Measurement of a Superconducting Energy Gap in a Homogeneously Amorphous Insulator

We present tunneling spectroscopy measurements that directly reveal the existence of a superconducting gap in the insulating state of homogenously disordered amorphous indium oxide films. Two films on both sides of the disorder induced superconductor to insulator transition show the same energy gap scale. This energy gap persists up to relatively high magnetic fields and is observed across the magnetoresistance peak typical of disordered superconductors. The results provide useful information for understanding the nature of the insulating state in the disorder induced superconductor to insulator transition.

Figure 1

Top: Temperature dependence of $R_{\square }$ for sample $S$. The corresponding AlO barrier resistance is $1\mathrm{M}\Omega$. Bottom: Temperature dependence of $R_{\square }$ for sample $I$ (heavy red line) and a fit to Eq. (1) (light black line) from which $T_0$ and $R_0$ are extracted. The corresponding AlO barrier resistance is $0.7\mathrm{M}\Omega$. Inset: $\ln (R)$ versus $1/T$ for sample $I$.

Figure 2

Normalized tunneling density of state obtained at 1 K for sample $I$ (full red circles) and sample $S$ (empty blue circles). The lines are fits to the BCS expression of Eq. (2) for sample $I$ (dashed red line) and sample $S$ (solid blue line). Inset: Raw $dI/dV$ versus $V$ data for sample $I$ at $H=0$ (heavy red line) and $H=11\mathrm{T}$ (light black line).

Figure 3

(a) Normalized tunneling density of state obtained at $T=0.5\mathrm{K}$ and at different magnetic fields for sample $I$. Inset: The corresponding magnetoresistance. (b) Normalized tunneling density of state obtained at 0.1 K and at different magnetic fields for sample $S$. Upper inset: The corresponding magnetoresistance for sample $S$. Lower inset: $\Delta$ versus $H$ for sample $I$ (empty black squares) and sample $S$ (full black circles), obtained from a fit to the BCS expression of Eq. (2).

Figure 4

Left: Tunneling density of state versus $V$ [linear scale (left) and logarithmic scale (right)] obtained at 1 K and 11 T for sample $I$ (full red circles) and for sample $S$ (blue line).