Abstract
Since the discovery of the organic superconductivity more than 10 years ago with a critical temperature (TS) of 1 K in quasi one dimensional (1D) conductors based on the tetramethyltetraselenafulvalene molecule, more than 40 organic superconductors are now known, achieving TS up to about 13 K. These salts are made of π quasi-planar donors or acceptors, orbitals of which overlap very anisotropically. As a consequence of the 1D or 2D anisotropy of the electron gas, the superconducting ground state competes with charge or spin density wave ground states and the electronic properties are strongly influenced by the occurrence of order-disorder transitions involving molecular orientational or conformational degrees of freedom. In this framework we review the present understanding of the physical properties of the main families of low dimensional organic superconductors and we compare their physical features with those shown by the family of 3D fullerenes exhibiting TS higher than 30 K.