Two distinct superconducting fluctuation diamagnetisms in Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$

Superconducting fluctuations was studied through the angular dependent torque measurements on a series of Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (BSLCO) single crystals. Two distinct superconducting fluctuation diamagnetism were observed: one is the superconducting thermal fluctuation, with a boundary close to the superconducting phase boundary; while another one, up to the temperature as high as about 180 K, showing maximum signal in the sample with hole carrier density $p=0.125$, could be due to preformed pairs. In addtion, we observed linearly temperature dependent paramagnetic torque signals in BSLCO samples, possibly a result of quantum criticality from a quantum critical point at the optimal doping.