Determination of the Superconductor-Insulator Phase Diagram for One-Dimensional Wires

We establish the superconductor-insulator phase diagram for quasi-one-dimensional wires by measuring a large set of MoGe nanowires. This diagram is roughly consistent with the Chakravarty-Schmid-Bulgadaev phase boundary, namely, with the critical resistance being equal to $R_Q=h/4e^2$. Deviations from this boundary for a small fraction of the samples prompt us to suggest an alternative phase diagram, which matches the data exactly. Transport properties of wires in the superconducting phase are dominated by phase slips, whereas insulating nanowires exhibit a weak Coulomb blockade behavior.

Figure 1

(a) $R$ vs $T$ data (●) for wires in the superconducting phase with fits (lines) to the AL formula given in the text. (b) $R$ vs $T$ for wires in the insulating phase.

Figure 2

(a) $V$ vs $I$ for a wire in the superconducting phase ($L=61\mathrm{nm}$, $T_c=3.3\mathrm{K}$) at $T=1.5$, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.6, 2.8, 3.0, 3.25, 3.5, 4.0, and 5.0 K. (Inset) $R$ vs $T$ for the same sample. (b) $dV/dI$ vs $I$ data (●) for a wire in the insulating phase ($L=140\mathrm{nm}$) at $T=0.3$, 0.5, 0.75, 1.0, 1.5, 2.0, and 2.5 K with fits to Coulomb blockade theory (lines). (Inset) $R$ vs $T$ for the same sample.

Figure 3

Phase diagram of all superconducting (○) and insulating (▪) wires in $L/R_N-L$ space. Dashed line is $R_N=R_Q$ as expected for a CSB transition.

Figure 4

Phase diagram of all superconducting (○) and insulating (▪) wires in $R_N/L-R_N$ space with the separatrix (dashed line) given in the text.