Phase transitions induced by a magnetic field in graphite

The subject of this chapter is the the so-called quantum limit of a three-dimensional metal, which is attained at a sufficiently strong magnetic field with only a few occupied Landau levels. Graphite, which has a small Fermi surface, is an ideal candidate to explore this limit. A magnetic field of 7.5T confines the carriers to their lowest Zeeman-split Landau level. In the early 1980s, a sharp increase in the in-plane magneto-resistance of graphite at high magnetic field (typically B >20 T) was discovered and attributed to a phase transition induced by the magnetic field. Numerous studies followed, and this phase transition is generally believed to be a density-wave instability triggered by the one-dimensional nature of the electronic spectrum and the enhancement of the electron-electron interactions in the quantum limit. Recent transport measurements up to 80T revealed that not one but two successive field-induced instabilities are present. After a brief description of the quantum limit, we review the rich and complex field phase diagram of graphite as a function of temperature and magnetic field. We discuss possible electronic states associated with these instabilities and end the chapter with a study of the quantum limit in other dilute metals, such as bismuth or lightly-doped semiconductors.