A short comment on the need for 3-band models

Prof. P A Lee, a protruding figure in condensed matter physics, in rally with P W Anderson, F C Zhang, X G Wen, N Nagaosa and et al, has done quite a lot to achieve a better and more satisfactory understanding of the fundamental aspects of cuprate superconductors. His opinion has been legibly given in a synopsis that was published two years ago [Rep.Prog.Phys., 71:012501(2008)]. This review serves as actually a concise version of an earlier one in 2006 [Rev. Mod.Phys., 78:17(2006)]. To be frank, it is always a great joy of reading his work. But I really cant agree on his stick to RVB picture, which in my eyes does not deserve such adherence. Put in other words, I would prefer a model that takes into account clearly the O2p orbital. In his review article, Lee has given his why such p-orbital need not be treated explicitly. He wrote, which I quote,

(d) Three band model. Since the copper–oxygen layer involves one copper and two oxygen per unit cell (excluding the apical oxygen), the minimal microscopic electronic model requires a dx2−y2 Cu orbital and two oxygen p orbitals. This is called the three band model [130, 131]. Various cluster calculations indicate that the low energy physics (below a scale of t ≈ 4 meV) can be adequately described by a one band Hubbard model [4]. Over the years this has become the majority view, but there are still workers who believe that the three band model is required for superconductivity. I think the original motivation for this view came from a period of nearly ten years when much of the community believed that the pairing symmetry is s-wave. It certainly is true that a repulsive Hubbard model cannot have an s-wave superconducting ground state. Three band models with further neighbour repulsion were introduced to generate the requisite effective attraction. The s-wave story was overturned once and for all by phase sensitive experiments in 1994 but some of the three band model proponents persevered. In particular, Varma introduced the idea of intra-cell orbital currents, i.e. a current pattern flowing between the Cu–O and O–O bonds as a model for the pseudogap [132]. This has the virtue of leaving the unit cell intact and this kind of order is very difficult to detect. With such a complicated model it is difficult to make a convincing case based on theory alone and a lot of attention has been focused on experimental detection of time-reversal symmetry breaking or spontaneous moments due to orbital currents. Unfortunately, the expected signals are very small and can easily be contaminated by a small amount of minority phase with AF order. Up to now there are no reliable results in support of this kind of orbital currents.

I don't quite consent with him on these remarks. For me, what urges people to take into account the O orbital is the qualitative differences between p-type cuprates and n-type cuprates. Were t-J model adequate for both types, such differences could hardly be justified. Especially the formation spin glass in the underdoped regime, in my opinion, can hardly reach compromise with t-J model. Spin glass shows up only in p-type materials. Recent experiments even more clearly showed the importance of O orbital. More detailed reasoning can be found in this work [J. Phys.: Condens. Matter 21 (2009) 075702].