Evidence of a universal relation between electron-mode coupling and ${T}_{c}$ in ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ superconductor from laser angle-resolved photoemission spectroscopy

Evidence of a universal relation between electron-mode coupling and $T_{c}$ in ${Ba}_{1 - x} K_{x} {Fe}_{2} {As}_{2}$ superconductor from laser angle-resolved photoemission spectroscopy

W. Malaeb, T. Shimojima, Y. Ishida, T. Kondo, K. Okazaki, Y. Ota, K. Ohgushi, K. Kihou, C. H. Lee, A. Iyo, H. Eisaki, S. Ishida, M. Nakajima, S. Uchida, H. Fukazawa, T. Saito, Y. Kohori, and S. Shin

Phys. Rev. B 90, 195124 – Published 13 November 2014

Abstract

We performed a laser angle-resolved photoemission spectroscopy (ARPES) study on a wide doping range of the ${Ba}_{1 - x} K_{x} {Fe}_{2} {As}_{2}$ (BaK) iron-based superconductor. We observed a robust low-binding energy (BE) kink structure (kink1) in the dispersion which is doping dependent whereby its energy peaks at the optimally doped level $(x \sim 0.4)$ and decreases towards the underdoped and overdoped sides. We attribute this kink to electron-mode coupling in good agreement with the inelastic neutron scattering (INS) and scanning tunneling microscopy (STM) results on the same compound where a similar bosonic mode associated with spin excitations was observed. The relation between the mode energy $(Ω)$ and the SC transition temperature $(T_{c})$ deduced from our laser ARPES data follow the universal relation deduced from INS and STM. In addition, we could resolve another kink at higher BE (kink2) showing less doping and temperature dependence compared to kink1 and which thus may be of different origin.

Received 15 March 2014
Revised 21 October 2014

DOI:https://doi.org/10.1103/PhysRevB.90.195124

Authors & Affiliations

W. Malaeb¹, T. Shimojima^2,3, Y. Ishida^1,3, T. Kondo¹, K. Okazaki^3,4, Y. Ota¹, K. Ohgushi^1,*, K. Kihou⁵, C. H. Lee⁵, A. Iyo⁵, H. Eisaki⁵, S. Ishida⁵, M. Nakajima⁶, S. Uchida⁴, H. Fukazawa⁷, T. Saito⁷, Y. Kohori⁷, and S. Shin^1,3

¹Institute for Solid State Physics (ISSP), University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8561, Japan
²Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
³CREST, JST, Chiyoda-ku, Tokyo 102-0075, Japan
⁴Department of Physics, University of Tokyo, Tokyo 113-8656, Japan
⁵National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan
⁶Department of Physics, Osaka University, Osaka 560-0043, Japan
⁷Department of Physics, Chiba University, Chiba 263-8522, Japan

^*Present address: Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan.

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Vol. 90, Iss. 19 — 15 November 2014

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Figure 1
Laser ARPES data of BaK with different dopings from UD to OD: [(a1)–(f1)] $E − k$ plots of a cut taken near the high-symmetry line with $V$ -polarized light at $T \sim 7$ K in the SC state of several doping levels. The black solid curves represent MDC peak positions determined from Lorentzian fitting which are displayed again in larger scale in panels (a2)–(f2), respectively. The black dotted horizontal lines denote the kink1 energy position $(E_{kink})$ and the thick colored lines around $E_{kink}$ reflect the uncertainty in the kink position arising from the analysis method (Appendix pp1). The red solid lines are guides to the eye for the linear sections in the low-BE region of the MDC dispersions. The thick gray horizontal lines represent an additional high-BE kink2 in the dispersion.
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Figure 2
(a) Inner holelike band EDCs in the SC state of BaK with several doping levels ranging from the UD to the OD region corresponding to the $E − k$ plots in Fig. 1. The kink energy $E_{kink}$ corresponding to the mode and which was determined from Fig. 1 is denoted by black bars. (b) Doping dependence of the mode energy $Ω$ (left $y$ axis) and the SC transition temperature $T_{c}$ (right $y$ axis). (c) The mode energy $Ω$ versus $T_{c}$ in BaK. The black dotted line is a linear fit of the data points implying the ratio $Ω / k_{B} T_{c} \sim 5.16$ . Overlapped on our laser ARPES points are STM and INS data points corresponding to several FeSC compounds, including BaK taken from literature [6, 7, 8]. Notice the color correspondence in all three panels of this figure.
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Figure 3
Temperature-dependent laser ARPES data of OP BaK with $x \sim 0.4$ . Upper panel: $E − k$ plots of a cut taken near the high-symmetry line with $V$ -polarized light at different temperatures. The data are divided by FD function. $k_{X}$ and $k_{Y}$ axes are along the Fe-As bond. Lower panel: Temperature dependence of the kink energy in BaK with $x \sim 0.4$ . The colored curves represent the dispersion corresponding to MDC peak positions determined from Lorentzian fitting at different temperatures. The kink energy position was estimated from the intersection points between two different slopes in the dispersion as in Fig. 1: The low-BE kink1 energy position is denoted by a black arrow and the high-BE kink2 is denoted by a thick gray horizontal line.
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Figure 4
Laser ARPES data of BaK with different dopings from UD to OD [(a2)–(f2)]: MDC dispersions corresponding to the $E − k$ plots in Figs. 1(a1)–1(f1) represented by black solid curves corresponding to the MDC peak positions determined from Lorentzian fitting. The blue solid lines overlapped on the ARPES data are used as an approximation of the dispersion expected in the absence of mode coupling effects. The low-BE kink1 energy position $E_{kink}$ for different dopings, denoted by black dotted horizontal lines, were estimated from the self-energy analysis in Fig. 5 and the thick colored lines around $E_{kink}$ reflect the uncertainty in the kink position arising from the linear fits in Fig. 5. The red solid lines are guides to the eye for the linear sections in the low-BE region of the MDC dispersions obtained from Fig. 5 analysis. The thick gray horizontal lines represent an additional high-BE kink2 in the dispersion.
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Figure 5
$Re Σ$ curves for different doping levels of BaK approximated by subtracting the blue solid lines from the MDC dispersion (black solid curves) in Fig. 4. The gray solid lines represent linear fits of straight sections of the $Re Σ$ curves and the black dotted lines are their extrapolation whose intersection is used to assign the energy position $(E_{kink})$ of kink1 in the dispersion (black vertical dotted lines). The thick colored lines around $E_{kink}$ reflect the uncertainty in the kink position arising from the linear fits, which is used to determine the error bars in Fig. 1 and Fig. 2. The black arrows represent an additional feature corresponding to the additional intensity at $\sim 10$ –13 meV in the $E − k$ plots of Fig. 1.
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Physical Review B

covering condensed matter and materials physics

Evidence of a universal relation between electron-mode coupling and $T_{c}$ in ${Ba}_{1 - x} K_{x} {Fe}_{2} {As}_{2}$ superconductor from laser angle-resolved photoemission spectroscopy

W. Malaeb, T. Shimojima, Y. Ishida, T. Kondo, K. Okazaki, Y. Ota, K. Ohgushi, K. Kihou, C. H. Lee, A. Iyo, H. Eisaki, S. Ishida, M. Nakajima, S. Uchida, H. Fukazawa, T. Saito, Y. Kohori, and S. Shin

Phys. Rev. B 90, 195124 – Published 13 November 2014

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Evidence of a universal relation between electron-mode coupling and Tc in Ba1−xKxFe2As2 superconductor from laser angle-resolved photoemission spectroscopy

W. Malaeb, T. Shimojima, Y. Ishida, T. Kondo, K. Okazaki, Y. Ota, K. Ohgushi, K. Kihou, C. H. Lee, A. Iyo, H. Eisaki, S. Ishida, M. Nakajima, S. Uchida, H. Fukazawa, T. Saito, Y. Kohori, and S. Shin

Phys. Rev. B 90, 195124 – Published 13 November 2014

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Evidence of a universal relation between electron-mode coupling and $T_{c}$ in ${Ba}_{1 - x} K_{x} {Fe}_{2} {As}_{2}$ superconductor from laser angle-resolved photoemission spectroscopy