Coulomb Interaction and First-Order Superconductor-Insulator Transition

The superconductor-insulator transition (SIT) in regular arrays of Josephson junctions is studied at low temperatures. We derived an imaginary time Ginzburg-Landau-type action properly describing the Coulomb interaction. The renormalization group analysis at zero temperature $T=0$ in the space dimensionality $d=3$ shows that the SIT is always of the first order. At finite $T$, a tricritical point separates the lines of the first- and second-order phase transitions. The same conclusion holds for $d=2$ if the mutual capacitance is larger than the distance between junctions.

Figure 1

Phase diagram of the JJA. The solid and double lines are the second and first order, respectively. Insets: (a) the two parameter RG flow for 3D JJA; (b) two parameter RG flow for 2D arrays with logarithmic interaction; (c) the projection of three parameter RG flow for the logarithmic and “moderate” Coulomb interaction $g_1(l=0)=0.65$.