pdf, 9 MiB - Infoscience - EPFL

3.4. RESULTS AND DISCUSSION 67
0
-0.02
e c
-0.04
-0.06
d +
AF / J
AF+d + / J
AF+d + / J / Ls
N=108
-0.08
1 1.1 1.2 1.3 1.4 1.5
Electron density n
Figure 3.7: Condensation energy per site e c versus electron doping for the 108
site lattice. We show different wavefunctions and also the best estimate in the
literature [82] at half-filling (open diamond).
the condensation energy per site (see Fig. 3.7) for different types of instabilities.
Very interestingly, the AF/J is even better than a simple d x 2 −y 2 + id xy RVB
state. Moreover, the RVB order only weakly increases the condensation energy in
presence of the antiferromagnetic background (AF + d + /J). This suggests that
superconductivity is only weakly present in the t−J model when n>1which
is also confirmed by the measurement of the superconducting gap (see Fig. 3.9).
The RV B/J wavefunction, although it allows to recover a very good variational
energy at half-filling, is not stabilized in the electron doping side of the phase
diagram (see Fig. 3.8). The superconducting order of our best wavefunction is
approximately 4 times smaller in amplitude and in range of stability than the
d-wave pairing in a 10 × 10 square lattice with the same boundary conditions.
For electron doping δ>0.04 we find that the d + BCS pairing symmetry has the
same energies as the d − one, and also as the wavefunctions with d x 2 −y 2 and d xy
pairings.
Very strikingly, the 120 ◦ magnetic order parameter is surviving up to high
doping δ =0.4, see Fig. 3.11. Long-range magnetic order at finite doping is
potentially caused by a limitation of the VMC method, since it is not possible in