Figure 1

(a) $dV/dI$ vs $I$ at 20 mK across the metal-insulator boundary for a Ta film with $T_c=0.23\mathrm{K}$, adapted from Ref. 8. (b) Current biased $I\mathrm{\text{−}}V$ curves of sample Ta 1 at 40 mK and the indicated $B$. (c) Our method of $I\mathrm{\text{−}}V$ measurements is illustrated. (d) The $T$ dependence of $\rho$ for sample Ta 2 at $B=0–1.0\mathrm{T}$ with a 0.1 T interval and 3.0 T, measured at 7 Hz with a current amplitude of 1 nA. The solid lines are to indicate the superconducting phase in the low $T$ limit, the dashed lines the metallic phase, and the dotted lines the insulating phase. (e) $I\mathrm{\text{−}}V$ curves in log-log scale for sample Ta 3. Solid triangles (open circles) are for the current increasing (decreasing) branch. The data density is reduced to make individual symbols visible. The arrow marks the critical current $I_c$ and voltage $V_c$.Reuse & Permissions

Figure 2

(a) $I\mathrm{\text{−}}V$ curves of sample Ta 4 at $B=0$ and the indicated $T$. Open (solid) circles are for the current increasing (decreasing) branch. (b) $T$ dependence of $\rho$ for sample Ta 4 at $B=0$. The arrow is to indicate the temperature $T^{*}$ where the hysteresis vanishes. (c) The $I\mathrm{\text{−}}V$ of the sample Ta 5 at $B=0$. The temperature of each trace is, from the top, 1.000, 0.994, 0.992, 0.990, 0.988, 0.984, and 0.976 K. (d) The $T$ dependence of $\rho$ for sample Ta 5 at $B=0$.Reuse & Permissions

Figure 3

(a) The $B$ dependence of the critical power $P_c=I_c\times V_c$ for sample Ta 3 at 0.5 K. The dashed line is to guide the eye. (b) $P_c$ vs $B$ plot for sample Ta 5 at 0.970 K.Reuse & Permissions

Figure 4

(a) An example of $V\mathrm{\text{−}}t$ trace at $I=24.5\mu \mathrm{A}$. The solid line is a fit to the exponential function shown. The dashed line is a fit to a logarithmic $t$ dependence for the first 3 s. (b) $\tau$ vs $I$ plot at the indicated $B$ and $T$. Solid (open) circles are for the current increasing (decreasing) branch. The dashed lines are to guide the eye. Inset: The slope of $I\mathrm{\text{−}}V$ curves in log-log scale at the same $B$ and $T$. (c) $\tau \mathrm{\text{−}}I$ plot at $B=0$. The temperature of each trace is, from the top, 0.984, 0.988, 0.990, 0.992, 0.994, and 1.000 K. Each trace is vertically shifted successively. For the bottom four traces, only the current increasing branch is shown. Inset: $d(\log V)/d(\log I)$ is plotted at the same $T$ and $B$. Each trace is vertically shifted successively.Reuse & Permissions