected twists and turns. In this section we discuss briefly the history of the concepts of Mott insulators, the Jahn–Teller effect, and the Peierls transition.

Mott insulators and Mott transitions

The notion of a Mott insulator as a state conceptually different from the standard band-like insulators and metals can be introduced using two approaches. In the main text, for example in Chapter 1 we described the approach that uses the Hubbard model (1.6) with short-range (on-site) electron-electron repulsion and attributes the insulating nature for strong interaction to the fact that an electron transferred to an already occupied site experiences repulsion from the electron already sitting on that site. This is the picture most often used nowadays to explain the idea of Mott insulators.

But historically these ideas first appeared in a different picture, presented in a paper by Mott published in 1949 (Mott, 1949) – although it already contained some hints about the picture mostly used nowadays, formalized in the Hubbard model. But the main arguments of Mott in this paper rely rather on the long-range character of Coulomb interaction, and the main statement is that, starting from an insulator, one cannot get a metal by exciting as mall number of electrons and holes.