Identifying the 'fingerprint' of antiferromagnetic spin fluctuations in iron pnictide superconductors

Journal name:
Nature Physics
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Published online

Cooper pairing in the iron-based high-Tc superconductors1, 2, 3 is often conjectured to involve bosonic fluctuations. Among the candidates are antiferromagnetic spin fluctuations1, 4, 5 and d-orbital fluctuations amplified by phonons6, 7. Any such electron–boson interaction should alter the electrons ‘self-energy, and then become detectable through consequent modifications in the energy dependence of the electrons momentum and lifetime8, 9, 10. Here we introduce a novel theoretical/experimental approach aimed at uniquely identifying the relevant fluctuations of iron-based superconductors by measuring effects of their self-energy. We use innovative quasiparticle interference (QPI) imaging11 techniques in LiFeAs to reveal strongly momentum-space anisotropic self-energy signatures that are focused along the Fe–Fe (interband scattering) direction, where the spin fluctuations of LiFeAs are concentrated. These effects coincide in energy with perturbations to the density of states N(ω) usually associated with the Cooper pairing interaction. We show that all the measured phenomena comprise the predicted QPI ‘fingerprint of a self-energy due to antiferromagnetic spin fluctuations, thereby distinguishing them as the predominant electron–boson interaction.

At a glance


  1. Electronic self-energy due to coupling to bosonic fluctuations.
    Figure 1: Electronic self-energy due to coupling to bosonic fluctuations.

    a, Electronic structure of the first Brillouin zone of FeAs superconductors; here shown using parameters specific to LiFeAs (the inner hole pockets are omitted for clarity). The γ band surrounds the Γ point, the β1 and β2 bands are hybridized surrounding the M point at the corner. The AFSF with Q = (π, π)/a0 (red arrow) can connect the hole-like bands surrounding the Γ point with the electron-like bands surrounding the M point. b, Diagram of the lowest order self-energy contribution from electron–boson interactions. c, Spectral function A(k, ω) ∝ ImG(k, ω) of a superconducting hole-like band (with unrenormalized normal-state dispersion shown as a red dashed line) with the superconducting gap Δ and the dispersion renormalization at energy Δ + Ω (arrow) due to coupling to a phonon of frequency Ω. d, Density of electronic states spectrum N(ω) associated with (c), showing a kink at energy Δ + Ω. e, Schematic view of the kinematic constraint in (k, ω)-space. We find that the self-energy features on the γ band can only appear at (k, ωkγ) if there exists a partner point (k − Q, ωk−Qm) withωk−Qm = ωkγΩΔ to satisfy the kinematic constraint. The blue surface at the centre and the yellow surfaces at the corners of the Brillouin zone are defined by the hole-band and the outer-electron-band dispersion. The red surface indicates the hole band displaced by the AFSF momentum Q = (π, π)/a0 (dark red arrow) and energy Ω (light red arrow). The points that satisfy the kinematic constraint (equation (1)) are defined by the intersection of the red and blue surfaces, and indicated with a solid black line. These points are expected to exhibit the strongest self-energy effects due to coupling to AFSF. The anisotropy of the black line demonstrates directly how the AFSF self-energy effects must exist at different ω in different k-space directions around a particular Fermi pocket (for example, the γ band in a).

  2. Comparison between scattering interference theory with AFSF-driven self-energy effects and the experiments.
    Figure 2: Comparison between scattering interference theory with AFSF-driven self-energy effects and the experiments.

    ad, Theoretically predicted QPI patterns g(q, ω) for LiFeAs with Greens function including the self-energy effect due to the coupling between electrons and resonant AFSF fluctuations, as described in Supplementary Section II. In these simulations, we suppressed the interband scattering visible in the data to highlight the QPI of the γ band that are the focus of this study. Note, in c,d the strong anisotropy induced by the kinematic constraint (equation (1)) with clear suppression of g(q, ω) forq along the Fe–Fe direction, which is strikingly different from the strong gap anisotropy that dictates the pattern in a. eh, Measured QPI patterns g(q, ω) (obtained from g(r, ω) of LiFeAs). e, QPI signature of anisotropic energy gaps. f, Expected isotropic signature of the complete Fermi surface of the γ band. g,h, Transition to a strongly anisotropic g(q, ω). Note the suppression of g(q, ω) occurring along the Fe–Fe direction. il, Real-space images of g(r, ω) from which eh were obtained. The insets show a zoom-in onto a particular impurity, revealing the real-space standing waves from QPI.

  3. /`Fingerprint[rsquor] distinguishing antiferromagnetic spin fluctuations from phonon generated orbital fluctuations in LiFeAs.
    Figure 3: ‘Fingerprint distinguishing antiferromagnetic spin fluctuations from phonon generated orbital fluctuations in LiFeAs.

    ac, Predicted QPI response calculated with self-energy driven by the Fe-Eg phonon. a,b, Sequential images of g(q, ω) for two different ω, one below and one near the coupling energy. c, Predicted g(q, ω) in three different directions in q-space, corresponding to the Fe–As direction (left), the Fe–Fe direction (right) and an intermediate direction (centre). Different grey lines correspond to different ω, with a 1 meV increase between each neighbouring pair, starting from the lowest bias ω = 0 at the bottom. The plots are offset for clarity, and the red dots indicate the maxima. The g(q, ω) on the γ band remains virtually isotropic, despite the momentum dependence of the electron–phonon coupling in our simulations. df, Predicted QPI response calculated with self-energy driven by resonant AFSF. d,e, Predicted g(q, ω) for the same energies as in a,b. f, Predicted g(q, ω) in three different directions in q-space, as in c. g(q, ω) on the γ band is predicted to be highly anisotropic. g, Predicted ReΣ(k(ω, θ), ω) at fixed energy ω = 10 meV calculated with self-energy driven by resonant AFSF (blue) and the Fe-Eg phonon (red) as a function of the angle θ (as defined in b,e) around the γ band.

  4. QPI measurements of anisotropic renormalization of dispersion due to self-energy in LiFeAs.
    Figure 4: QPI measurements of anisotropic renormalization of dispersion due to self-energy in LiFeAs.

    a, Measured g(q, ω) represented in q–ω space for 0 < ω < 30 meV, with the (0, 1) and (1, 1) directions highlighted. The inset shows the measured data up to ω = 60 meV. Red arrow indicates the energy ω ~ 12 meV at which sudden changes in dispersion and isotropy of g(q, ω) are observed. See Supplementary Movie 1, in which this effect is vivid. b, The N(ω) measured simultaneously with g(q, ω) and normalized by N(ω) at T = 16 K. Vertical red arrows indicate the energy ω ~ 12 meV at which features associated with Cooper pairing are observed. The inset shows the original N(ω) ~ dI/dV (ω). ce, Lineplots of measured g(q, ω) data for different energies ω along the Fe–As direction (left), the Fe–Fe direction (right) and an intermediate direction (centre). The data at different ω are offset vertically for clarity. The angle indicated is θ measured from the Fe–As direction. The red lines represent fits as discussed in Supplementary Section VIII. f, Dispersion of the maxima in g(q, ω) extracted from line cuts as in ce (Supplementary Section VIII). The angle indicated is θ measured from the Fe–As direction. These dispersions are to be compared with the predictions in Fig. 3a–c or Fig. 3d–f. g, Measured ΔE, the departure of the dispersion of the maxima in g(q, ω) from a model with no self-energy effect, as a function of the angle θ around the γ band of LiFeAs. This is to be compared with the theoretical prediction in Fig. 3g.


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Author information

  1. These authors contributed equally to this work.

    • M. P. Allan,
    • Kyungmin Lee &
    • A. W. Rost


  1. LASSP, Department of Physics, Cornell University, Ithaca, New York 14853, USA

    • M. P. Allan,
    • Kyungmin Lee,
    • A. W. Rost,
    • M. H. Fischer,
    • F. Massee,
    • J. C. Davis &
    • Eun-Ah Kim
  2. CMPMS Department, Brookhaven National Laboratory, Upton, New York 11973, USA

    • M. P. Allan,
    • F. Massee &
    • J. C. Davis
  3. School of Physics and Astronomy, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland

    • A. W. Rost &
    • J. C. Davis
  4. Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan

    • A. W. Rost
  5. Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan

    • K. Kihou,
    • C-H. Lee,
    • A. Iyo &
    • H. Eisaki
  6. JST, Transformative Research-Project on Iron Pnictides (TRIP), Tokyo 102-0075, Japan

    • K. Kihou,
    • C-H. Lee,
    • A. Iyo &
    • H. Eisaki
  7. Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan

    • T-M. Chuang
  8. Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA

    • J. C. Davis


M.P.A., A.W.R., F.M. and T-M.C. performed the experiments and analysed the data; K.K., A.I., C-H.L. and H.E. synthesized the samples; K.L. and M.H.F. performed the theoretical calculations of the self-energy and simulation of quasiparticle interference. This project was initiated by the experimental discovery of the strongly anisotropic QPI features in the electron–boson energy range (A.W.R.) and by the resulting hypothesis that they are self-energy effects; J.C.D. and E-A.K. supervised the investigation and wrote the paper with contributions from M.P.A., A.W.R., F.M., K.L. and M.H.F. The manuscript reflects the contributions of all authors.

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