Characterizing the insulator adjacent to the superconductor in Bi${}_2$Sr${}_{2-x}$La${}_x$CuO${}_{6+\delta }$ ($x=0.3$)

The time-averaged and low–frequency noise transport properties were investigated in the vicinity of the superconductor–insulator transition for a Bi${}_2$Sr${}_{2-x}$La${}_x$CuO${}_{6+\delta }$ ($x=0.3$) thin film. The results are consistent with a superconductor (metal) embedded in a strong insulator, the latter showing two-dimensional variable range hopping properties. The weak insulator behavior – if any – is attributed to the metallic inclusions only.