Protonation-induced discrete superconducting phases in bulk FeSe single crystals

Yan Meng, Xiangzhuo Xing, Xiaolei Yi, Bin Li, Nan Zhou, Meng Li, Yufeng Zhang, Wei Wei, Jiajia Feng, Kensei Terashima, Yoshihiko Takano, Yue Sun, and Zhixiang Shi

Phys. Rev. B 105, 134506 – Published 11 April 2022

Abstract

The superconducting transition temperature, $T_{c}$ , of FeSe can be significantly enhanced several-fold by applying pressure, electron doping, intercalating spacing layer, and reducing dimensionality. Various ordered electronic phases, such as nematicity and spin density waves, have also been observed accompanying high- $T_{c}$ superconductivity. In this paper, we have found a series of discrete superconducting phases, with a maximum $T_{c}$ up to 44 K, in $H^{+}$ -intercalated FeSe single crystals using an ionic liquid gating method. Accompanied with the increase of $T_{c}$ , suppression of the nematic phase and evolution from non-Fermi-liquid to Fermi-liquid behavior was observed. An abrupt change in the Fermi surface topology was proposed to explain the discrete superconducting phases. A band structure that favors the high- $T_{c}$ superconducting phase was also revealed.

Received 16 December 2021
Revised 4 March 2022
Accepted 30 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.134506

Physics Subject Headings (PhySH)

Hall effect Superconducting phase transition Superconductivity

Chalcogenides Iron-based superconductors Superconductors

Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yan Meng^1,2, Xiangzhuo Xing^1,3,*, Xiaolei Yi¹, Bin Li ⁴, Nan Zhou¹, Meng Li¹, Yufeng Zhang ¹, Wei Wei¹, Jiajia Feng¹, Kensei Terashima², Yoshihiko Takano², Yue Sun ^1,5,†, and Zhixiang Shi^1,‡

¹School of Physics, Southeast University, Nanjing 211189, China
²International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
³School of Physics and Physical Engineering, Qufu Normal University, Qufu 273165, China
⁴Information Physics Research Center, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
⁵Department of Physics and Mathematics, Aoyama Gakuin University, Sagamihara 252-5258, Japan

^*Corresponding author: xzxing@qfnu.edu.cn
^†Corresponding author: sunyue@phys.aoyama.ac.jp
^‡Corresponding author: zxshi@seu.edu.cn

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Vol. 105, Iss. 13 — 1 April 2022

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Images

Figure 1
Schematic of the experimental setup used for protonation.
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Figure 2
(a)–(c) Temperature dependence of the normalized resistivity, $ρ (T) / ρ_{200 K}$ , for different $H_{x}$ -FeSe single crystals during the protonation process with different protonation times. (e)–(g) $ρ (T) / ρ_{200 K}$ curves for $H_{x}$ -FeSe single crystals that have been protonated for 20 days [SP20, shown in (c)] in the deprotonation process with different deprotonation time. The curves have been vertically shifted for clarity. Black arrows indicate the nematic transition at $T_{s}$ . Thick vertical lines are guides for the eye and highlight onset SC transition temperatures, $T_{c n}$ ( $n$ = 1, 2, 3, and 4), for different SC phases. $T_{s}$ and $T_{c n}$ ( $n$ = 1, 2, 3, and 4) are respectively defined as the dip and peak positions in the temperature derivative of $ρ (T) / ρ_{200 K}$ , as shown in Supplemental Material Fig. S1 [41]. Black dotted lines represent fits to the formula $ρ (T) / ρ_{200 K} = ρ_{0} + A T^{α}$ (see text for details). (d) and (h) summarize the evolution of $T_{c}$ with (d) protonation and (h) deprotonation time.
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Figure 3
(a) XRD patterns of $H_{x}$ -FeSe single crystals with different protonation times performed in a powder x-ray diffractometer. Inset shows the lattice constants $a$ and $c$ of FeSe, deduced from $2 θ$ values of ( $00 l$ ) reflections and refined from single-crystal XRD data, respectively. (b) Summary of the relationship between $T_{c}$ and $d$ in a variety of intercalated FeSe samples. The vertical line is a guide for the eye.
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Figure 4
(a)–(d) Field dependence of Hall resistivity, $ρ_{x y}$ , for $H_{x}$ -FeSe single crystals at different temperatures: (a) pristine FeSe single crystal (SP0), $H_{x}$ -FeSe single crystal with a protonation time of (b) 18 days (SP8), (c) 16 days (SP16), and (d) 20 days (SP20). (e) Temperature dependence of Hall coefficients of $H_{x}$ -FeSe with different protonation times (for the pristine FeSe, $R_{H} = ρ_{x y} / H$ was calculated by linear fitting of $ρ_{x y}$ versus $H$ at high magnetic fields). (f) Protonation time dependence of $R_{H}$ and $n_{H}$ (Hall number $n_{H} = 1 / e R_{H}$ ) at $T = 50$ K.
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Figure 5
(a) and (b) Phase diagrams of $H_{x}$ -FeSe single crystals derived from the (a) protonation and (b) deprotonation processes. Color maps represent the temperature dependence of the exponent, $α$ , extracted from $d ln (ρ - ρ_{0}) / d ln (T)$ . (c) and (d) Schematics describing the evolution of FS topology with (c) protonation and (d) deprotonation. Blue and red lines represent the electron and hole FSs, respectively.
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