Magnetic-field-driven superconductor-insulator transition in underdoped La$_{2-x}$Sr$_x$CuO$_4$

We use magnetotransport measurements to probe the magnetic-field-driven superconductor-insulator transition in both an MBE-grown thin film ($x=0.07$ and $T_c=4$~K) and a single crystal ($x=0.06$ and $T_c=6$~K) underdoped La$_{2-x}$Sr$_{x}$CuO$_4$ samples in $T$ range of 0.1--30~K and fields up to 35~T. Surprisingly, it is possible to perform scaling analysis in both low- and high-temperature regions, where two different scaling exponents and scaling functions are obtained. These results and a detailed analysis of the temperature dependence of the resistivity suggest that a possible intermediate state exists between the superconducting state at zero field and the insulating state at high fields. This intermediate state may be related to the existence of a large region with superconducting fluctuations in ($T,H$) parameter space. Furthermore, the insulating state in high fields shares similar 2D variable-range hopping behavior as non-superconducting samples with lower doping.