The Mott criterion: So simple and yet so complex

Abstract

September 30, 2015 marks the 110th anniversary of the birth of the famous English physicist N. F. Mott. This article is dedicated to his memory. Here we consider the problem of metal-insulator transition. It is shown that the Mott criterion $a_{B}(n_{c})^{1/3} \approx 0.25$ is applicable not only to heavily doped semiconductors, but also to many other materials and systems, including strongly correlated transition-metal and rare-earth-metal compounds, such as vanadium oxides. A special emphasis is placed to the 'paramagnetic metal - antiferromagnetic insulator' transition in $V_{2}O_{3}$ doped with chromium. In Supplement we also briefly consider the history and state of the art of the Mott transition problem.