  For doped two-dimensional Mott insulators in their normal state, the
challenge is to understand the evolution from a conventional metal at high
doping to a strongly correlated metal near the Mott insulator at zero doping.
To this end, we solve the cellular dynamical mean-field equations for the
two-dimensional Hubbard model using a plaquette as the reference quantum
impurity model and continuous-time quantum Monte Carlo method as impurity
solver. The normal-state phase diagram as a function of interaction strength
$U$, temperature $T$, and filling $n$ shows that, upon increasing $n$ towards
the Mott insulator, there is a surface of first-order transition between two
metals at nonzero doping. That surface ends at a finite temperature critical
line originating at the half-filled Mott critical point. Associated with this
transition, there is a maximum in scattering rate as well as thermodynamic
signatures. These findings suggest a new scenario for the normal-state phase
diagram of the high temperature superconductors. The criticality surmised in
these systems can originate not from a T=0 quantum critical point, nor from the
proximity of a long-range ordered phase, but from a low temperature transition
between two types of metals at finite doping. The influence of Mott physics
therefore extends well beyond half-filling.
