The magnetic fluctuations associated with a quantum critical point (QCP) are widely believed to cause the non-Fermi liquid behaviors and unconventional superconductivities, for example, in heavy fermion systems and high temperature cuprate superconductors. Recently, superconductivity has been discovered in iron-based layered compound with =26 K\cite{yoichi}, and it competes with spin-density-wave (SDW) order\cite{dong}. Neutron diffraction shows a long-rang SDW-type antiferromagnetic (AF) order at $\sim 134$ K in LaOFeAs\cite{cruz,mcguire}. Therefore, a possible QCP and its role in this system are of great interests. Here we report the detailed phase diagram and anomalous transport properties of the new high-Tc superconductors discovered by us\cite{chenxh}. It is found that superconductivity emerges at 0.07, and optimal doping takes place in the 0.20 sample with highest 54 K. While increases monotonically with doping, the SDW order is rapidly suppressed, suggesting a QCP around 0.14. As manifestations, a linear temperature dependence of the resistivity shows up at high temperatures in the regime, but at low temperatures just above in the regime; a drop in carrier density evidenced by a pronounced rise in Hall coefficient are observed, which mimic the high- cuprates. The simultaneous occurrence of order, carrier density change and criticality makes a compelling case for a quantum critical point in this system.

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