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Coherent quasi-particles-to-incoherent hole-carriers crossover in underdoped cuprates

In underdoped cuprates, only a portion of the Fermi surface survives as Fermi arcs due to pseudogap opening. In hole-doped La$_{2}$CuO$_4$, we have deduced the "coherence temperature" $T_{coh}$ of quasi-particles on the Fermi arc above which the broadened leading edge position in angle-integrated photoemission spectra is shifted away from the Fermi level and the quasi-particle concept starts to lose its meaning. $T_{coh}$ is found to rapidly increase with hole doping, an opposite behavior to the pseudogap temperature $T^*$. The superconducting dome is thus located below both $T^*$ and $T_{coh}$, indicating that the superconductivity emerges out of the coherent Fermionic quasi-particles on the Fermi arc. $T_{coh}$ remains small in the underdoped region, indicating that incoherent charge carriers originating from the Fermi arc are responsible for the apparently metallic transport at high temperatures.