pdf, 9 MiB - Infoscience - EPFL

164 CHAPTER 6. ORBITAL CURRENTS IN THE CUPRATES
ducting instability in terms of the holes in the three-band Hubbard model. The
symmetry that was found in our calculations, by the energy minimization of the
RVB wavefunction, is shown in Fig. 6.19. We note that for a reference site i, ∆ ij
consists of four strong plaquettes (bold square in Fig. 6.19) around the reference
site. The sign of the pairing has a d-wave symmetry for these latter plaquettes,
and additionally, inside each of the plaquette the sign is alternating identically
to the Zhang-Rice singlet d ↑ (p x↓ − p −x↓ + p y↓ − p −y↓ ) symmetry.
6.11 Role of the Apical oxygens
The theoretical challenge is to find the simplest model of the copper-oxygen plane
which would contain all the essential physical aspects. The electronic structure
calculations suggest that a good starting point is provided by the previously
discussed three-band model, including coper 3d x2−y2 orbitals and oxygen 2p σ
orbitals. It has been repeatedly argued that the two dimensional plane contains
the essential of the low energy physics. Zhang and Rice pointed out that a hole
in a copper d x2−y2 orbital and a hole in the oxygen orbital form a local singlet
for the realistic parameters of the three-band Hamiltonian, and the three-band
model does reduce to an effective single-band t-J model.
However, one of the issues related to a breakdown of such a mapping is related
to the presence of additional apical oxygens. It was proposed for example that
a triplet states could be favored, instead of the singlet state, and stabilized by
the occupancy of apical oxygens and copper d 3z 2 −r 2 orbitals. Indeed, since the
early days of high-temperature superconductivity, the question of a possible role
of apical sites in cuprates superconductors has been controversially discussed.
A part of the measurements were consistent with the conjecture that there is a
significant influence of the apical site on high-Tc superconductivity.
Moreover, further theoretical investigations using a six-band Hubbard model
interaction scheme showed that some holes with Cu3d 3z2−r2 orbital character do
exist (experimental evidence for this can be found in Ref. [145]), and that a
fraction of them is hybridized with the apical oxygen [146]. This can easily be
understood, since there is a strong Coulomb repulsion between the holes at Cu
sites, the extra holes introduced by doping residing primarily on oxygen sites.
Furthermore, it has been pointed out that for a realistic description of the
principal features of the cuprates superconductors, like for example the insulating
gap in the undoped parent compounds, one has to include also the orbitals of
apical oxygens.
Several experiments indicate that the out-of-plane apical oxygen orbitals are
also involved in accommodating some of the holes doped into the CuO 2 planes.
One of the most exciting ones is that there might exist a correlation between the
maximal critical temperature T c reached in different cuprates and the copper-toapex
bonding, as well as the Madelung potential at the apical oxygen measured