Universal $2{\mathrm{\ensuremath{\Delta}}}_{max}/{k}_{B}{T}_{c}$ scaling decoupled from the electronic coherence in iron-based superconductors

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Universal $2 Δ_{max} / k_{B} T_{c}$ scaling decoupled from the electronic coherence in iron-based superconductors

H. Miao, W. H. Brito, Z. P. Yin, R. D. Zhong, G. D. Gu, P. D. Johnson, M. P. M. Dean, S. Choi, G. Kotliar, W. Ku, X. C. Wang, C. Q. Jin, S.-F. Wu, T. Qian, and H. Ding

Phys. Rev. B 98, 020502(R) – Published 9 July 2018

Abstract

Here, we use angle-resolved photoemission spectroscopy to study superconductivity that emerges in two extreme cases, from a Fermi-liquid phase (LiFeAs) and an incoherent bad-metal phase ( ${FeTe}_{0.55} {Se}_{0.45}$ ). We find that although the electronic coherence can strongly reshape the single-particle spectral function in the superconducting state, it is decoupled from the maximum-superconducting-gap and $T_{c}$ ratio $2 Δ_{max} / k_{B} T_{c}$ , which shows a universal scaling that is valid for all iron-based superconductors (FeSCs). Our observation excludes pairing scenarios in the BCS and the BEC limit for FeSCs and calls for a universal strong-coupling pairing mechanism for the FeSCs.

Received 28 February 2018
Revised 10 June 2018

DOI:https://doi.org/10.1103/PhysRevB.98.020502

Physics Subject Headings (PhySH)

Multiband superconductivity Pairing mechanisms Superconducting gap Superconductivity

Pnictides Single crystal materials Unconventional superconductors

Angle-resolved photoemission spectroscopy DFT+DMFT

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Miao^1,2,*, W. H. Brito², Z. P. Yin³, R. D. Zhong², G. D. Gu², P. D. Johnson², M. P. M. Dean², S. Choi², G. Kotliar^2,4, W. Ku⁵, X. C. Wang¹, C. Q. Jin^1,6, S.-F. Wu¹, T. Qian¹, and H. Ding^1,6,†

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
³Department of Physics and Center for Advanced Quantum Studies, Beijing Normal University, Beijing 100875, China
⁴Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
⁵Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, China
⁶Collaborative Innovation Center of Quantum Matter, Beijing 100190, China

^*hmiao@bnl.gov
^†dingh@iphy.ac.cn

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Vol. 98, Iss. 2 — 1 July 2018

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Figure 1
Schematic phase diagram of ${LiFe}_{1 - x} {Co}_{x} As$ and ${FeTe}_{1 - x} {Se}_{x}$ . ${LiFe}_{1 - x} {Co}_{x} As$ has a simpler phase diagram, where superconductivity emerges in the pristine LiFeAs and the SC transition temperature $T_{c}$ is linearly suppressed via electron doping. ${FeTe}_{1 - x} {Se}_{x}$ , however, has competing ground states, where superconductivity is induced by suppressing BC-AFM order and remains robust against Se substitutions. (a) Temperature-dependent resistivity of LiFeAs. The dashed line is a power function $a + b T^{n}$ fitting of the data. $n = 2$ is found in LiFeAs, demonstrating a Fermi-liquid behavior up to 60 K. (b) Experimentally determined FS topology of LiFeAs. The dashed orange ellipse at the $Γ$ point is moved from the $M$ point to show the FS size difference $δ$ that gives rise the incommensurate low-energy spin excitations [15]. (c) BC-AFM order of FeTe that is better described by the strong-coupling $J_{1} - J_{2} - J_{3}$ model and is not obtained by the FS nesting scenario. (d) Temperature-dependent resistivity of SC ${FeTe}_{0.55} {Se}_{0.45}$ shows a bad-metal normal state with $n = 0.5$ . The superconducting coherence lengths $ξ_{SC}$ of LiFeAs and ${FeTe}_{0.55} {Se}_{0.45}$ are 40 and 20 Å, respectively [16, 17].
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Figure 2
(a), (b) DFT+DMFT calculated $A (k, ω)$ without spin-orbit coupling of LiFeAs and ${FeTe}_{0.55} {Se}_{0.45}$ , respectively. The color scales of (a) and (b) are the same. Colored circles are experimentally determined band dispersions along the $Γ - M$ direction. The data point at $k_{∥} < 0$ is symmetrized from the data point at $k_{∥} > 0$ . Orbital contributions of each band are shown in different colors. In the presence of spin-orbital coupling, the $α^{'}$ band will be pushed upward and cross $E_{F}$ near the $Γ$ point [25, 26]. We note that the shallow electron pocket at the $Γ$ point in ${FeTe}_{0.55} {Se}_{0.45}$ is not evident in our raw data, but has been clearly observed in laser-ARPES with improved momentum resolution [27, 28]. ARPES measured EDCs below and above $T_{c}$ in LiFeAs and ${FeTe}_{0.55} {Se}_{0.45}$ are shown in (c), (d) and (e), (f), respectively. The shaded areas in (e) and (f) cover the $d_{x y}$ band near $E_{F}$ . The thick EDCs at $0.4 π / a$ in LiFeAs and $0.1 π / a$ in ${FeTe}_{0.55} {Se}_{0.45}$ are corresponding to their $k_{F}^{β}$ . Due to the intrinsic incoherence of the $β$ band in ${FeTe}_{0.55} {Se}_{0.45}, k_{F}^{β}$ is determined by the minimum gap position in the SC phase and consistent with previous studies [24, 27, 29, 30].
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Figure 3
(a), (b) EDCs at $k = k_{F}^{β}$ and $k > k_{F}^{β}$ ( $0.45 π / a$ ) in LiFeAs. The inset panels show the symmetrized EDCs in (a) and (b). (c), (d) EDCs at $k = k_{F}^{β}$ and $k > k_{F}^{β}$ ( $0.2 π / a$ ) in ${FeTe}_{0.55} {Se}_{0.45}$ show enhanced total spectral weight in the SC phase. (e) Temperature-dependent symmetrized EDCs at $k = k_{F}^{β}$ . The 20-K data are subtracted from each symmetrized EDC. The inset shows the temperature-dependent raw data at $k = k_{F}^{β}$ . (f) The integrated intensity of the data in (e) follows the trend of temperature-dependent superfluid density in ${FeTe}_{1 - x} {Se}_{x}$ [33]. The temperature-dependent EDCs are normalized by their total counting time.
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Figure 4
Summary of $2 Δ_{SC}^{\max} / k_{B} T_{c}$ in various FeSCs that are determined by ARPES [29, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52]. The dashed line is a linear function fit of the data points.
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Physical Review B

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Universal $2 Δ_{max} / k_{B} T_{c}$ scaling decoupled from the electronic coherence in iron-based superconductors

H. Miao, W. H. Brito, Z. P. Yin, R. D. Zhong, G. D. Gu, P. D. Johnson, M. P. M. Dean, S. Choi, G. Kotliar, W. Ku, X. C. Wang, C. Q. Jin, S.-F. Wu, T. Qian, and H. Ding

Phys. Rev. B 98, 020502(R) – Published 9 July 2018

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Physical Review B

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Universal 2Δmax/kBTc scaling decoupled from the electronic coherence in iron-based superconductors

H. Miao, W. H. Brito, Z. P. Yin, R. D. Zhong, G. D. Gu, P. D. Johnson, M. P. M. Dean, S. Choi, G. Kotliar, W. Ku, X. C. Wang, C. Q. Jin, S.-F. Wu, T. Qian, and H. Ding

Phys. Rev. B 98, 020502(R) – Published 9 July 2018

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Universal $2 Δ_{max} / k_{B} T_{c}$ scaling decoupled from the electronic coherence in iron-based superconductors