Iron-based superconductors

In recent years, my group has been actively involved in studying the new problems posed by the discovery in February 2008 of high-temperature Fe-based superconducting ma- terials. The enormous interest generated by the new superconductors has to do with their technological potential (they tend to be more 3D materials than the cuprates, yet with remarkably high critical fields for the corresponding Tc's); with the fact that superconductivity exists in Fe-based materials at all; and with the opportunity, now that a second class of HTS materials exists, to learn about the origins of HTS via the comparison with the cuprates. While there is some evidence that these materials are simpler to understand than the cuprates because they are less strongly correlated, they are also more complicated because several Fe bands play a role near the Fermi level. Thus to approach this problem it is important to have expertise in electronic structure theory as well as phenomenology and microscopic modelling. Recent projects Spin fluctuation pairing in multiband systems Weak-coupling approaches to the pairing problem in the iron pnictide superconductors have predicted a wide variety of superconducting ground states. We performed Random Phase Approximation (RPA) calculations of the magnetic susceptibility and pairing interaction within a 5-band model accounting for Hubbard and Hund's rule interactions on each Fe site. We discuss the robustness of these results for different dopings, interaction strengths, and variations in band structure. Within the parameter space explored, an anisotropic, sign-changing s-wave state and a d state are nearly degenerate, due to the near nesting of Fermi surface sheets. The near degeneracy is a natural consequence of the nearly nested cylindrical Fermi sheets, and may give rise to interesting new phenomena such as order parameter collective modes.

Figure 1 (Left) RPA static magnetic susceptibility vs. q near the for a choice of Hubbard U, intraorbital U', Hund's rule couplings J and J'. (Middle) Dependence of pairing eigenvalue on Hubbard interaction in various pairing channels. (Right) Sign-changing s-wave state with nodes on the Fermi surfaces. The 5-band model was based on the Density Functional Theory (DFT) calculations of Cao et al. and yields a Fermi surface shown in Fig. 1(c). For undoped systems the peak in (q,w) at (pi,0) in the reduced Brillouin zone, but at finite doping and Hund's rule coupling becomes incommensurate, as shown in Fig. 1(a). The pairing interaction arises overwhelmingly from spin fluctuations near this point. Because of the near nesting of the Fermi surface sheets, a d-wave cos kx - cos ky state and s-wave cos kx+ cos ky state have the highest pairing eigenvalues. The s-wave state changes sign between sheets, but also exhibits nodes on the sheets. The near-degeneracy of several pairing states may account for the fact that in different materials with different dopings both indications of isotropic quasiparticle spectrum as well as nodes have been reported. Collective modes of the Bardasis-Schrieffer type may be visible in optics and Raman experiements. Within the interaction parameter set we explored, nodes were robust, but in the case of the s-wave (A1g) state found will be lifted by disorder. This is another possible explanation for the observation of isotropic spectrum as observed, e.g. in photoemission. If low energy excitations are observed, we proposed that the best way to determine the topology of nodal states in bulk materials is to perform a specific heat experiment in rotating magnetic field[3]. References [1] S. Graser et al, New J. Phys. 11, 025016 (2009). [2] C. Cao, P.J.Hirschfeld, and H.-P. Cheng, Phys. Rev. B 77, 220506 (2008). [3] S. Graser et al., Phys. Rev. B77, 180514 (2008)..

Role of disorder in superconducting state At present experiments on the superconducting state present many apparent paradoxes, with some interpreted in terms of a fully gapped superconducting state, and others indicating low-energy excitations[1]. While some of these differences may arise due to differences in electronic structure and local interactions, it is also possible that disorder may account for some. 5-orbital spin fluctuation theories of these systems typically find leading pairing channels corresponding to "anisotropic sign-changing s-wave" order[2], as shown in Fig. 1a. In this work[3], the effect of nonmagnetic intraband scattering on such a state was considered. If intraband scattering processes are assumed to dominate, they simply average the angular structure of the order parameter on each Fermi surface sheet, as in the conventional s-wave case. This has the effect of eventually lifting the nodes of the superconducting order parameter. Thus if intraband scattering dominates, clean systems will display the low-energy excitations characteristics of nodes, while dirty systems will be gapped.

Figure 1 For a clean order parameter on the beta sheets defined as (1+r cos 2 ), we plot the spectral gap as function of angle around sheet for various values of the scattering rate with r=1.3 and Tc0=0 (dashed), 0.3 (dotted), 1.0 (solid), and 3.1 (dashed-dotted), showing that as the gap is averaged, nodes "lift".

Unlike in the d-wave case, where nonmagnetic disorder "smears" the nodes of the unconventional order parameter, the anisotropic s-wave (A1g) states being considered as ground states for the Fe-based superconductors display a more complicated behavior. For weak disorder, there will be smearing, and concomitant "dirty nodal" power laws in, e.g. the temperature dependence of the superfluid density (l-l0~T2). However, with increasing disorder, one may expect a transition to a fully gapped state with no residual low-lying quasiparticle states. A different picture obtains if interband scattering plays an important role[4] References [1] K. Ishida et al., J. Phys. Soc. Jpn. 78, 062001 (2009). [2] S. Graser et al., New J. Phys. 11, 025016 (2009). [3] V. Mishra et al, Phys. Rev. B 79, 094512 (2009). [4] D. Parker et al, Phys. Rev. B 78, 134524 (2008); A.V. Chubukov et al., Phys. Rev. B 78, 134512 (2008).