Missing Quasiparticles and the Chemical Potential Puzzle in the Doping Evolution of the Cuprate Superconductors

The evolution of ${\mathrm{C}\mathrm{a}}_{2-x}{\mathrm{N}\mathrm{a}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_2{\mathrm{C}\mathrm{l}}_2$ from Mott insulator to superconductor was studied using angle-resolved photoemission spectroscopy. By measuring both the excitations near the Fermi energy as well as nonbonding states, we tracked the doping dependence of the electronic structure and the chemical potential with unprecedented precision. Our work reveals failures in the standard weakly interacting quasiparticle scenario, including the broad line shapes 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 wave vector with the chemical potential.