Introductory Chapter

Abstract

This book deals with the recent advancements in two topical subjects of condensed matter physics, superfluidity, and superconductivity. In principle, the two phenomena are very similar because they occur as a function of temperature and in the presence of the vanishing of a physical quantity marking a phase transition below a critical temperature. A superfluid is a fluid having zero viscosity while a superconductor is a conductor with zero resistance. Superfluidity occurs in liquid helium and in ultracold atomic gases while superconductivity is typical of elements like niobium and lead, of some niobium alloys, or compounds like yttrium barium and copper oxide and compounds containing iron. Regarding the latter, since the first discoveries, the interplay between superconductivity and magnetism has also been investigated finding that the magnetic state of superconductors can be described as ideal diamagnetism. The behaviour toward the external magnetic field allows to distinguish between firstand second-type superconductors. Instead, the critical temperature in correspondence of which superconductivity arises allows to distinguish between lowand high-critical temperature superconductors. After their initial discovery, superfluidity was explained as a quantum mechanical phenomenon, while superconductivity was described first according to a phenomenological and classical theory and only in a second moment in terms of a microscopic quantum mechanical theory.