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 T_{c}'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.
Weak-coupling approaches
to the pairing problem in the iron pnictide superconductors have predicted a
wide variety of superconducting ground states. The usual paradigm assumes that
the repulsive Coulomb interaction creates an effective interaction ("spin
fluctuation pairing") proportional to the magnetic susceptibility (right)
strongly peaked at pi,0, the near-nesting vector of the
small hole and electron Fermi surface pockets. To solve the gap equation with
repulsive interaction, the gap must change sign between the pockets. In a
realistic material-specific calculations, there are some modifications of this
simple scheme. The Hirschfeld group 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 [1]. We discussed 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 were
found to be 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.
The 5-band
model was based on the Density Functional Theory (DFT) calculations of Cao et
al.[2] and yielded the Fermi surface shown middle right. 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.
More recently, these calculations have expanded to account for the 3D nature of
the
real materials. We have studied both KFe_{2}Se_{2}, an unusual
material with missing central hole pocket, and a likely highly anisotropic s or
d wave system. In addiiton, we explored the LiFeAs system together with the
Dresden group, based on an ARPES-derived tight-binding band (right). This is a
major challenge for the theory due to the very small 3D hole pockets present at
the Fermi surface, and presence of incipient bands nearby.
Sign-changing s-wave state with nodes on the Fermi surfaces.
a) Nodal s_{+/-} and s_{++} states. b) Sequences of gap structure (top) and density of states (bottom) as disorder increases in an s_{+/-} state. Only the last step in the sequence (bound state formation due to interband scattering) is unique to this 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. If intraband scattering processes (left) 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. If interband dominates, the gap nodes will simply be smeared.
In the presence of several bands and both intra- and interband scattering the resultant behavior can be quite complex. For example, a number of experiments on the suppression of T_{c} by disorder have declared that T_{c} suppression is "too slow" for an s_{+/-}, since it is slower than the Abrikosov-Gor'kov like rate expected for a symmetric 2-band system with opposite sign gaps and inter- and intraband scattering equal (maximum pairbreaking rate). In Ref. 1, Wang et al. showed that essentially any T_{c} suppression rate is possible when plotted against an obsevable measure of disorder, e.g. residual resistivity.
Thus it is difficult to use controlled disorder to identify s_{+/-} states. One exception is the remakable behavior in a nodal system P-doped Ba122 identified by Mizukami et al. [2], who measured a nonmonotonic exponent in the low-T penetration depth (see left for a schematic description of what happens in a nodal s-wave system with intra and inter-band scattering). Another possiblity is discussed in this paper on quasiparticle interference .
Fe-based superconducting materials are known to exhibit strong "electronic nematic" tendencies, i.e. the electronic system has a large susceptibility to deform, breaking C4 symmetry, when a weak tetragonal symmetry breaking perturbation is applied. Impurities are known to be able to "freeze" fluctuations of these ordered phase around themselves, creating an emergent defect state. In a phase in proximity to magnetic stripe order characteristic of Fe-based superconductors, these "nematogens" take the form shown on the right: they elongate and grow above the transition, then freeze below into remarkably long defect structures which have been seen in STM. Recently, the PI and group calculated the scattering rate anisotropy to be expected from such objects, and were able to explain a number of puzzling aspects of transport experiments on BaFe2As2.