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.

Figure 1

(a) Valence band spectra for $x=0$, 0.05, 0.10, and 0.12 compositions at $\mathbf{k}=(0,0)$ and $(\pi ,\pi )$. O $2p_z$ and O $2p_{\pi }$ states are marked by triangles and circles, respectively. (b) Shifts of the O $2p_z$ and O $2p_{\pi }$ peaks shown on an expanded scale. (c) Doping dependence of $\mu$ determined from (b). (d) Valence band at $\mathbf{k}=(\pi /2,\pi /2)$, showing the lower Hubbard band ($A$) on an expanded scale.

Figure 2

(a) Illustrations of the coherent quasiparticle scenario (CQS) and the Franck-Condon broadening (FCB) model. (b) ${\mathrm{C}\mathrm{a}}_2{\mathrm{C}\mathrm{u}\mathrm{O}}_2{\mathrm{C}\mathrm{l}}_2$ at $\mathbf{k}=(\pi /2,\pi /2)$ with fits to a Lorentzian spectral function (dashed) and Gaussian (red or gray). $A$ and $B$ denote the peak maximum and the onset of spectral weight, respectively. Comparison with ${\mathrm{S}\mathrm{r}}_2{\mathrm{R}\mathrm{u}\mathrm{O}}_4$ is shown (thin black). Upper inset shows photoemission spectra from ${\mathrm{H}}_2$, after Ref. 26. (c) Dispersion of $A$ and $B$ along $(0,0)-(\pi ,\pi )$, along with experimental values for $\mu$ (lines).

Figure 3

(a)–(d) EDC spectra from $x=0$, 0.05, 0.10, and 0.12 from $(0.2\pi ,0.2\pi )$ to $(0.72\pi ,0.72\pi )$ with hump positions marked by open symbols and ${\mathbf{k}}_{\mathrm{F}}$ shown in bold. Data are plotted on a relative energy scale referenced to the shift in $\mu$ shown in Fig. 1c.

Figure 4

(a) Summary of hump (symbols) and MDC dispersions (lines) from Fig. 3. (b) Doping dependence of spectra from ${\mathbf{k}}_{\mathrm{F}}$ along with a schematic of the proposed distribution of coherent (blue or dark gray) and incoherent (pink or light gray) spectral weight.