Doping Controlled Superconductor-Insulator Transition in ${\mathrm{Bi}}_2{\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$

We show that the doping-controlled superconductor-insulator transition (SIT) in a high critical temperature cuprate system (${\mathrm{Bi}}_2{\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$) exhibits a fundamentally different behavior than is expected from conventional SIT. At the critical doping, the sheet resistance seems to diverge in the zero-temperature limit. Above the critical doping, the transport is universally scaled by a two-component conductance model. Below, it continuously evolves from weakly to strongly insulating behavior. The two-component conductance model suggests that a collective electronic phase-separation mechanism may be responsible for this unconventional SIT behavior.

Figure 1

Doping-controlled SIT over a very small range of doping levels. (a) and (b) are the same data plotted on different horizontal scales. Note that each curve is indexed by a number 1 through 13 in the order of increasing doping.

Figure 2

Scaling of superconducting curves. Each index represents the corresponding curve from Fig. 1b. (a) Rescaled plot of curves 6–13 from Fig. 1b. (b) The two-component scaling function plotted together with curves 3–13. Curves 6–13 are used to obtain the scaling function. Curves 4–5 are fit to the obtained scaling function with $T_p$ and $R_p$ as the fitting parameters. As for curve 3, any choice of $T_p$ below $\sim 0.5\mathrm{K}$ gives reasonably good fitting; three curves with $T_p=0.1\mathrm{K}$, 0.01 K, and 0.001 K are shown from left to right as examples. (c) $R_p$ vs $T_p$ for the 10 superconducting curves (4–13). The solid line represents the best fitting for the 8 measured data points (curves 6–13), which corresponds to $R_p=1.72T_p^{-0.149}$. (d) $T_p$ vs doping. Conductance at 150 K is also shown on the top axis. The solid line, $T_p=4.02\times {10}^5\times (d-d_c{)}^{1.8}$, is the best fitting for $d>d_c$.

Figure 3

$R_S$ vs $1/T^{1/3}$ for insulating doping levels. Linearity in this plot implies 2D-VRH. Curves 1 and 2 from Fig. 1 are reproduced for comparison. Inset shows how curve $a$ compares with other curves from Fig. 1.

Figure 4

($T,d$) phase diagram near the critical doping. $T_p$ and $T_{\min }$ are determined by the resistance data, and $T_c$ is evaluated as $0.065\times T_p$ according to the scaling analysis. Fitting curves for each of these crossover temperatures are plotted as well. Unlike other crossover temperatures, $T_i$ is only marginally defined in our experiment.