Thursday, August 16, 2007

Joerg Schmalian: Superconductivity in a Shastry-Sutherland model.

Joerg discussed a special case of a doped Mott insulator, namely
doping the Shastry-Sutherland model, that is closely realized
experimentally in SrCu_2(BO_3)_2. The Shastry-Sutherland model
consists of an antiferromagnet on a square lattice with exchange
coupling J and frustrating couplings along alternating diagonals
with strength J'. For J'/J > 2 the ground-state was shown by Shastry and Sutherland to be given by a product state of singlets on the alternating diagonals. Later numerical results showed that this is
so for J'/J larger that approx. 1.44. In this regime, the ground-state is exactly described by a RVB wavefunction, i.e. a projected BCS wavefunction, making this case an appealing one for describing a doped Mott-insulator within the RVB frame.

The doped cases include single-particle hopping t along the bonds
of the square lattice and t' along the alternating diagonals. Joerg
and his collaborators considered both electron and hole doping,
that in the frame of a t-J model correspond to a change of sign in
t' after a particle-hole transformation for the electron doped case.

The electron doped case had strong singlet correlations along the
alternating diagonals, i.e. strong spin correlations for sites i and j
on the same diagonal but decaying fast for i and j further away.
In spite of the fact that the RVB wavefunction was based on a BCS
one, no off-diagonal long range order (ODLRO) could be detected after projection, such that although local pairing was present,
ODLRO could not be preserved. Also, a finite Drude weight was
found. A question (Andy Millis) arose about Pauli susceptibility.

In contrast, the hole doped case showed d-wave superconductivity
after 3% doping. The amplitude of the order parameter was around
10% of the BCS value. Coexisting with such a state, plaquette
ordering was obtained on the plaquettes containing the alternating
diagonals. In such a state Joerg and collaborators found that
ODLRO is strongly enhanced in comparison to a homogeneous state.

Yong-Baek Kim remarked that he had slightly different results
using different methods (bond operators in contrast to variational
Monte Carlo). Chandra Varma asked if there is any property that
differs from BCS after projection. Zlatko Tesanovic remarked that
at half-filling, after full projection, gauge invariance is restored.
Finally, it was asked whether Dzyaloshinski-Moriya interaction
present in the actual materials may change the situation.
Although they were not considered explicitely by the authors, the
expectation was that they would mostly change the triplon
dispersion but not the findings discussed by Joerg.


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