Spin Polaron Theory for the Photoemission Spectra of Layered Cobaltates

Recently, strong reduction of the quasiparticle peaks and pronounced incoherent structures have been observed in the photoemission spectra of layered cobaltates. Surprisingly, these many-body effects are found to increase near the band-insulator regime. We explain these unexpected observations in terms of a novel spin-polaron model for ${\mathrm{CoO}}_2$ planes, which is based on a fact of the spin-state quasidegeneracy of ${\mathrm{Co}}^{3+}$ ions in oxides. Scattering of the photoholes on spin-state fluctuations suppresses their coherent motion. The observed “peak-dip-hump” type line shapes are well reproduced by the theory.

Figure 1

(a) A conventional $t$ hopping within the low-spin $t_{2g}$ states. (b) $\tilde{t}$-hopping process creating an excited ${\mathrm{Co}}^{3+}$ $S=1$ state. Because of the Hund coupling $J_H$, this state is quasidegenerate to the $t_{2g}^6$ $S=0$ state; i.e., the excitation energy $E_T\sim 10Dq-2J_H$ is low. In terms of Eq. (1), a fermionic hole moves to the left leaving behind $\mathcal{T}$ excitation. (c) Bond directions $a$, $b$, and $c$ in the triangular lattice of Co ions and $\tilde{t}$-coupled orbitals on these bonds. (d) Self-energy of the $\mathcal{T}$ excitation. (e) Self-energy of the holes in a self-consistent Born approximation.

Figure 2

Comparison of the analytical results at 10% doping (left) and from exact diagonalization (right). (a) Spectral functions and a quasiparticle weight $Z$ obtained from Eqs. (2, 5) with bare $E_T=1.2t$ (renormalized to ${\tilde{E}}_T/t\approx 1$ by interactions) and (b) the corresponding density of states $N(E)$. The incoherent structure dominates $N(E)$. A peak around $2t$ corresponds to the van Hove singularity smeared by interaction effects. (c) Spectral functions from exact diagonalization at $E_T/t=1$. (d) The 7-site cluster in direct space (the dashed line defines the supercell) and in reciprocal space (full line is the Brillouin zone boundary). The allowed $\mathbf{k}=\Gamma$, $X$ points are indicated by • and $\circ$.

Figure 3

Intensity map of the spectral density $A(\mathbf{k},E)$ of the ${\mathrm{Co}}^{4+}$ holes along the $M\mathrm{\text{−}}\Gamma \mathrm{\text{−}}K$ path in the Brillouin zone calculated at 30% doping and $E_T=2t$. As the hole energy reaches the renormalized spin-excitation energy ${\tilde{E}}_T$, the qp peak broadens and its weight is transferred to a broad, incoherent structure. This results in a “peak-dip-hump” profile of $A(\mathbf{k},E)$ seen also in Fig. 2. The top of the smoothed hump structure is indicated by triangles. The dashed line shows the bare dispersion. The Fermi surface is shown in the inset.

Figure 4

Top panel: Full energy width at half maximum of the quasiparticle peak along the $M\mathrm{\text{−}}\Gamma$ dispersion curve (see bottom-right panel) plotted as a function of the binding energy. The part from $k_F$ to $M$ is accessible by ARPES experiments. Strong qp damping below $\sim -1.4t$ is due to a scattering on $S=1$ excitations. The spectral weight of the qp peak obtained by a direct integration is indicated by squares. When damping is small, it coincides with a conventional qp residue $(1-\partial {\Sigma }^{\prime }/\partial \omega {)}^{-1}$. Lower panel: The $\mathcal{T}$-exciton spectral function (left), and renormalized hole dispersion (right).