Single band or double band ?

It is frequently disputed in the field of cuprate superconductors that, the essential physics may be encapsulated more adequately by a single (let's call it d) or double (s-d) band model. Fairly speaking, throughout the whole span of this arena, from the early days till now, as initialized by Anderson and pushed by Zhang and Rice et al., the d-model has been at the center and unchallenged. This situation was further corroborated by the thinking that, the s-d model can be mapped onto the d-model rigorously [see Ref.1 for a review]. Nevertheless, this situation ha to change for two reasons: (1) the d-model can not address the intervening spin glass phase; (2) the d-model can hardly explain the checkerboard pattern observed at low doping.

Why cant the spin glass phase exist within the d-model ? Suppose one has a half-filled single-band Hubbard model. Now add an extra electron to it. What can this electron do ? It shall try to hop from one site to another. Due to Pauli's principle, to render this hopping, the electrons on the two sites must have their spins aligned parallel. This means that, this extra electron tends to align the already existing electrons. On the other hand, the already existing electrons also try to hop and require their neighbors anti-parallel. And these two effects cancel exactly, because the two electrons on the same site have exactly the same hopping amplitude.

Obviously, in the s-d model, the effects don't cancel. This is where the difference gets in.

[1]SPIN POLARONS AND HIGH-Tc SUPERCONDUCTIVITY, A. L. Chernyshev†,* and R. F. Wood Solid State Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831;