Superconductor-to-insulator transition in linear arrays of Josephson junctions capacitively coupled to metallic films

We study the low-temperature properties of linear Josephson-junction arrays capacitively coupled to a proximate two-dimensional diffusive metal. Using bosonization techniques, we derive an effective model for the array and obtain its critical properties and phases at $T=0$ using a renormalization-group analysis and a variational approach. While static screening effects given by the presence of the metal can be absorbed in a renormalization of the parameters of the array, backscattering originated in the dynamically screened Coulomb interaction produces a nontrivial stabilization of the insulating ground state and can drive a superconductor-to-insulator transition. We study the consequences for the transport properties in the low-temperature regime. In particular, we calculate the resistivity as a function of the temperature and the parameters of the array, and obtain clear signatures of a superconductor-to-insulator transition that could be observed in experiments.

Figure 1

Scheme of the system under study. The 1DJJA is capacitively coupled to the metallic film, which controls the electromagnetic environment. A gate voltage changes the sheet resistance $R_{\square }$ of the film, modifying the dissipative environment of the 1DJJA.

Figure 2

Schematic phase diagram of the 1DJJA in the $K_0-{\eta }_{\phi ,0}$ plane, obtained from the integration of the RG flow Eqs. 24–27, with the initial parameter ${\lambda }_0\equiv \lambda \left(l=0\right)={10}^{-3}$. An increase of $R_{\square }$ in the 2DEG, and consequently, of the dissipative parameter ${\eta }_{\phi }$, can induce a SIT.

Figure 3

Dimensionless SCHA parameters $\Delta$ and $\zeta$ as a function of $K$, calculated for the parameters ${\eta }_{\phi }=0.01$, $\lambda =0.05$. We obtain nonvanishing values only in the region $K\lesssim 2$ (note the abrupt increase in that region), consistent with the results of the RG analysis.

Figure 4

dc resistivity $\varrho \left(T\right)$ of the 1DJJA, normalized to a “high-temperature” value $\varrho \left(T_0\right)$, as a function of $T/T_0$, calculated for the parameters ${\lambda }_0=0.01$ and ${\eta }_{\phi ,0}=0.01$, and for different values of $K$. A low-temperature upturn of $\varrho \left(T\right)$ signals the formation of the insulating phase.

Figure 5

Resistivity of the 1DJJA (in units of $h/e^{2}a$) as a function of $T/T_0$, calculated for parameters $K_0=2.3$ and ${\lambda }_0=0.01$ and for different values of ${\eta }_{\phi ,0}$. Although in the absence of dissipation, the array is in the superconducting phase, a dissipation-driven SIT occurs upon increasing ${\eta }_{\phi ,0}$, consistent with the results in Fig. 2. The curve $\varrho \left(T\right)\sim T^{2K-3}$ is shown for comparison.