Torque measurements in underdoped Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ single crystals*

We report in-plane and out-of-plane angular-dependent torque measurements on underdoped Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ single crystals both below and above the zero-field superconducting transition temperature $T_{c}(0)$ and in applied magnetic fields $H$ up to 14 T. The out-of-plane torque data show that a diamagnetic signal persists into the normal state, which is consistent with previous reports on Bi$_2$Sr$_2$Ca$_2$CuO$_{8+\delta}$. These data also reveal that the vortex matter in the superconducting state has lower dimensionality compared to the one in the normal state. Furthermore, in-plane torque measurements show that the presence of vortices above $T_c(0)$ destroys the phase coherence of the Cooper pairs.