Dimensional crossover in the electronic structure of (Bi,Pb)$_2$(Sr,La)$_2$CuO$_{6+\delta}$

The hole-concentration $(p)$ dependence of the 3D energy- momentum ($\varepsilon -{\mbox{\boldmath $k$}}$) dispersion in Bi2201 was investigated by ARPES. We observe a significant $\varepsilon - k_z$ dispersion ($\sim$10 meV wide) around $(\pi,0)$ in a heavily overdoped sample ($T_c \le 0.5$ K). This $\varepsilon - k_z$ dispersion shrinks with decreasing $p$, and is not observed in lightly overdoped and optimally doped samples ($T_c = 21$ K and 35 K, respectively) indicating a crossover from a 3D to 2D electronic structure.