Low-Lying Quasiparticle States and Hidden Collective Charge Instabilities in Parent Cobaltate Superconductors

We report a state-of-the-art photoemission (angle-resolved photoemission spectroscopy) study of high quality single crystals of the ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ series focusing on the fine details of the low-energy states. The Fermi velocity is found to be small ($<0.5\mathrm{eV}\AA$) and only weakly anisotropic over the Fermi surface at all dopings, setting the size of the pair wave function to be on the order of 10–20 nm. In the low-doping regime, the exchange interlayer splitting vanishes and two-dimensional collective instabilities such as 120°-type fluctuations become kinematically allowed. Our results suggest that the unusually small Fermi velocity and the unique symmetry of kinematic instabilities distinguish cobaltates from most other oxide superconductors.

Figure 1

(a) Low-energy electron diffraction image of the cleaved (001) surface exhibits hexagonal symmetry of the cobalt layers. No surface reconstruction is observed. (b) Temperature cycling ($20\mathrm{K}\leftrightarrow 100\mathrm{K}$) was found to have no effect on the momentum distribution of the quasiparticles. Only one peak is observed at $x=0.57$ and lower dopings. (c) The valence band overlaid with band calculations [9] shows narrowing due to electron correlations.

Figure 2

Evolution of low-lying states: Single-particle removal spectra for (a) $x=0.33$, (b) $x=0.57$, and (c) $x=0.80$ along the $\Gamma \mathrm{\text{−}}M$ and $\Gamma \mathrm{\text{−}}K$ cuts. Low-doped samples [(a),(b)] exhibit only one Fermi crossing, while high-doped samples [(c)] show two Fermi crossings. Doping evolution of Fermi surface size ($k_F$) is shown in (d) and Fermi velocity in (e). Fermi velocity increases with increasing doping. Bonding (BB) and antibonding (AB) bands are identified at high doping. Note that the average ($\mathrm{BB}+\mathrm{AB}$) Fermi velocity decreases in approaching $x=1$. (f) Dispersion plots along the $M\mathrm{\text{−}}\Gamma$ and $K\mathrm{\text{−}}\Gamma$ cuts.

Figure 3

Collective instabilities: (a) Momentum distribution of electrons in the $x=0.33$ sample measured in a simultaneous azimuthal scan mode with an energy window of 10 meV. (b) Electron distribution shown in an extended zone scheme. (c),(d) Real-space arrangement of cobalt atoms and 120°-type order and their corresponding reciprocal lattices. (e) Average electron-hole excitation wave vector ($2k_F$) as a function of Na doping $x$. In the low-doping regime, the measured data points (open circles) fall on the 2D Luttinger theorem (solid) line. Horizontal solid lines represent two commensurate instabilities. The 120° order line ($G^{\prime }$) intersects the ($2k_F$) line near $x=0.34$ and the $2G/3$ lattice vector line intersects near $x=0.25$, enclosing the superconducting phase boundaries [14].

Figure 4

(a),(b) A two-band (double) crossing behavior is observed for $x>2/3$. Systematics of data are shown for $x=0.8$ where samples exhibit 3D SDW order. The data can be modeled with two Lorentzians. (c) The Fermi surface topology is compared with interlayer splitting in LDA calculation [9]. The observed FS consumes the area of the corner pockets.