  By using a 60 T magnetic field to suppress superconductivity in La2-pSrpCuO4,
(LSCO) we reveal an anomalous peak in the Hall number, located at optimum
doping and developing at temperatures below the zero-field superconducting
transition temperature, Tc. The anomaly bears a striking resemblance to
observations in Bi2Sr2-xLaxCuO6+delta (BSLCO) [F. F. Balakirev et al., Nature
(London) 424, 912 (2003)], suggesting a normal state phenomenology common to
the cuprates that underlies the high-temperature superconducting phase. The
peak is ascribed to the transformation of the "Fermi arcs" into a conventional
FS, the signature of a Fermi surface reconstruction associated with a quantum
phase transition (QPT) near optimum doping and co-incident with the collapse of
the pseudogap state.
