Unconventional pairing in a weakly doped antiferromagnet on the honeycomb lattice:: Mechanism of symmetry selection

We discuss the mechanism of pairing-symmetry selection in the weakly electron-doped t-J model on the honeycomb lattice. Our analysis is motivated by some recent suggestions that due to charge ordering, which may take place in the unconventional superconductor NaxCoO2 center dot yH(2)O at doping levels near x=1/3, the physics of CoO2 planes may be effectively described in terms of a model for a weakly electron-doped antiferromagnet on the honeycomb lattice. By applying the so-called string picture, we demonstrate that spin fluctuations may induce in the honeycomb lattice the formation of an unconventional two-particle bound state. This mechanism may give rise to unconventional pairing upon the condensation of bound particles. We do not evaluate the critical value of the ratio J/t, which is sufficient to induce binding. We assume instead that, in the case of cobaltates, some additional isotropic attractive interaction, for example, phonon mediated, is active. Nevertheless, the symmetry of the paired state is selected by the anisotropic interaction mediated by spin fluctuations. The relevant point group for the t-J model on the honeycomb lattice is C-3v. We argue that the bound state of two additional electrons doped to the half-filled antiferromagnetically ordered system has zero total momentum and p-wave symmetry of the irreducible representation E. Since the honeycomb lattice does not possess the inversion symmetry, the expected paired state is a mixture of a singlet and a triplet. This is an explicit prediction for the form of the superconducting order parameter in a weakly doped antiferromagnet on the honeycomb lattice.