Zlatko Tesanovic: d-wave duality and its reflections in cuprates

In an inspired talk, Zlatko Tesanovic described his latest work on the on-going research program that attempts to understand the physics of cuprates as strongly fluctuating d-wave superconductors. The talk was mostly conceptual, and those interested in fine technical points are advised to look at his preprint arXiv:0705.3836.

Zlatko began by dividing all (singlet) superconductors into two general classes: the weakly correlated, BCS-Eliashberg type, and the strongly correlated, to which presumably all of the cuprates belong. It is for the second class, which inevitably suffer from strong phase fluctuations, that the notion of duality becomes useful. Duality was first discussed in a simpler problem of the negative, strong-U Hubbard model, which exhibits local singlet pairs. If one freezes the amplitude of the gap, the remaining theory for the fluctuating phase degrees of freedom may be cast in the dual language, in terms of the "disorder parameter" that signals the proliferation of infinitely large vortex loops. In this formulation, the dual condensate represent the non-superconducting phase. The theory has therefore two phases: superconducting, in which the original order parameter is finite while the dual vanishes, and the non-superconducting, in this case a charge-density-wave, in which the reverse is true. Zlatko mentioned an example of compound (BaKPb)BiO3 in which the observed strongly diamagnetic CDW phase may possibly be an example of a such "phase incoherent" superconductor. (For an introduction to the standard "Peskin-Dasgupta-Halperin" duality, see my book, "A modern approach to critical phenomena", Ch. 7.)

Turning to the d-wave superconductors, Zlatko observed that unlike in the s-wave case, pairs here are necessarily non-local objects which live on bonds. The phase of the superconducting order parameter is therefore a bond variable, which leads to richer physics. In the continuum limit, the bond-phases get approximated by the site-phases, at which point some information about the phase configuration, namely the relative (fluctuating) phase between two bonds emanating from the same site is lost. To retain the complete set of configurations of the bond-phases Zlatko wrote it as a sum of the "center of mass" and the "relative phase". The quantum disordering of the former then leads to the old QED3 theory of the cuprates, and the concomitant pseudogap phase which, essentially being just the disorder d-wave superconductor naturally exhibits a large Nernst effect and the surviving nodal quasiparticles. (Although a small gap at the nodes, which would signal an incommensurate SDW order is possible as well.) Disordering of the relative phase, on the other hand, proliferates the monopole configurations in the emergent U(1) gauge field of the QED3, and erases the last memory of the d-wave superconductor. Zlatko identifies this final state with the transition into the commensurate Neel antiferromagnet near half filling.

In the question period several people raised the issue of what should all this mean on the electron-doped side (Eschrig, Castellani), to which the answer was that the electron-doped superconducting state appears to be more of the BCS, non-fluctuating variety, and the transitions therefore more mean-fieldish, or first-order (for the dSC-AF transition). Muramatsu wanted to know what kind of topological singularities are actually present in the theory: vortex loops and monopole-antimonopole configurations. Castellani went back to the negative-U example, and if I heard correctly, guessed that a finite doping in the dual theory would appear as a finite magnetic field, which is correct. Abrahams asked about the difference between the SDW that arises as the chiral instability of the QED3 and the Neel antiferromagnet at half-filling. Zlatko's answer was that the latter obviously does not show a large diamagnetism, while the former does, and that there is presumably a quantum phase transition between the two. Kee wondered where would the place for the standard Fermi liquid be in the whole story. The answer was that Fermi liquid is actually outside the present theory, which assumes a finite amplitude of the gap; setting the amplitude to zero would restore the Fermi liquid. Monien asked about the status of the experiment at low dopings and temperatures, to which Zlatko replied that there is a large Nernst signal there as well, so the ground state itself should be a disordered d-wave superconductor below the critical doping. Finally, Pepin could not see the difference between the present theory and the gauge theories of several other prominent workers in the field. Zlatko, after admitting he was sad to hear this, explained that the crucial difference is that those fatal monopole configuration that more often than not undermine the usefulness of the (compact) gauge theories in condensed matter here are kept in check by the BdG quasiparticles and the associated Higgs mechanism. And on this uplifting note the discussion was ended.