Lara BENFATTO (La Sapienza) -- Superconducting properties of pnictides within a low-energy multiband approach

Lara started by comparing the iron-based high Tc superconductors to the older cuprates. There are similarities like the close relation between superconductivity and magnetism and a potential role of spin fluctuations in the superconductivity mechanism. However, there are crucial differences as well, and she stressed the multiband nature of superconductivity in pnictides, in contrast to the effective single band description of cuprates. Furthermore, cuprates are near half-filling of this single band while iron-pnictides involve nearly filled or nearly empty bands and there is significant particle-hole asymmetry.

There are three main aspects of superconductivity in iron-pnictides: they are multiband superconductors; the interband pairing interaction related to nesting among electron and hole pockets on the Fermi surface (FS) is the dominant mechanism of superconductivity; and there is strong particle-hole asymmetry in the problem. Lara proceeded to explain that these different features are studied within a general multiband Eliashberg-style formalism, in which a fermion self-energy is computed in presence of a coupling to a bosonic mode at energy \omega_0. Among other quantities, this allows one to compute a quasiparticle renormalization factor, Z(\omega \to 0), and extract the interaction-renormalized effective mass m^* from m^*= Zm_b \sim (1+\lambda)m_b, where m_b is the band mass and \lambda is the dimensionless coupling to the boson mediating superconductivity. The results can be compared to the available experimental information, including the ARPES and specific heat measurements from which the effective mass and other dynamical information can be extracted. She pointed out that the general model is still too and perhaps unnecessarily complicated and the further simplifications included ignoring electron-phonon coupling and intraband repulsion which are too weak and irrelevant under RG, respectively, and retaining only the repulsive interband interaction.

Even this simplified version of the model is still a challenge. Two main questions, important for understanding of experiments, were addressed: How many bands are necessary to reproduce experimental data? Does one really need the full Eliashberg formalism or are the retardation effects relatively unimportant and the BCS theory will suffice? At the end of the talk, it turned out that the answers to these questions are “four” and “yes.” Thus, the minimal model needed all four bands and the full Eliashberg calculation was necessary to reproduce different superconducting gap amplitudes observed in experiments like ARPES. The anisotropic orbital character of the interband interactions also had to be included.

Some important results of the work were presented (the full account can be found in L. Benfatto et al, arXiv:0909.3735). One example is that BCS model is not sufficient since it produces the wrong hierarchy of gap sizes. Second, the theory gives a good agreement with m^* extracted from experiments, and, in particular, \lambda \sim 1, which indicates a reasonably strong degree of coupling.

Next, it turns out there are three different gaps whose magnitude can be fitted rather well to the experimental observations. Interestingly, while these magnitudes cannot easily arise within a BCS theory, once we adopt their T = 0 values from the full Eliashberg approach, a reasonable account of quasiparticle thermodynamics does in fact follows from the two-band BCS treatment. Finally, the kinks in the ARPES dispersion are also reproduced with a similar \lambda \sim 1. Lara also mentioned an alternative approach (arXiv:1001.1074) which gives somewhat larger \lambda.

The rest of the talk dealt with the dHvA experiments and the issue of renormalization of the size of electron and hole pockets. Such renormalization arises naturally within a multiband Eliashberg approach. Lara made an insightful observation that interband interactions lead to shrinking of FS pockets and that this is just what is observed, when the experimental dHvA FS cross-sections are compared to those derived from LDA (band-structure) calculations. She also discussed the experimental results using the optical sum rule to estimate effective masses of carriers. This is a more complex exercise in multiband systems and many in the audience asked questions and made comments concerning just how should optical sum rule be interpreted (Alloul), pointing the fact that not all pockets change in the same way (Hirschfeld), debating whether or not Luttinger theorem holds (it does, Chubukov), what is the shift in the chemical potential, and other assorted issues (Nevidomskyy, Burch), etc.

Blogged by Zlatko Tesanovic.