  The evolution of Ca$_{2-x}$Na$_{x}$CuO$_{2}$Cl$_{2}$ from Mott insulator to
superconductor was studied using angle-resolved photoemission spectroscopy. By
measuring both the excitations near the Fermi energy as well as non-bonding
states, we tracked the doping dependence of the electronic structure and the
chemical potential with unprecedented precision. Our work reveals failures in
the conventional quasiparticle theory, including the broad lineshapes of the
insulator and the apparently paradoxical shift of the chemical potential within
the Mott gap. To resolve this, we develop a model where the quasiparticle is
vanishingly small at half filling and grows upon doping, allowing us to unify
properties such as the dispersion and Fermi wavevector with the behavior of the
chemical potential.
