Research ArticlePHYSICAL SCIENCES

Quasi-particle interference of heavy fermions in resonant x-ray scattering

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Science Advances  14 Oct 2016:
Vol. 2, no. 10, e1601086
DOI: 10.1126/sciadv.1601086
  • Fig. 1 STM studies on heavy fermion CeCoIn5.

    (A) Illustration of heavy fermion band formation as a result of hybridization below the T* coherence temperature of the Kondo lattice. (B) Temperature dependence of the averaged tunneling spectra on surface B of pure CeCoIn5 and CeRhIn5 (dashed line). Data are from Aynajian et al. (32). (C and D) Real-space conductance map near the Fermi energy on surface B of CeCo(In1−xCdx)5 at x = 0.15 doping level, which shows clear heavy–quasi-particle interference waves (Vbias = −100 mV, Iset point = 1.6 nA). (E and F) Fourier transforms of the real-space conductance maps at the corresponding energies, which display dispersing peaks in the [H,H] direction. Red dot indicates the (0.4,0.4) point in the reciprocal space. (G and H) Energy-momentum cuts of the Fourier transforms in the [H,H] direction [dashed line on (E)] for x = 0.15 and x = 0.0075. The heavy fermion band formation and quasi-particle interference are unaffected by the Cd doping. rlu, reciprocal lattice units; PSD, power spectral density.

  • Fig. 2 Resonant transition of the heavy 4f state.

    (A) Linearly polarized XAS spectra [measured through the total electron yield (TEY)] on CeCo(In1−xCdx)5 at x = 0 (blue) and x = 0.1 (green) doping level at 10 K, which demonstrates the transition between the 3d and 4f states. The curves are shifted vertically for clarity. (B) RXS scattering geometry, with the scattering plane lying at 45° relative to the a and b axes.

  • Fig. 3 RXS measurements on CeCoIn5.

    (A) On-resonance θ scans showing the RXS diffraction signal on pure CeCoIn5 at the Ce-M4 edge in both the [H,H] and [H,0] directions and as a comparison at the Co-L2 edge in the [H,H] direction at T = 22 K. The curves are shifted vertically for clarity. (B) Energy dependence of the RXS spectrum on and off the Ce-M4 edge. Inset shows the XAS around the M4 edge, with arrows indicating the energies where RXS spectra were measured. (C) Comparison of the RXS cross section at the M4 edge on CeCo(In1−xCdx)5 at x = 0 (red) and x = 0.1 (blue) doping level at T = 10 K. The RXS signal exhibits the same shape independently from the doping level. (D) Detailed temperature evolution of the RXS peak on pure CeCoIn5, which reveals strong temperature dependence. (E) RXS scans measured on CeRhIn5 at T = 20 and 100 K. The cross sections display no significant temperature dependence. (F) Comparison of the RXS peak height with the hybridization peak height measured by STM (from Fig. 1B) as a function of temperature. Both signals exhibit a sharp uprise at the T* Kondo temperature, suggesting the common origin of the features.

  • Fig. 4 Quasi-particle interference and RXS.

    (A) Energy-momentum structure of the quasi-particle band in the [H,H] direction on surface B, with white dashed lines indicating the boundary of the integral (Eq. 1) used to calculate the RXS intensity. (B) Calculated RXS intensity, which exhibits a broad kink starting around H = 0.2 rlu. The momentum range, where the broad peak appears, is indicated by green dashed lines on both (A) and (B). (C) Experimentally measured RXS intensity on CeCoIn5 at T = 22 K, which shows a broad peak around 0.2 < H < 0.4 rlu. The corresponding momentum range is indicated by dashed lines.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/10/e1601086/DC1

    STM measurements and data analysis

    RXS comparison on Cd-doped sample

    L dependence of the RXS enhancement

    Anomalous drop in the RXS signal

    fig. S1. STM measurements on CeCo(In1−xCdx)5.

    fig. S2. Symmetrization of the conductance map.

    fig. S3. Comparison of the RXS cross section on CeCo(In1−xCdx)5.

    fig. S4. L dependence of the RXS measurement.

  • Supplementary Materials

    This PDF file includes:

    • STM measurements and data analysis
    • RXS comparison on Cd-doped sample
    • L dependence of the RXS enhancement
    • Anomalous drop in the RXS signal
    • fig. S1. STM measurements on CeCo(In1−xCdx)5.
    • fig. S2. Symmetrization of the conductance map.
    • fig. S3. Comparison of the RXS cross section on CeCo(In1−xCdx)5.
    • fig. S4. L dependence of the RXS measurement.

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