In a class of materials known as strongly correlated electron systems, the standard model of electrons in solids breaks down because strong electronic interactions are present. When strong enough, this interaction forces electrons, which in ordinary metals behave as delocalised waves, to localise and behave as particles. Those materials show a luxuriant array of fascinating new states of matter in which magnetic, charge, orbital and structural orders compete for the ground state. In addition to being one of the most complex and greatest intellectual challenges of modern science, some of those materials also have great technological potential : cuprate superconductors and high thermoelectric power materials provide new technological solutions to growing problems of energy storage, transportation and production.

We study high-Tc cuprate superconductors. Those materials have the highest known superconducting critical temperature at ambient pressure. Their phase diagram features several baffling mysteries. The basic questions we are trying to answer are: what is the organizing principle of the phase diagram of high-Tc cuprates? what is the mechanism for high-Tc superconductivity? We use high magnetic fields to suppress superconductivity in order to reach and determine the nature of the electronic interactions at play in the phase diagram and in the pairing mechanism of those systems.

A magnetic field can induce unusual electronic ground states, such as the quantum Hall effect for a twodimensional
(2D) electron gas. In the limit where only the n = 0 Landau level is populated (the so-called quantum limit), electron interactions are responsible for the appearance of a variety of many-body ground states such as the fractional quantum Hall effect. In contrast to the 2D case, the electrons in the quantum limit of a three-dimensional (3D) gas has been poorly explored. We study semimetals, such as graphite, where the quantum limit can be achieved with current magnet technologies.