Temperature-dependent conductivity of ultrasmall Josephson junctions

In this paper we analyse the transport properties of Josephson junctions em bedded in an electromagnetic environment caused by pads and leads near to t he junctions. At sufficiently low temperatures we find that the conductivit y of the Josephson junctions at low bias is strongly suppressed due to the Coulomb blockade of Cooper pair tunnelling. At high enough temperatures, th e conductivity of the Josephson junctions is also reduced due to thermal ac tivated phase dip processes. As a consequence, transport of supercurrent wi th maximal conductivity is reached at an intermediate temperature. The depe ndence of various transport regimes on the Josephson energy and the chargin g energy is discussed.