Upper critical field from normal state fluctuations in Bi$_2$Sr$_2$CuO$_{6+\delta}$

The in-plane magnetoresistance of an epitaxial Bi$_2$Sr$_2$CuO$_{6+\delta}$ thin film was systematically investigated as a function of doping, above $T_c$. The orbital magnetoconductance is used to extract the crossover field line $H_{c2}^*(T)$ in the fluctuation regime. This field is found in good agreement with the upper critical field obtained from resistivity data below $T_c$, and exhibits a similar upward curvature, thus pointing toward the existence of a critical correlation length. The consequences regarding the nature of the resistive transition are discussed.