Visualization of electron nematicity and unidirectional antiferroic fluctuations at high temperatures in NaFeAs

Journal name:
Nature Physics
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Superconductivity in the iron pnictides is often closely connected to a nematic state in which the tetragonal symmetry of the crystal is spontaneously broken. Determining the dominant interactions responsible for this symmetry breaking is essential to understanding the superconducting state. Here, we use atomic-resolution variable-temperature scanning tunnelling spectroscopy to probe the nanoscale electronic structure of the nematically ordered, parent pnictide NaFeAs and compare it with non-nematic LiFeAs. Local electronic nematicity is only manifest in NaFeAs and is found to persist to high temperatures in the nominally tetragonal phase of the crystal. The spatial distribution and energy dependence of the electronic anisotropy at high temperatures is explained by the persistence of large-amplitude, short-range, unidirectional, antiferroic fluctuations, indicating that strong density-wave fluctuations exist and couple to near-Fermi surface electrons even far from the structural and density-wave phase boundaries.

At a glance


  1. Topographic STM and STS maps of LiFeAs and NaFeAs at low temperatures.
    Figure 1: Topographic STM and STS maps of LiFeAs and NaFeAs at low temperatures.

    a, Constant-current STM topograph of LiFeAs (V = − 120mV, I=270pA,T=39K). The alkali atoms are observed on the surface layer, and the underlying iron atoms are illustrated at the lower left side. The two inequivalent positions of the iron atoms are shown with filled and unfilled circles. An alkali vacancy is identified with a black arrow, and red lines indicate the size and orientation of iron site defects. Grey arrows identify the alkali–alkali directions, and cyan arrows identify the orientation of the Fe–Fe lattice (continued for the rest of Fig. 1). b, Differential conductance (dI/dV) map (V = − 120mV, I=270pA,T=39K) of LiFeAs. The iron defects have prominent signatures in the dI/dV maps with the same size and symmetry as the topographic features, as indicated by the red lines. c, dI/dV map of NaFeAs (V = − 100mV, I=300pA,T=26K) showing prominent features that are oriented along one Fe–Fe direction at 45 to the crystallographic axes. The size and orientation of iron site defect that produce the features are indicated by red lines. di, dI/dV maps at different energies of the area shown in c, showing a clear variation in the contrast and size of the features as a function of energy. j, Large-area dI/dV image of NaFeAs (same junction conditions and temperature as d) showing the universality of the spectroscopic features and the presence of domains where the unidirectional features rotate by 90.

  2. STS maps of NaFeAs in real and Fourier space in the SDW phase.
    Figure 2: STS maps of NaFeAs in real and Fourier space in the SDW phase.

    ad, Large-area differential conductance maps on NaFeAs (V = − 100mV, I=300pA,T=26K). Arrows in c indicate ferromagnetic (FM) and antiferromagnetic (AFM) directions. eh, Corresponding FFT images. The FFT images show well-defined structures whose wavelengths and intensities are energy dependent. The size of the images is half of the single Fe unit cell Brillouin zone.

  3. Temperature dependence of anisotropic STS features in real and Fourier space.
    Figure 3: Temperature dependence of anisotropic STS features in real and Fourier space.

    a,c,e,g,i,k, Large-area maps of the differential conductance at 10 meV at different temperatures on NaFeAs. The raw images show that the unidirectional features persist up to the highest temperatures shown. However, the intensity of the unidirectional features decreases with increasing temperature and becomes weak above 80 K. b,d,f,h,j,l, The corresponding FFT images (same scale as Fig. 2e–h). Junction settings for 26, 38, 46 and 61 K are V = − 100mV and I=300pA. Junction settings for 54 and 75 K are V =−50mV and I=300pA. It is seen that the same basic structure exists in all the FFT images, even above TSDW=41K andTS=52K. Images in ad and el are from different samples.

  4. Comparison between STS and ARPES JDOS.
    Figure 4: Comparison between STS and ARPES JDOS.

    ac, Fourier transforms of STS images at the Fermi energy for 26, 46 and 61 K respectively. All three STS images show the presence of a strong scattering intensity at Qx=0 and Qx= ± qD (green dot). d, ARPES intensity at the Fermi surface in the SDW (T < TSDW) phase38. Magenta arrows indicate scattering that produces 45 peaks in the JDOS, and the yellow arrow corresponds to 0/180 intensity. e, JDOS from autocorrelation of SDW ARPES intensity. f, SDW STS from a placed above the SDW JDOS from e. Colour-coded dotted-line contours correspond to scattering peaks that are produced by same coloured scattering vectors as in d. g, JDOS for OPM phase. The Fermi surface is shown in Supplementary Fig. 5. h,i, Line cuts of the JDOS and STS along the dotted orange lines in a and e for different phases/temperatures. Clear peaks arising from reconstructed Fermi surface scattering in the STS data only matches the SDW JDOS.

  5. Theoretical bandstructure and short-range SDW calculations.
    Figure 5: Theoretical bandstructure and short-range SDW calculations.

    a,b, Model Fermi surface density of states (N(k)) in a, and QPI (|δN(q)|) in b in the presence of long-range SDW order. c, QPI in the presence of short-range (ξ=8a0) SDW order (see Supplementary Information). d, Line cuts along the orange dotted line in c for different values of correlation length (in units of a0). Split peaks develop with increasing correlation length, in analogy to STS data.

  6. Energy and temperature dependence of electronic anisotropy.
    Figure 6: Energy and temperature dependence of electronic anisotropy.

    a, Visual depiction of the anisotropy map calculation procedure. The average spectroscopic image around a single defect in the SDW phase at E=10meV and T=26K is displayed on the left. We rotate the image by 90 (around the centre), subtract it from the original image, and plot the difference (anisotropy map) on the right. bd, Anisotropy maps at various energies calculated at the same temperature as a and plotted on the same colour scale. The strength of the anisotropy is seen to decrease with increasing energy. e, Total anisotropy as a function of energy at various temperatures (junction conditions are the same for all temperatures). It is seen that the anisotropy is maximum at an energy E=10meV and falls off at higher energy. The average spectrum of the sample at each temperature is shown in the inset. The maximum of the anisotropy is located close to the midpoint of the gap, and the energy range of the anisotropy is comparable to the size of the low-temperature gap.


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Author information


  1. Department of Physics, Columbia University, New York, New York 10027, USA

    • E. P. Rosenthal,
    • E. F. Andrade,
    • C. J. Arguello,
    • A. J. Millis &
    • A. N. Pasupathy
  2. School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA

    • R. M. Fernandes
  3. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

    • L. Y. Xing,
    • X. C. Wang &
    • C. Q. Jin


STM experiments and data analysis: E.P.R., E.F.A., C.J.A. and A.N.P. Theoretical analysis: R.M.F. and A.J.M. Sample synthesis and characterization: L.Y.X., X.C.W. and C.Q.J. All authors participated in writing the manuscript.

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The authors declare no competing financial interests.

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