We argue that superconductivity in the coexistence region with spin-density-wave (SDW) order in weakly doped Fe-pnictides differs qualitatively from the ordinary s +− state outside the coexistence region, as it develops an additional gap component which is a mixture of intra-pocket singlet (s ++ ) and inter-pocket spin-triplet pairings (the t−state). The coupling constant for the t−channel is proportional to the SDW order and involves interactions that do not contribute to superconductivity outside of the SDW region. We argue that the s +− and t−type superconducting orders coexist at low temperatures, and the relative phase between the two is in general different than 0 or π, manifesting explicitly the breaking of the time-reversal symmetry promoted by long-range SDW order. We show that this exotic state emerges already in the simplest model of Fe-pnictides, with one hole pocket and two symmetry-related electron pockets. We argue that in some parameter range time-reversal gets broken even before long-range superconducting order develops. IntroductionIron-based superconductors (FeSCs) have been the subject of intense study since 20081 . Their rich phase diagram includes the regions of superconductivity (SC), spin density wave (SDW), nematic order, and a region where SDW, SC, and nematic order coexist 2 . Outside the SDW/nematic region, SC develops in the spin-singlet channel and in most of Fe-based superconductors has s−wave symmetry with a π phase shift between the SC order parameters on hole and on electron pockets ( s +− gap structure) 3,4 . It has been recently argued by several groups that the multiband structure of FeSCs allows for superconducting states with more exotic properties 5-11,14-21 . Of particular interest are SC states that break time-reversal symmetry (TRS), as such states have a plethora of interesting properties like, e.g., novel collective modes 12,13,15,20 . TRS-broken states emerge when the phase differences ψ i between SC order parameters on different Fermi surfaces (FS) are not multiples of π.The two current proposals for TRS breaking in FeSCs are s + id 5,[9][10][11]19 and s + is states 6,15,20,21 . The first emerges when attractions in the d−wave and s−wave channels are of near-equal strength. The second emerges when there is a competition between different s +− states favored by inter-pocket and intra-pocket interactions. Both of these proposals were, however, argued to be applicable only to strongly hole or electron-doped FeSCc. For weakly/moderately doped FeSCs the common belief is that s +− superconductivity is robust. In this communication we argue that an exotic state which breaks TRS can emerge already at low doping, in a range where SC is known [22][23][24][25][26][27][28][29][30] to emerge from a pre-existing SDW state. Previous works on SC in the coexistence region focused on the SDW-induced modification of the form of s +− gap 31-37 . We argue that there is another effect -SDW order also induces attraction in another pairing channel, for which the order parameter is an admix...
We perform theoretical analysis of polarization-sensitive Raman spectroscopy on NaFe1−xCoxAs, EuFe2As2, SrFe2As2, and Ba(Fe1−xCox)2As2, focusing on two features seen in the B1g symmetry channel (in one Fe unit cell notation): the strong temperature dependence of the static, uniform Raman response in the normal state and the existence of a collective mode in the superconducting state. We show that both features can be explained by the coupling of fermions to pairs of magnetic fluctuations via the Aslamazov-Larkin process. We first analyze magnetically-mediated Raman intensity at the leading two-loop order and then include interactions between pairs of magnetic fluctuations. We show that the full Raman intensity in the B1g channel can be viewed as the result of the coupling of light to Ising-nematic susceptibility via Aslamazov-Larkin process. We argue that the singular temperature dependence in the normal state is the combination of the temperature dependencies of the Aslamazov-Larkin vertex and of Ising-nematic susceptibility. We discuss two scenarios for the resonance below Tc. In one, the resonance is due to the development of a pole in the fully renormalized Ising-nematic susceptibility. The other is the orbital excitonic scenario, in which spin fluctuations generate an attractive interaction between low-energy fermions.
We study the effects of hybridization between the two electron pockets in Fe-based superconductors with s-wave gap with accidental nodes. We argue that hybridization reconstructs the Fermi surfaces and also induces an additional inter-pocket pairing component. We analyze how these two effects modify the gap structure by tracing the position of the nodal points of the energy dispersions in the superconducting state. We find three possible outcomes. In the first, the nodes simply shift their positions in the Brilluoin zone; in the second, the nodes merge and disappear, in which case the gap function has either equal or opposite signs on the electron pockets; in the third, a new set of nodal points emerges, doubling the original number of nodes.
The spin resonance observed in the inelastic neutron scattering data on Fe-based superconductors has played a prominent role in the quest for determining the symmetry of the order parameter in these compounds. Most theoretical studies of the resonance employ an RPA-type approach in the particle-hole channel and associate the resonance in the spin susceptibility χS(q, ω) at momentum Q = (π, π) with the spin-exciton of an s +− superconductor, pulled below 2∆ by residual attraction associated with the sign change of the gap between Fermi points connected by Q. Here we explore the effect of fluctuations in the particle-particle channel on the spin resonance. Particle-particle and particle-hole channels are coupled in a superconductor and to what extent the spin resonance can be viewed as a particle-hole exciton needs to be addressed. In the case of purely repulsive interactions we find that the particle-particle channel at total momentum Q (the πchannel) contributes little to the resonance. However, if the interband density-density interaction is attractive and the π−resonance is possible on its own, along with spin-exciton, we find a much stronger shift of the resonance frequency from the position of the would-be spin-exciton resonance. We also show that the expected doublepeak structure in this situation does not appear because of the strong coupling between particle-hole and particle-particle channels, and ImχS(Q, ω) displays only a single peak.
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