Temperature-dependent conductivity of ultrasmall Josephson junctions

In this paper we analyse the transport properties of Josephson junctions embedded in an electromagnetic environment caused by pads and leads near to the junctions. At sufficiently low temperatures we find that the conductivity of the Josephson junctions at low bias is strongly suppressed due to the Coulomb blockade of Cooper pair tunnelling. At high enough temperatures, the conductivity of the Josephson junctions is also reduced due to thermal activated phase slip processes. As a consequence, transport of supercurrent with maximal conductivity is reached at an intermediate temperature. The dependence of various transport regimes on the Josephson energy and the charging energy is discussed.