$^{77}\mathrm{Se}$-NMR evidence for spin-singlet superconductivity with exotic superconducting fluctuations in FeSe

${}^{77}{Se}$ -NMR evidence for spin-singlet superconductivity with exotic superconducting fluctuations in FeSe

J. Li, B. L. Kang, D. Zhao, B. Lei, Y. B. Zhou, D. W. Song, S. J. Li, L. X. Zheng, L. P. Nie, T. Wu, and X. H. Chen

Phys. Rev. B 105, 054514 – Published 23 February 2022

Abstract

Although the nature of the superconducting state has been intensively studied in FeSe, many fundamental issues including the pairing symmetry and superconducting fluctuations are still highly controversial. Here, we report a revised ${}^{77}{Se}$ -nuclear magnetic resonance (NMR) study on the superconducting state of ${}^{77}{Se}$ -enriched bulk FeSe. Below the superconducting temperature ( $T_{c}$ ), by carefully avoiding the rf heating effect, a remarkable linewidth broadening and obvious reduction of the Knight shift are observed under external magnetic field along both in-plane and out-of-plane directions, suggesting an intrinsic superconducting nature. These exotic results unambiguously rule out the possibility of chiral $p$ -wave pairing, and favor a pairing scenario with the mixing of $s^{\pm}$ and $d$ wave. A slight decrease of the Knight shift well above $T_{c}$ is also revealed under a moderated external magnetic field, suggesting exotic superconducting fluctuations beyond phase fluctuations in the two-dimensional limit. These renewed NMR results provide valuable constraints for the theoretical models on the exotic superconductivity in FeSe.

Received 27 September 2021
Revised 4 February 2022
Accepted 7 February 2022

DOI:https://doi.org/10.1103/PhysRevB.105.054514

Physics Subject Headings (PhySH)

Superconducting phase transition

Iron-based superconductors Unconventional superconductors

Nuclear magnetic resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Li¹, B. L. Kang¹, D. Zhao¹, B. Lei², Y. B. Zhou¹, D. W. Song¹, S. J. Li¹, L. X. Zheng¹, L. P. Nie¹, T. Wu ^1,2,3,4,*, and X. H. Chen^{1,2,3,4,5,†}

¹Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
²CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
³CAS Center for Excellence in Superconducting Electronics (CENSE), Shanghai 200050, China
⁴Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
⁵CAS Center for Excellence in Quantum Information and Quantum Physics, Hefei, Anhui 230026, China

^*wutao@ustc.edu.cn
^†chenxh@ustc.edu.cn

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Vol. 105, Iss. 5 — 1 February 2022

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Figure 1
Nuclear spin-lattice relaxation and NMR spectra measurements on the superconducting transition of bulk FeSe by utilizing optimized rf pulses. (a) Temperature-dependent $\frac{1}{T_{1} T}$ . $T_{p}$ is the onset of the decrease of $\frac{1}{T_{1} T}$ . The inset shows the photograph of the measured sample. (b),(c) NMR spectra deep inside the superconducting state of the bulk FeSe. The nearly unchanged spectra are incomprehensible as the missing of the expected Redfield pattern (see Supplemental Material for a detailed analysis).
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Figure 2
Characterization of the rf-pulse heating effects and the evolution of the intrinsic NMR spectra in the superconducting state with $H ∥$ ( $b$ ). (a) rf-pulse energy-dependent NMR spectra. The two fitted Lorentzian peaks are shown as the blue and red dashed lines. The black dashed lines track the peak positions which represent the NMR spectra of the two orthogonal nematic domains. (b) Temperature-dependent NMR spectra measured with fixed unheated rf-pulse energy.
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Figure 3
Intrinsic NMR characterization on the superconducting transition with $H ∥ c$ . (a) Comparison of the NMR spectra measured with heated and unheated rf pulse. The dash-dotted lines indicate the peak positions of the heated and unheated spectra. (b) Temperature-dependent NMR spectra measured with unheated rf-pulse condition. The vertical dashed lines draw the peak-frequency range of the temperature-dependent NMR spectra. (c) Comparison among $\frac{1}{T_{1} T} (T), K (T),$ and $w (T)$ . Dashed lines are a guide for the eye. (d) 2D color map of the simulated $h_{l} (r)$ . (e) Comparison among the observed NMR line (blue), the simulated Redfield pattern (red), and the calculated convolution (shaded area).
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Figure 4
NMR evidence for exotic superconducting fluctuations above $T_{c}$ . (a)–(d) $K (T)$ under several external magnetic fields. The insets of (b)–(d) are the zoom-in views of the region around the onset temperature of the slight decline of $K (T)$ . (e)–(h) $w (T)$ under several external magnetic fields. (i) A sketch of the superconducting phase diagram of bulk FeSe. The black dashed line and the blue solid line are adapted from Ref. [31]. Note: These data are scaled to match our sample, whose zero field $T_{c} \sim 7.2$ K and zero temperature $H_{c 2} \sim 12 T$ . As indicated by the red dotted line, extrapolating the experimental data to the zero-field limit yields $T_{c} (0) \sim T_{p} (0)$ , which is consistent with the missing pseudogap in the STM/STS and angle-resolved photoemission spectroscopy measurements at zero field [10, 19]. The gradient background color indicates a crossover character of the phase diagram. (j) Scaling relation between $K (H)$ and $γ (H)$ (reproduced from Ref. [28]) at 0.5 K. Error bars in (i) are defined as the temperature interval of the data around the declining point of $K (T)$ .
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Physical Review B

covering condensed matter and materials physics

${}^{77}{Se}$ -NMR evidence for spin-singlet superconductivity with exotic superconducting fluctuations in FeSe

J. Li, B. L. Kang, D. Zhao, B. Lei, Y. B. Zhou, D. W. Song, S. J. Li, L. X. Zheng, L. P. Nie, T. Wu, and X. H. Chen

Phys. Rev. B 105, 054514 – Published 23 February 2022

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Physical Review B

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Se77-NMR evidence for spin-singlet superconductivity with exotic superconducting fluctuations in FeSe

J. Li, B. L. Kang, D. Zhao, B. Lei, Y. B. Zhou, D. W. Song, S. J. Li, L. X. Zheng, L. P. Nie, T. Wu, and X. H. Chen

Phys. Rev. B 105, 054514 – Published 23 February 2022

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${}^{77}{Se}$ -NMR evidence for spin-singlet superconductivity with exotic superconducting fluctuations in FeSe