Thursday, August 16, 2006
Andy Millis gave a talk titled "Are the cuprates really Mott insulators? Comparison of optics and DMFT"

Andy started by stating that this is a quantitative question which may have conceptual implications and went on to say "In 1987 Phil Anderson proposed that the high Tc materials were Mott insulators. I want to suggest maybe that is not quite true."

Andy reviewed the optical conductivity data for the cuprates in both the antiferromagnetic state and the doped state. In the AFM state the conductivity turns on around 1.8eV (for LCO) with a peak and a dip before increasing at higher frequencies. The peak structure near 1.8eV contains about half of the oscillator weight, and with doping this weight is shifted to a Drude peak at low frequency.

Chandra Varma argues that it is wrong to talk about electrons in a CuO2 antibonding band, and Andy responds that he will assume this is fine for scales below 2eV.

Andy poses the questions: How fast does the Drude peak fill in with doping and what does this tell us about correlations? He then turns to results from single-site DMFT to study this problem. This ignores spatial correlations but allows a description of the Mott insulator. The 1-site DMFT phase diagram for the half-filled Hubbard model shows a critical value of U, Uc2~1.5W, above which one has a Mott insulator at zero temperature, and a first order line extending to lower U at finite temperature. Comparing the spectral weight transfer below 1eV, Andy concludes that U~0.8Uc2 for LCO. In other words, the cuprates are not Mott insulators, but, rather, the gap at zero doping is due to the formation of a spin density wave.

Andy summarizes by saying that within the uncertainties of this model, the insulating behavior is due to magnetic order and the doping properties are not due solely to strong correlations, but also to magnetic correlations.

In the questions, there were objections to the use of 1-site DMFT and the absence of the physics associated with the energy scale J. Andy responds that cluster DMFT with J correlations gives support to his analysis.