Competition between superconductivity and weak localization in metal-mixed ion-implanted polymers

We study the effects of varying the preimplant film thickness and implant temperature on the electrical and superconducting properties of metal-mixed ion-implanted polymers. We show that it is possible to drive a superconductor-insulator transition in these materials via control of the fabrication parameters. We observe peaks in the magnetoresistance and demonstrate that these are caused by the interplay between superconductivity and weak localization in these films, which occurs due to their granular structure. We compare these magnetoresistance peaks with those seen in unimplanted films and other organic superconductors and show that they are distinctly different.

Figure 1

(Color online) (a) The normalized four-terminal resistance, $R\left(T\right)/R\left(T_{\text{max}}\right)$, versus temperature, $T$, for $200\text{Å}$ Sn:Sb films implanted at 77 K (solid blue line) and 300 K (dashed red line). The critical temperature, $T_c$, and transition width, $\Delta T$, are 3.0 and 0.63 K for the 77 K sample, and 2.9 and 1.0 K for the 300 K sample. The higher $R\left(T\right)$ for $T>T_c$, reduced $T_c$ and larger $\Delta T$ point to a higher disorder for the 300 K sample. (Inset) A photograph of a typical ion-implanted sample. Panels (b) and (c) show the resistance, $R$, versus applied perpendicular magnetic field, $B$, at temperatures, $T$, ranging between 1.5 and 4.0 K for the 77 K and 300 K samples, respectively. At $T=1.5\text{K}$, the critical field, $B_c$, and transition width, $\Delta B$, are 0.33 and 0.19 T for the 77 K sample and 0.31 and 0.24 T for the 300 K sample, respectively. The lower $B_c$ and larger $\Delta B$ again confirm the higher disorder in the 300 K sample.

Figure 2

The critical field, $B_c$, versus the angle, $\theta$, of the field relative to the film normal for the $200\text{Å}$ sample implanted at 77 K. The line is a fit of Eq. (1) to the experimental data, and the quality of this fit demonstrates that this sample is two dimensional.

Figure 3

The two-terminal resistance $R$ versus $T$ measured (a) along the $x$ direction and (b) along the $y$ direction for the $100\text{Å}$ sample implanted at 300 K. These two measurements along perpendicular edges of the sample utilize a common contact.

Figure 4

(Color online) (a) An Arrhenius plot of $\text{ln}{\sigma }_y$ versus $1/T$, where ${\sigma }_y=R_y^{-1}$ and (b) a plot of $R_y$ versus $\text{ln}T$ for the data presented in Fig. 3b. An Arrhenius model only fits the data in (a) for $T<4\text{K}$ and gives a value for the energy gap $\Delta /k_B\le 1\text{K}$. In contrast, the linear dependence in (b) suggests that the insulating behavior in this sample is due to weak localization.

Figure 5

(Color online) (a) $R_x$ and (b) $R_y$ as a function of applied field, $B$, at several different temperatures for the $100\text{Å}$ sample implanted at 300 K. The $R_x$ data has a deep minima centered on $B=0$ that does not reach zero, indicating that the superconductivity in this sample is local and not global. In contrast, the $R_y$ data shows a broad negative magnetoresistance (peak) that diminishes with temperature, consistent with weak localization. The superimposed positive magnetoresistance feature (minima) is due to local superconductivity in the sample and has the same width as the minima in (a). $B_{\text{peak}}$ and $\Delta R_y$ for $T=1.6\text{K}$ are indicated in (b).

Figure 6

The peak resistance, $\Delta R_y=R_y\left(T,B_{\text{peak}}\right)-R_y\left(T,B_{\text{max}}\right)$, for data in Fig. 5b (the high-resistance direction of the $100\text{Å}$ sample implanted at room temperature) as a function of temperature. ($B_{\text{max}}=3.5\text{T}$ is the maximum field studied.) The behavior of the peaks does not change significantly at the temperature where the resistive transition is observed in the $x$ direction (marked in the figure as “$T_{c,x}$ sample”) and the peaks continue up until at least the $T_c$ of bulk tin, also marked in the figure, consistent with a granular structure.

Figure 7

(Color online) Four-terminal magnetoresistance $R$ at various temperatures between 1.3 and 5.0 K for the unimplanted $200\text{Å}$ sample. Of particular note are the peaks in the magnetoresistance on the normal side of the field-induced superconducting-normal transition (cf. Figs. 1 and 2 in Ref. 29). $B_{\text{peak}}$ and $\Delta R$ for $T=3.5\text{K}$ are indicated in (b).

Figure 8

(a) Location of the peaks in magnetic field, $B_{\text{peak}}$, and (b) the peak resistance defined as $\Delta R=R\left(T,B_{\text{peak}}\right)-R\left(T,B_{\text{max}}\right)$, where $B_{\text{max}}=1.0\text{T}$, for data in Fig. 7 as a function of temperature, for comparison with data in Refs. 29, 30.