Impurity Effects in Sign-Reversing Fully Gapped Superconductors: Analysis of FeAs Superconductors

Abstract

To understand the impurity effect on Tc in FeAs superconductors, we analyze a simple two-band BCS model with a repulsive interband interaction. The realized fully gapped superconducting state with sign reversal, which is predicted by spin fluctuation theories in this compound, is suppressed by impurities due to the interband hopping of Cooper pairs, if the interband impurity scattering I ′ is equal to the intraband one I. When |I ′ /I| < 1, in high contrast, Tc is almost unchanged by strong impurity scattering since interband scattering is almost prohibited by the multiple scattering effect. Since |I ′ /I| ∼ 0.5 is expected, the robustness of superconductivity against impurities in FeAs superconductors is naturally understood in terms of the sign-reversing fully gapped state.Keywords: iron pnictides, impurity effect, sign-reversing multiband superconductorAfter the discovery of the superconductor La(O,F)FeAs (T c = 26 K) [1], high-T c superconductors with FeAs layers have been studied intensively [2][3][4][5]. The ground state of the undoped compound is the spin density wave (SDW) state, where the ordered magnetic moment is ∼ 0.3 µ B and the ordering vector is Q ≈ (π, 0) or (0, π) [6][7][8][9]. The superconducting state is realized next to the SDW state by carrier doping [9,10] According to NMR study, the singlet superconducting state is realized in FeAs [11][12][13]. In the first-principle band calculations [14,15], the Fermi surfaces in FeAs are composed of two hole-like Fermi pockets around the Γ = (0, 0) point (FS1 and FS2 in Fig. 3) and two electron-like Fermi pockets around M= (π, 0), (0, π) points (FS3 and FS4 in Fig. 3). Theoretically, there are several possible pairing states: According to the random phase approximation (RPA) based on a realistic five-orbital tight-binding model [16], the nesting between the hole and electron pockets gives rise to the strong antiferromagnetic (AF) fluctuations with Q ≈ (π, 0), which is consistent with experimental results. Then, a fully gapped s-wave state with sign reversal is expected to emerge since AF fluctuations works as the repulsion interaction between hole and electron pockets [16][17][18][19][20][21]. Although AF fluctuations due to the nesting between two electron pockets [q ∼ (π, π/2)] can induce the d x 2 -y 2 -wave state with line nodes on the hole pockets, the obtained T c is rather low [16,[18][19][20]. On the other hand, the conventional s-wave state without sign reversal will be realized if the charge fluctuations or electron-phonon interactions are strong.Experimentally, a fully gapped superconducting state has been determined by recent penetration depth measurement [22], angle-resolved photoemission spectroscopy (ARPES) [23][24][25], and specific heat measurement [26]. The resonance peak observed by inelastic neutron measurement below T c supports the sign-reversing superconducting gap mediated by AF fluctuations [27,28]. Anomalous transport phenomena (such as Hall coefficient and Nernst signal) in the normal state in FeAs, which are similar to those...

Penetration depth, lower critical fields, and quasiparticle conductivity in Fe-arsenide superconductors

“…This systematic change indicates that the superfluid density is quite sensitive to disorder in this system and disorder promotes quasiparticle excitations significantly. It is tempting to associate the observed effect with unconventional superconductivity with sign reversal such as the s ± state [11], where impurity scattering may induce in-gap states in clear contrast to the conventional s-wave superconductivity [54,55]. Indeed, T c determined by n s → 0 is noticeably reduced for samples with large 1/τ [ Table I], consistent with theoretical studies [55].…”

“…It is tempting to associate the observed effect with unconventional superconductivity with sign reversal such as the s ± state [11], where impurity scattering may induce in-gap states in clear contrast to the conventional s-wave superconductivity [54,55]. Indeed, T c determined by n s → 0 is noticeably reduced for samples with large 1/τ [ Table I], consistent with theoretical studies [55]. At present stage, however, the microscopic nature of disorder inherent in our crystals is unclear, and a more controlled way of varying degrees of disorder is needed for further quantitative understanding of the impurity effects in Fe-based superconductors.…”

Microwave Surface-Impedance Measurements of the Magnetic Penetration Depth in Single CrystalBa1−xKxFe2As2Superconductors: Evidence f

“…This systematic change suggests that the superfluid density is quite sensitive to disorder in this system and disorder promotes quasiparticle excitations significantly. It is tempting to associate the observed effect with unconventional superconductivity with sign reversal such as the s ± state [3], where impurity scattering may induce in-gap states in clear contrast to the conventional s-wave superconductivity [16,17]. Indeed, T c determined by n s → 0 is noticeably reduced for samples with large 1/τ [ Table I], consistent with theoretical studies [17].…”

“…It is tempting to associate the observed effect with unconventional superconductivity with sign reversal such as the s ± state [3], where impurity scattering may induce in-gap states in clear contrast to the conventional s-wave superconductivity [16,17]. Indeed, T c determined by n s → 0 is noticeably reduced for samples with large 1/τ [ Table I], consistent with theoretical studies [17]. Also, the impurity-induced change of δλ ab (T ) from the exponential to T 2 dependence has been suggested theoretically [26], in good correspondence with our results.…”

Anisotropic quasiparticle lifetimes in Fe-based superconductors

“…Furthermore, we have neglected impurity scattering. In multi-band impurity models 35,36 , the ratio of intra-to inter-band scattering is taken as a parameter, and the scattering rate asymmetry between electrons and holes is weak. One might expect that an "orbital impurity" model, where an impurity introduces a local Coulomb potential for electrons in all d-orbitals, might produce a scattering rate anisotropy in k-space due to the matrix elements a n,λ k , just as in the inelastic scattering case.…”