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52 CHAPTER 3. T-J MODEL ON THE TRIANGULAR LATTICE
with the Haldane gap of S=1 chains or S=1/2 two-leg ladders. The theoretical
understanding of these properties is at best very primitive, and reliable numerical
results are called for.
The recent discovery of superconductivity at low temperatures in the triangular
Na x CoO 2 .yH 2 O layered compounds [74] is a very interesting event, since it
may be the long sought low-temperature resonating valence bond superconductor,
on a lattice which was at the basis of Anderson’s original ideas on a possible
quantum spin liquid state. Na x CoO 2 .yH 2 O consists of two dimensional CoO 2
layers separated by thick insulating layers of Na + 2 ions and H 2O molecules. It is
a triangular net of edge sharing oxygen octahedra; Co atoms are at the center of
the octahedra forming a 2D triangular lattice.
Many interesting behaviors occur in Na x CoO 2 .yH 2 O . In the high doping limit
where charge conduction is present, the magnetic susceptibility shows a strange
behavior. In a usual metal, the fraction of spins that can be field-aligned is small
and shrinks to zero with decreasing temperature. In contrast, in Na x CoO 2 ,the
spin population that contributes to the susceptibility just equals the population
of holes and stays the same when temperature falls. The susceptibility is therefore
like the one of a Mott insulator. This ambivalence between the metallic behavior
in the charge conduction and the insulator behavior in the spin susceptibility has
led to call the high-doping phase a spin-density wave metal.
Equally puzzling at high doping is the fact that Na x CoO 2 has a large thermopower.
In metals, an electrical (or charge) current involves the flow of electrons
and is usually accompanied by an electronic heat current. The thermo-power
measures the ratio of the heat to the charge current. In most metals the thermopower
is very small. A clue to understand the large thermo-power is that at
low temperature T =2K, the thermo-power is suppressed by a magnetic field.
Measurements confirm that the vanishing of the thermo-power coincides with the
complete alignment of the spins by the field. Consequently, this implies that the
thermo-power is mostly coming from the spin entropy carried by the holes in the
spin-density wave metallic phase.
Very interestingly, it was also observed that when the compound is cooled
below T =4K [74], it becomes a superconductor when the doping is lying between
1/4