Quantum Effects in Granular Superconductors

Granular superconductors are strongly inhomogeneous systems consisting of locally superconducting grains in an insulating matrix. In these lectures we will discuss the consequences of the Coulomb interaction on the mesoscopic scale of grains and of dissipative effects in these systems. Throughout we assume that the granular system may be modelled as a network of tunnel junctions which are normal junctions above and Josephson junctions below the transition to local superconductivity at T c l . The lectures are organized as follows: section 2 starts with a discussion of tunneling in non-superconducting granular systems and in particular the behavior of the conductance due to the effects of finite size and charging in small grains. In section 3 we discuss the appearance of local superconductivity within the grains and the Josephson coupling between them. It is shown that both thermal fluctuations and Coulomb effects may lead to a destruction of global superconductivity. The influence of dissipative effects associated with normal electron tunneling is treated in section 4 for single junctions. In section 5 we determine the phase diagram at zero temperature of one and two-dimensional (2 D) networks of quantum Josephson junctions including dissipation. Finally in section 6 we discuss corresponding experiments on artificially created Josephson junction arrays and very thin granular films.