Rick Greene (Maryland): Correlation between spin fluctuations and pairing in electron-doped cuprates

Greene started by comparing electron- and hole-doped cuprates (or n- and p-doped, respectively). There is by now an enormous amount of phenomenology on these systems and some of the main features and theoretical ideas that surround them are reviewed for RMP by Greene and collaborators in arXiv: 0906.2931. He stressed that the main issues in the field are now revolving around the nature of the so-called pseudogap state in the hole-doped cuprates: Is it a phase-fluctuating superconductor or a competing ground state of some other symmetry? These issues have their echoes in electron-doped cuprates. For example, is there a pseudogap state at all in n-doped cuprates? Greene’s Nernst effect measurements show very small region of phase fluctuations, far smaller than what is seen in hole-doped cuprates by Ong et al.

He illustrated some of these issues by referring to an earlier talk by Kapitulnik and acknowledged that there might be some time-reversal symmetry breaking in n-doped cuprates as well but there does not seem to be evidence for this actually taking place. However, he stressed that, while there well might be an unknown order parameter competing with superconductivity in the pseudogap state of p-doped cuprates, in the n-doped materials it is the 2D AF spin fluctuations that are the main culprit involved in interplay with superconductivity. Greene then showed old Greven’s data illustrating the phase diagram of n-doped materials as strongly supporting this view. The antiferromagnetic (AF) state is rapidly suppressed as it approaches the superconductor (SC) but some coexistence is possible and perhaps indicated in other experiments. Coleman asked whether the considerably different behavior of n- and p-doped cuprates might be related to the different location of the doped electrons (holes): in hole-doped systems, the holes go to oxygen sites and form Zhang-Rice singlets around neighboring copper atoms, while the doped electrons simply go straight to coppers, into their so-called “upper Hubbard band,” most likely the d_x^2-y^2 orbital. The answer is “yes.”

More review of the various data followed: the Hall effect seems to know about the SC transition. Optical conductivity does see the opening of the SC gap. AF correlation length drops precipitously near the SC. There are very detailed ARPES data (Armitage et al) showing well-developed Fermi surface. AF state tends to be commensurate, in contrast to a typically incommensurate AF that is formed in hole-doped cuprates. Such commensurate AF results in the reconstruction of the Fermi surface and various small electron and hole pockets are formed (similar to what is seen in newer iron-pnictide SC) in the underdoped regime. Both the reconstructed and the original large Fermi surface in the overdoped regime have been seen in SdH oscillation experiments, but the small electron pockets seem to be missing. Various weakly and more strongly correlated SDW theories have been used to explain the data [Amicus Bloggerius: The Hall coefficient (at 300mK) vs doping was done in the normal state (H>Hc2) and showed a kink at a doping near Ce=0.17. This is a slightly overdoped composition (optimal doping is 0.15 in PCCO). Nothing unusual is seen at the doping near Ce=0.14 where Greven claims the LRO AF disappears. The Hall data is consistent with a FS reconstruction at this doping, Ce=0.17. The optics measures the opening of a partial gap in the ab plane optical conductivity at T*. As a function of doping this “normal state gap or pseudogap” disappears near Ce=0.17, thus being consistent with the Hall data and the ARPES and the quantum oscillation experiments and the onset of magnetic fluctuations in Greven’s work.]

Greene then moved to the resistivity experiments and his data. There are some interesting developments here: the goal is to carefully examine various resistivity fits that have appeared in the literature (Taillefer’s analysis of data on various SCs suspected of being associated with spin fluctuations is mentioned here). Should one fit resistivity to the form like \rho = \rho_0 + A(x)T + B(x)T^2 + C(x)T^n or should different T-dependencies be considered separately? Kapitulnik remarked from the audience that often a guiding theoretical model decides when we should consider them all together; for example, when separating the Fermi liquid electronic contribution from the one due to phonons. Greene’s old resistivity data (Fournier et al) shows linear T behavior near AF, on the underdoped side. Flint asked whether finite H experiments were done to see what happens to the AF state; at that moment, Greene was not aware of any that would be relevant here but later recalled neutron scattering experiments cited in their RMP. Then, he showed a change in behavior from T^2 near the SC state to T^\beta with \beta < 2 on the AF side. In between, there is a linear behavior, apparently associated with the quantum critical (QC) point. There is also an upturn in resistivity on the AF side. Chubukov asked whether the AF state might be extending further into the optimally and even overdoped regime of the phase diagram. Greene said the situation was not entirely clear but he did stress that many viewed reports of coexistence between AF and SC as less than firmly established, and likely due to various alien phases. Sachdev’s recent phase diagram of SDW + SC states was shown. [Amicus Bloggerius: The T^2 resistivity is seen at low temperatures in a 10T field above the 0.17 doping. Data looks like the funnel phase diagram expected near a QCP. The issue of coexistence of SC and AFM at doping between 0.13 and 0.17 is not really resolved at this time because of possible sample quality issues among the different groups that have done neutron scattering experiments.]

Next, very recent data were presented. Greene explained why he viewed the separate analysis of different T power laws as a better way of approaching the data. Questions were asked and answered here concerning the reliability of the AT + B^T^2 fits done by others in p-type cuprates. Greene observed that in their new data that connects resistivities of different n-doped cuprates one has to contend with the uncertainties in the doping levels of different chemically doped materials. There is little one can do about this except to assume that the optimal nominal doping levels correspond to the same actual doping; this is suggested by the similarity of Hall effect data, both magnitude and T dependence. When looking at the overdoped systems, they see linear T behavior as well. It appears that the coefficient A is associated with the superconducting Tc and vanishes at the same doping. After that, only T^2 term is left, with finite B(x) coefficient. Greene suggested that A should be associated with the scattering mechanism, probably some form of spin fluctuations that are also responsible for SC. A lively debate followed, focusing on the relation, if any, with the observed linear behavior in the regime near the QC point.

In their data, the application of finite magnetic field H suppresses both SC and the regime over which the linear term is present in the resistivity. Greene also remarked that \rho_0 is pretty big and thus the materials are quite dirty compared to finest YBCO crystals, although still in the range of LSCO. The full phase diagram was inferred, including the effect of H (see picture). The audience found this very interesting and many questions and comments followed. Blumberg asked whether the finite H resistivity could be associated with the flux flow in the mixed state, along the lines of the recent experiment by Boebinger et al. Probably not. Also, Nernst data are not available at this time. Buehler-Paschen asked how reliable are the fits. \rho_0 is fixed in the fitting procedure. There is also a linear magnetoresistance which is not understood at the moment. Aronson asked about specific heat data. Not possible, answered Greene, these are films. Takagi asked about contribution of spin fluctuations to resistivity. Keimer inquired about the quality of their n-doped materials (by now, p-doped crystals are extremely good for YBCO, although the ones of BSCCO and LSCO are not any better than n-doped cuprates). Greene responded that materials are very good based on x-ray diffraction.


Blogged by Zlatko Tesanovic.