High-field termination of a Cooper-pair insulator

We conducted a systematic study of the disorder dependence of the termination of superconductivity, at high magnetic fields $\left(B\right)$, of amorphous indium oxide films. Our lower disorder films show conventional behavior where superconductivity is terminated with a transition to a metallic state at a well-defined critical field, $B_{\mathrm{c}2}$. Our higher-disorder samples undergo a $B$-induced transition into a strongly insulating state, which terminates at higher $B$'s forming an insulating peak. We demonstrate that the $B$ terminating this peak coincides with $B_{\mathrm{c}2}$ of the lower disorder samples. Additionally, we show that, beyond this field, these samples enter a different insulating state in which the magnetic field dependence of the resistance is weak. These results provide crucial evidence for the importance of Cooper-pairing in the insulating peak regime.

Figure 1

$R_{\square }$ vs $B$ obtained from four a:InO films with different disorder, measured at $T$ ranging from 0.035 to 1 K. The highest-disorder sample, H34S03, is insulating at $B=0$ (top). The lowest disordered samples, J069 and J071, were measured in a four-terminal configuration with ac excitation current of 10 nA. The higher-disordered films, GR12H6 and H34S03 were measured in a two-terminal configuration with ac excitation voltages of 100 and $500 \mu \mathrm{V}$, respectively. The inset shows the $B=0$ superconducting transitions of the three superconducting films.

Figure 2

(a) $B_{\mathrm{c}2}$ vs $T$ for low disordered a:InO samples (see Table 1). (b) $B_{\mathrm{c}2}$ vs $T$ in our low-$T$ range for four different low disordered a:InO samples including J036 [see (c)]. The solid lines in (a) and (b) are the BCS-fitting curves [37]. (c) $R_{\square }$ vs $B$ for one of our cleanest a:InO samples, J036, which is similar to J013 and J069 at $T$ from 0.044 to 1.75 K.

Figure 3

Sheet resistance $R_{\square }$ as a function of $T^{-1/3}$ of our highest-disordered superconducting film GR12H6 and the insulating film H34S03 at different magnetic fields, ranging from 15 to 25 T. The data points are extracted from the $R_{\square }$ versus $B$ measurements shown in Fig. 1.