Magnetic oscillations in multi-band conductors

Quantum oscillations of the magnetization in conductors as function of an applied external magnetic field (de Haas-van Alphen effect) are considered as a fundamental tool to probe the existence and structure of Fermi surfaces and from which effective masses can be measured. The theory of these oscillations is based on semi-classical methods. One physical interpretation of this effect is directly linked to the geometrical properties of Fermi surfaces as well as the quasi-particle spectrum. The underlying theory is in fact an extension of the classical cyclotron motion for free electrons to the case of interacting fermions in solids. Organic conductors represent a rich class of almost two-dimensional conductors where electronic properties can be studied using experimental pulsed fields (several tens of Tesla). In this review we present theoretical developments based on experiments where magnetic oscillations show evidence of complex Fermi surfaces possessing multiple sheets connected by quantum tunneling effect (magnetic breakdown).