Pines' Questions

Some general questions for discussion the week of August 1-5

1. The interplay between localization, Fermi surface jumps, magnetic fluctuations,and superconductivity in unconventional superconductors  

*Assuming there is a jump in the Fermi surface from p to 1+p as localized electron behavior ends, this  should occur at finite temperature and, if so, one should be able to use experiment to define a temperature/doping or temperature/pressure line, T_L, along which it occurs in the cuprates and iron-based superconductors, as has proved possible for the 115 heavy electron materials?

*For the two heavy electron materials that have been studied in detail, Co115 and Rh 115, the proposed T_L line intersects the sc T_c dome at, or very near the doping/pressure at which T_c is maximum. Does this happen for the cuprates or any of the iron-based materials?

*Were this to happen for the cuprates T_L would begin at a doping level of p~0.19 and cross T_c at a doping level of 0.16 or so. It would closely resemble T*/3, where T* is the nearest neighbor interaction between localized electrons, as determined from their fit to the 2d Heisenberg model for localized spin behavior in their two-fluid model, that enabled  Barzykin and Pines to identify T*/3  with the onset of pseudogap behavior.

*So if to the right of T*/3, one had only itinerant electrons {I’ll have to check but as best I recall this is not the case, one would then have T_L=T*/3..  Assuming the latter is not true, the T*/3 line could still mark one boundary for QC behavior with the other being a T_L line, likewise beginning at p=0.19, but increasing with increasing doping, below which one had Fermi liquid behavior. This possibility should be checked out.

*The fact that T/”3 intersects T_c at, or very close to, [T_c]_max is, in any event,  telling us something important about the doping dependence of T_c in the cuprates. 

*Another interesting question is why, for the cuprates, a Fermi surface jump is not accompanied by a jump in T_c. We have some ideas for why it is not for heavy electrons: does one find a similar situation here?

*Would be great to have high magnetic field Knight shift and spin-lattice relaxation rate measurements in the vicinity of the QCP’s at 0.19 and 0.08 for the cuprates.

2.Connections between the heavy d-electron behavior that was recently established in Iron-based superconductors and the heavy f- electron behavior seen in the 115 heavy electron materials

Wu et al [http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.147001] have discovered emergent Kondo lattice {KL} behavior in the iron based superconductors,

AFe₂As₂ (A=K, Rb, Cs).Among the questions this raises are:

*Do these then resemble the f-electron 115 family, in that they possess a delocalization line, T_L,,  that marks a transition from localized to itinerant behavior and ends in a QCP?

*If so, does T_L, intersect T_C in the vicinity of [T_C]_max ?

*Are there any indications of emergent KL behavior in the other iron-based superconductors?

 

3. Charge and spin ordering and glassy behavior in the underdoped cuprates

*Keimer and his collaborators {Haug et al, New Journal of Physics 2010] assume that they are measuring incommensurate spin density waves and incommensurate short range nematic spin order. But given the argument [lack of any measurable leakage onto the O spin lattice relaxation rate] in favor of discommensuration rather than incommensuration for the spin density fluctuation spectrum, their result needs reinterpretation and one should take a close look at the role played by the accompanying inhomogeneity in other measurements.

*Is there any connection between the doping dependence of discommensuration seen in the spin fluctuation spectrum and that found by the Keimer group  for either spin nematic or sdw behavior?

*The presence of a CDW state that is not accompanied by AF order tells us that the spins on the charge localized electrons are not aligned. Question: is there any measurable change in the uniform susceptibility on crossing the charge order line? Cannot be substantial or it would have already been noted.

*When glassy behavior is observed, it is obvious that it is accompanied by inhomogenous behavior, ie hole rich and hole poor regions. But we argue above that inhomogeneous behavior is not confined to regions in which glassy behavior has been clearly identified. Why is this the case?

*What happens physically at a doping level of .08 to end both the CDW and the ’nematic" spin behavior and give rise to the mass divergence reported in Sebastian et al. PNAS 107, 6175 (2010)?

*Can one pin down the temperature dependence of the doping dependent diverging qp mass? For heavy electrons near the delocalization QCP, it varies as ln T*/T as T* approaches zero at the QCP.

4. Hybridization and hybridization gaps

There is now overwhelming evidence that the hybridization of f-electron local moments with background conduction electrons is collective and controlled by the interaction between nn local moments and good reason to believe that this may be the case as well for the cuprates.

Inter alia, this means that the hybridization gap is given by