Observation of Momentum-Confined In-Gap Impurity State in ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$: Evidence for Antiphase ${s}_{\ifmmode\pm\else\textpm\fi{}}$ Pairing

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Observation of Momentum-Confined In-Gap Impurity State in ${Ba}_{0.6} K_{0.4} {Fe}_{2} {As}_{2}$ : Evidence for Antiphase $s_{\pm}$ Pairing

P. Zhang, P. Richard, T. Qian, X. Shi, J. Ma, L.-K. Zeng, X.-P. Wang, E. Rienks, C.-L. Zhang, Pengcheng Dai, Y.-Z. You, Z.-Y. Weng, X.-X. Wu, J. P. Hu, and H. Ding

Phys. Rev. X 4, 031001 – Published 3 July 2014

Abstract

We report the observation by angle-resolved photoemission spectroscopy of an impurity state located inside the superconducting gap of ${Ba}_{0.6} K_{0.4} {Fe}_{2} {As}_{2}$ and vanishing above the superconducting critical temperature, for which the spectral weight is confined in momentum space near the Fermi wave-vector positions. We demonstrate, supported by theoretical simulations, that this in-gap state originates from weak scattering between bands with opposite sign of the superconducting-gap phase. This weak scattering, likely due to off-plane nonmagnetic (Ba, K) disorder, occurs mostly among neighboring Fermi surfaces, suggesting that the superconducting-gap phase changes sign within holelike (and electronlike) bands. Our results impose severe restrictions on the models promoted to explain high-temperature superconductivity in these materials.

Received 3 January 2014

DOI:https://doi.org/10.1103/PhysRevX.4.031001

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Published by the American Physical Society

Authors & Affiliations

P. Zhang¹, P. Richard^1,2,*, T. Qian¹, X. Shi¹, J. Ma¹, L.-K. Zeng¹, X.-P. Wang¹, E. Rienks³, C.-L. Zhang^4,5, Pengcheng Dai^1,4, Y.-Z. You⁶, Z.-Y. Weng^6,2, X.-X. Wu¹, J. P. Hu^1,2,7, and H. Ding^1,2,†

¹Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Collaborative Innovation Center of Quantum Matter, Beijing, China
³Helmholtz-Zentrum Berlin, BESSY, D-12489 Berlin, Germany
⁴Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
⁵Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA
⁶Institute for Advanced Study, Tsinguha University, Beijing 100084, China
⁷Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA

^*p.richard@iphy.ac.cn
^†dingh@iphy.ac.cn

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Superconductivity is an electronic state of matter observed in some materials below a critical temperature $T_{c}$ , at which electrons pair, and a gain in energy characterized by the opening of an energy gap is achieved. In general, this superconducting gap is a complex macroscopic quantity represented by an amplitude and a phase, both of which are necessary for identifying microscopic interactions by which the electrons form pairs. Although the amplitude of the superconducting gap can be measured by several experimental techniques, the phase is difficult to assess, particularly for multiband systems such as high-temperature, Fe-based superconductors, for which this issue remains unsolved; some researchers propose that the phase remains constant while other scientists maintain that the phase alternates sign. We determine the phase of the superconducting gap in the Fe-based superconductors, critical for understanding how high-temperature superconductors function.

We use angle-resolved photoemission spectroscopy to investigate the superconducting state of ( $T_{c} \sim 37$ K), an optimally doped Fe-based superconductor. We observe a nondispersive in-gap state around 6 meV, with a spectral weight confined near the Fermi momenta. Using numerical simulations, we show that this feature appears because of weak scattering with a nonmagnetic impurity. More importantly, we demonstrate that the sign of the superconducting-gap phase varies in the momentum space. Interestingly, our calculations indicate that the orbital antiphase $S_{\pm}$ configuration, proposed recently, is the most likely in this system. In fact, the antiphase $S_{\pm}$ state may be common to all families of Fe-based superconductors.

By providing a momentum-resolved description of the phase of the superconducting gap, our results impose severe constraints for the model proposed to explain unconventional high-temperature superconductivity in the Fe-based superconductors.

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Vol. 4, Iss. 3 — July - September 2014

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Figure 1
(a),(b) ARPES intensity plots for a cut passing through $Γ$ and oriented along $Γ − M$ , recorded at 1 K, using $σ$ and $π$ incident-light polarizations, respectively. The dashed blue and red lines indicate the positions of the MDCs in (l) and (m). (c) Sum of the ARPES intensity plots in (a) and (b). The solid turquoise and pink curves represent the band dispersions extracted from the MDCs and EDCs in (a) and (b), respectively. (d) ARPES intensity plot for a cut passing near the $M$ point, measured at 4.2 K with unpolarized light. (e)–(g) EDC plots corresponding to the cuts shown in (a), (b), and (d), respectively. The EDCs in black correspond to the $k_{F}$ positions. (h)–(j) Near- $E_{F}$ zooms corresponding to the the dashed boxes in (e), (f), and (g), respectively. Circles and squares are used to identify the $α / α^{'}$ band and the impurity state, respectively, as obtained by the maximum positions in the EDCs. (k) Schematic representation of the polarization configurations. (l) Comparison of the MDCs recorded with $σ$ and $π$ polarizations at the MDC#1 position (7 meV below $E_{F}$ ) in (a) (blue curve) and (b) (red curve). The vertical dashed lines are guides to the eye for the peak positions. (m) Same as (l) but for the MDC#2 position (22 meV below $E_{F}$ ).
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Figure 2
(a)–(d) Temperature evolution, from (a) 15 K to (d) 40 K, of the ARPES intensity plots for the cut presented in Fig. 1. The red arrows indicate the in-gap states. The EDCs at $k_{F}$ are also displayed in red. The EDC in (d) does not show any in-gap state, as suggested by a fit (in green) to the Fermi-Dirac function convoluted with the resolution function. (e) Temperature evolution of the SC-gap amplitude (red) and the position of the in-gap-state peak, as determined from EDC analysis. (f) Temperature dependence of the spectral weight of the SC coherent peak (red) and in-gap-state peak at $k_{F}$ , as determined from EDC analysis. The intensity is normalized to the area under the fit curve of the SC quasi-particle (QP) peak at 1 K. The inset illustrates how the spectral weight is extracted. After symmetrizing the EDCs to approximately remove the Fermi cutoff and removing a background shown by a dashed line, we fit the left part of the subtracted symmetrized EDC using two Lorentzian curves. The spectral weight is given by the area below each Lorentzian curve.
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Figure 3
(a) Schematic illustration of an impurity level below a dispersive band. (b) Comparison of the MDC at the impurity state levels IS1 and IS2 from (c) and (d). (c),(d) Numerical simulations of the spectral weight for a system with a dispersive band of the form $ϵ (k) = t \cos (π k)$ (with $t = - 1 eV$ ) scattering on 5% of impurities, according to Eq. (1), with $V_{0} / | t | = - 3.0$ and $V_{0} / | t | = - 1.2$ , respectively. (e) Impurity state in Si-doped $β − {Ga}_{2} O_{3}$ , from Ref. [13]. The red curve represents the band structure obtained from local density approximation calculations.
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Figure 4
(a)–(c) Numerical simulations of the spectral weight for a system with an impurity interacting with two dispersive bands according to Eq. (3) in the normal state ( $Δ_{1} = Δ_{2} = 0$ ), in the in-phase SC state ( $Δ_{1} = \frac{1}{2} Δ_{2} \neq 0$ ), and in the antiphase SC state ( $Δ_{1} = - \frac{1}{2} Δ_{2} \neq 0$ ), respectively. In all cases, we use $V_{0} / | t | = - 1$ . The dashed red lines represent the electronic dispersion in the normal state. (d) Simulation of the energy position of the in-gap impurity state as a function of $| Δ_{2} |$ for a fixed $| Δ_{1} |$ . (e) Zoom on the impurity state found experimentally near the $α$ band of ${Ba}_{0.6} K_{0.4} {Fe}_{2} {As}_{2}$ . (f)–(i) Numerical simulation of the zoom near the impurity state corresponding to the dashed box from (c) (antiphase SC), as a function of $| Δ_{2} |$ , for $| Δ_{1} | = 6 meV$ (antiphase gaps). The dashed red line in (f) represents the bare band dispersion.
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Figure 5
(a) Calculated scattering strength as a function of momentum transfer (see the text). (b) Schematic FS of ${Ba}_{0.6} K_{0.4} {Fe}_{2} {As}_{2}$ , with the FS sheets drawn in red and blue having opposite SC-gap-phase sign.
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Physical Review X

Observation of Momentum-Confined In-Gap Impurity State in Ba0.6K0.4Fe2As2: Evidence for Antiphase s± Pairing

P. Zhang, P. Richard, T. Qian, X. Shi, J. Ma, L.-K. Zeng, X.-P. Wang, E. Rienks, C.-L. Zhang, Pengcheng Dai, Y.-Z. You, Z.-Y. Weng, X.-X. Wu, J. P. Hu, and H. Ding

Phys. Rev. X 4, 031001 – Published 3 July 2014

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Observation of Momentum-Confined In-Gap Impurity State in ${Ba}_{0.6} K_{0.4} {Fe}_{2} {As}_{2}$ : Evidence for Antiphase $s_{\pm}$ Pairing