Superconductivity-Related Insulating Behavior

We present the results of an experimental study of superconducting, disordered, thin films of amorphous indium oxide. These films can be driven from the superconducting phase to a reentrant insulating state by the application of a perpendicular magnetic field ($B$). We find that the high-$B$ insulator exhibits activated transport with a characteristic temperature, $T_I$. $T_I$ has a maximum value ($T_I^p$) that is close to the superconducting transition temperature ($T_c$) at $B=0$, suggesting a possible relation between the conduction mechanisms in the superconducting and insulating phases. $T_I^p$ and $T_c$ display opposite dependences on the disorder strength.

Figure 1

Zero magnetic field $\rho$ versus $T$ curves of a single film at two different stages of annealing, Ma1a and Ma1f. Ma1a is insulating with $T_I=4.3\mathrm{K}$. Inset: $\rho$ versus $T^{-1}$ curve for Ma1a (solid line), and the fit to Eq. (1) (dashed line). At low $T$, deviation from the activated behavior is observed. Vertical arrow in the main figure marks $T_c$ ($=1.5\mathrm{K}$) of the superconducting film Ma1f.

Figure 2

$\rho$ versus $B$ isotherms (a) at a low $B$ range for film Ma1f at $T=0.24$, 0.60, 0.78, 0.98, and 1.13 K (b) at a large $B$ range for sample Na1c at $T=0.07$, 0.16, 0.35, 0.62, and 1.00 K. The critical point of the $B$-driven SIT, $B_c$, is indicated by the vertical arrow.

Figure 3

Inset: $\rho$ versus $T^{-1}$ at $B=6$ (squares), 9 (circles), and 12 T (triangles) for sample Na1c. The solids lines are fits to Eq. (1). The lowest $T$ data points do not fit to the Arrhenius behavior. The main figure shows $T_I$, calculated from the fits to Eq. (1), as a function of $B$. $T_I$ has a peak at 9 T. $T_I$ estimates for $4\mathrm{T}>B>14\mathrm{T}$ suffer from large errors since the low-$T$ $\rho$ value is not high enough to ensure activated behavior. The vertical arrow marks $B_c$ ($=0.45\mathrm{T}$), where $T_I=0$. The dashed line is a guide to the eye.

Figure 4

$T_c$s at $B=0$ for several superconducting samples are plotted against $T_I^p$s at the high-$B$ insulating peaks. Each physical sample is marked with a different symbol and samples have been annealed to vary $T_c$. Error bars indicated are typical of most data points.

Figure 5

Experimental phase diagram for $a:\mathrm{InO}$ superconducting thin films. The crosses mark the $B_c$ of each sample at the SIT. The dashed line best fits the $B_c$ data. Empty and filled triangles mark the positions of the $B$-induced insulating peak for samples that, at $B=0$, are insulating and superconducting, respectively.