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We investigate pairing mechanism in multiband superconductors. To put our feet on firm ground, unbiased renormalization group analysis is carried out for iron-based superconductors. It is quite remarkable that, after integrating out quantum fluctuations, the renormalization-group flows agree exceedingly well with a mean-field Hamiltonian where interband pair hopping plays an essential role. Through interband pair hopping, electrons can overcome the repulsive interaction between them and form resonating Cooper pairs between different bands. Unlike the conventional superconductors, the pairing mechanism in multiband superconductors is resonating pair hopping between different bands, just like the resonating chemical bonds in benzene. The effective mean-field Hamiltonian spots a small parameter dictating the critical temperature and also explains how interband pair hopping always enahnces spin fluctuations at the nesting momentum connecting the Fermi surfaces. In short, no attractive glue is needed and resonating interband pair hopping is the key to Cooper pair formation in unconventional superconductors. Implications to cuprates and related issues are also discussed at the end.
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We have computed alpha^2Fs for the hole-doped cuprates within the framework of the one-band Hubbard model, where the full magnetic response of the system is treated properly. The d-wave pairing weight alpha^2F_d is found to contain not only a low energy peak due to excitations near (pi,pi) expected from neutron scattering data, but to also display substantial spectral weight at higher energies due to contributions from other parts of the Brillouin zone as well as pairbreaking ferromagnetic excitations at low energies. The resulting solutions of the Eliashberg equations yield transition temperatures and gaps comparable to the experimentally observed values, suggesting that magnetic excitations of both high and low energies play an important role in providing the pairing glue in the cuprates.
Disorder - impurities and defects violating an ideal order - is always present in solids. It can result in interesting and sometimes unexpected effects in multiband superconductors. Especially if the superconductivity is unconventional thus having other than the usual s-wave symmetry. This paper uses the examples of iron-based pnictides and chalcogenides to examine how both nonmagnetic and magnetic impurities affect superconducting states with $s_pm$ and $s_{++}$ order parameters. We show that disorder causes the transitions between $s_pm$ and $s_{++}$ states and examine observable effects these transitions can produce.
In iron selenide superconductors only electron-like Fermi pockets survive, challenging the $S^{pm}$ pairing based on the quasi-nesting between the electron and hole Fermi pockets (as in iron arsenides). By functional renormalization group study we show that an in-phase $S$-wave pairing on the electron pockets ($S^{++}_{ee}$) is realized. The pairing mechanism involves two competing driving forces: The strong C-type spin fluctuations cause attractive pair scattering between and within electron pockets via Cooperon excitations on the virtual hole pockets, while the G-type spin fluctuations cause repulsive pair scattering. The latter effect is however weakened by the hybridization splitting of the electron pockets. The resulting $S^{++}_{ee}$-wave pairing symmetry is consistent with experiments. We further propose that the quasiparticle interference pattern in scanning tunneling microscopy and the Andreev reflection in out-of-plane contact tunneling are efficient probes of in-phase versus anti-phase $S$-wave pairing on the electron pockets.
We consider a problem of superconductivity coexistence with the spin-density-wave order in disordered multiband metals. It is assumed that random variations of the disorder potential on short length scales render the interactions between electrons to develop spatial correlations. As a consequence, both superconducting and magnetic order parameters become spatially inhomogeneous and are described by the universal phenomenological quantities, whereas all the microscopic details are encoded in the correlation function of the coupling strength fluctuations. We consider a minimal model with two nested two-dimensional Fermi surfaces and disorder potentials which include both intra- and inter-band scattering. The model is analyzed using the quasiclassical approach to show that short-scale pairing-potential disorder leads to a broadening of the coexistence region.
I review theoretical ideas and implications of experiments for the gap structure and symmetry of the Fe-based superconductors. Unlike any other class of unconventional superconductors, one has in these systems the possibility to tune the interactions by small changes in pressure, doping or disorder. Thus, measurements of order parameter evolution with these parameters should enable a deeper understanding of the underlying interactions. I briefly review the standard paradigm for $s$-wave pairing in these systems, and then focus on developments in the past several years which have challenged this picture. I discuss the reasons for the apparent close competition between pairing in s- and d-wave channels, particularly in those systems where one type of Fermi surface pocket -- hole or electron -- is missing. Observation of a transition between $s$- and $d$-wave symmetry, possibly via a time reversal symmetry breaking $s+id$ state, would provide an importantconfirmation of these ideas. Several proposals for detecting these novel phases are discussed, including the appearance of order parameter collective modes in Raman and optical conductivities. Transitions between two different types of $s$-wave states, involving various combinations of signs on Fermi surface pockets, can also proceed through a ${cal T}$-breaking $s+is$ state. I discuss recent work that suggests pairing may take place away from the Fermi level over a surprisingly large energy range, as well as the effect of glide plane symmetry of the Fe-based systems on the superconductivity, including various exotic, time and translational invariance breaking pair states that have been proposed. Finally, I address disorder issues, and the various ways systematic introduction of disorder can (and cannot) be used to extract information on gap symmetry and structure.
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