Superconductivity inCoO2layers and the resonating valence bond mean-field theory of the triangular latticet−Jmodel

Abstract

Our recent paper [1] contains an error in the formula for the high frequency Hall constant for the experimentally relevant case of electron doping. Eq(3) giving the high frequency Hall constant for the case of electron filling, i.e. electron density n > 1, should correctly readwhere δ = |1 − n|. This differs essentially from the quoted answer by a minus sign that was missed by us, and by a factor of 2. This equation is obtained from Eq(2) in the paper, calculated for the case of hole doping n < 1, by a particle hole transformation. Performing a canonical transformation c i,σ ↔ c † i,σ in the Kubo formulas for models of lattice fermions (see e.g. [2] Eqn(1,2) ) yields:The crucial overall minus sign arises from the fact that the Hall constant involves a three current propagator, and each current picks up a minus sign under the transformation. Incidentally this identity results in a vanishing at half filling for bipartite lattices of the Hall function R H (1, t, ω, T ) for any value of T, ω and the interaction strength.The changed sign in Eq(3') has a few implications which we would like to state explicitly. The recent experiment of Wang, Rogado, Cava and Ong [3] on the transport Hall constant, actually sees the predicted linear T behaviour over a wide temperature range 200 0 K ≤ T ≤ 400 0 K with a positive slope. From Eq(3') above, we deduce that the appropriate t − J model description of the system has t < 0, i.e. belongs to case B(ii) in our notation, at least at the composition x ∼ .7.We note that with this correction, the sign of the hopping t suggested by our calculation is the same as the one favoured by Refs [4,5], at least for the non superconducting range x ∼ .7. In this composition range, photoemission data [6,7] also suggest the same sign of t, with an unoccupied region around the center of Brillouin zone, namely the Γ point. Motivated by the recent discovery of superconductivity in two dimensional CoO2 layers, we present some possibly useful results of the RVB mean field theory applied to the triangular lattice. An interesting time reversal breaking superconducting state arises from strongly frustrated interactions. Away from half filling, the order parameter is found to be complex, and yields a fully gapped quasiparticle spectrum. The sign of the hopping plays a crucial role in the analysis, and we find that superconductivity is as fragile for one sign as it is robust for the other. NaxCoO2 · yH2O is argued to belong to the robust case, by comparing the LDA fermi surface with an effective tight binding model. The high frequency Hall constant in this system is potentially interesting, since it is pointed out to increase linearly with temperature without saturation for T > T degeneracy .

Charge Ordering, Commensurability, and Metallicity in the Phase Diagram of the LayeredNaxCoO2

“…However, at 1 2 , commensurability effects are weakest and charge ordering is not favored. We also note that the density of states calculated in 2D tight-binding approximation [14,15,16] The phase diagram in Fig. 2 reveals a characteristic feature of Na x CoO 2 , namely, the strong influence of the Na ions on the electronic properties.…”

“…Recently, several groups have applied the tJ Hamiltonian to Na x CoO 2 [14,15,16,17]. The derived phase diagram is strongly informed by the classical lattice-gas model which predicts that, on the triangular lattice, the electrons (holes) crystallize into a [17].…”

Topological states with broken translational and time-reversal symmetries in a honeycomb-triangular lattice

“…4(b) shows the areas where this happens in a triangular lattice for U = V = 5. Although it is known that TRS can be broken in a triangular lattice due to NN interactions [52], we have shown here that simultaneous breaking of time-reversal and translational symmetries in the superfluid order parameter of a two-component fermion system may happen both in honeycomb-triangular and triangular lattices.…”

“…We also note that the threshold for TRS breaking becomes higher when U is raised. TRS breaking also happens in the triangular lattice [52], but the phase diagram shown in Fig. 4(b) is exceedingly simple compared to the rich phase diagram of Fig.…”

“…1(a) and 1(b). We consider a simple situation in which the long-range order parameter has the same norm 1 along all bonds, but different phases are allowed for the different bonds [52]. In equation form, the ansatz reads…”