Low Energy Electronic States and Triplet Pairing in Layered Cobaltate

The structure of the low-energy electronic states in layered cobaltates is considered starting from the Mott insulating limit. We argue that the coherent part of the wave functions and the Fermi-surface topology at low doping are strongly influenced by spin-orbit coupling of the correlated electrons on the $t_{2g}$ level. An effective $t$-$J$ model based on mixed spin-orbital states is radically different from that for the cuprates, and supports unconventional, pseudospin-triplet pairing.

Figure 1

(a) The $t_{2g}$-orbital degeneracy of ${\mathrm{C}\mathrm{o}}^{4+}(d^5)$ ion is lifted by trigonal distortion and spin-orbit interaction. A hole with pseudospin one-half resides on the $f$ level. Its wave function contains both $E_g^{\prime }$ and $A_{1g}$ states mixed up by spin-orbit coupling. (b) The hopping geometry on the triangular lattice of Co ions. $\alpha \beta (\gamma )$ on bonds should read as $t_{\alpha \beta }=t$, $t_{\gamma \gamma }=-t^{\prime }$, and $\alpha ,\beta ,\gamma \in \{a,b,c\}$ with $a=d_{yz}$, $b=d_{xz}$, $c=d_{xy}$. The $t$ hopping stems from the charge-transfer process via oxygen ions, while $t^{\prime }$ stands for the direct $d$-$d$ overlap.

Figure 2

(a) Quasiparticle dispersion curves in a slave-boson mean-field approximation. (b) Density of states (in units of $1/t$) near the Fermi level. The latter is indicated by thin gray lines. (c) Fermi surface in the Brillouin zone. $\Gamma =(0,0)$, $M=(0,2\pi /\sqrt{3})$, $K=(4\pi /3,0)$. In all the panels, solid (dashed) lines correspond to the doping level $x=0.2$ ($x=0.3$). Parameters used: $t^{\prime }/t=0.8$, $\lambda /t=0.7$, $\Delta /t=1.0$.

Figure 3

(a) Doping $x$ and (b) trigonal field splitting $\Delta$ dependences of the mean-field superconducting transition temperature $T_c$. Parameters used: $t^{\prime }/t=0.8$, $\lambda /t=0.7$, $J_f/t=0.05$.