Investigating the superconductor-insulator transition in thin films using drag resistance: Theoretical analysis of a proposed experiment

The magnetically driven superconductor-insulator transition in amorphous thin films (e.g., InO and Ta) exhibits several mysterious phenomena, such as a putative metallic phase and a huge magnetoresistance peak. Unfortunately, several conflicting categories of theories, particularly quantum-vortex condensation, and normal region percolation, explain key observations equally well. We present a experimental setup, an amorphous thin-film bilayer, where a drag resistance measurement would clarify the role quantum vortices play in the transition, and hence decisively point to the correct picture. We provide a thorough analysis of the device, which shows that the vortex paradigm gives rise to a drag with an opposite sign and orders of magnitude larger than the drag measured if competing paradigms apply.

Figure 1

(a) A typical MR curve of amorphous thin film superconductors. As the magnetic field $B$ increases, the superconducting phase is destroyed, and a possible metallic phase emerges. After which the system enters an insulating phase, where the MR reaches its peak. The resistance drops down and approaches normal state value as $B$ is further increased. (b) Our proposed bilayer setup for the drag resistance measurement. A current bias $I_1$ is applied in one layer, and a voltage $V_2$ is measured in the other layer. The drag resistance $R_D$ is defined as $R_D=V_2/I_1$.

Figure 2

Drag resistance $R_D$ (in Ohms) between two identical films as in Fig. 2b of Ref. 5 (a) vs magnetic field $B$, according to the vortex picture (Ref. 10) (log scale); (b) vs normal metal percentage $p$ (corresponding to magnetic field), according to the percolation picture (Ref. 12). The drag resistance in (a) has been smoothened to avoid discontinuity at the boundary between the metallic and the insulating phase. Center-to-center layer separation $a=25\text{nm}$, temperature $T=0.07\text{K}$ and 0.35 K. Insets: single-layer magnetoresistance (MR, log scale) reproduced in each theory. The parameters are tuned to make the MR resemble the experimental data in Fig. 2b of Ref. 5. In the quantum vortex picture, $R_D$ has a peak at the steepest point $\left(\sim 8\text{T}\right)$ of the MR, which is due to the fact that $R_D$ is proportional to the square of the slope of the MR in the small magnetic field side of the peak. Also, $R_D$ is larger at lower temperature, because the MR curve is then much steeper. Carrying out the experiments at even lower temperatures may further enhance the vortex drag effect. In the percolation picture, the sign of the voltage drop of the passive layer is opposite to that of the driving layer, and the maximum magnitude value of $R_D$ is much smaller, $\sim {10}^{-12}\Omega$.