Preformed Cooper Pairs in Layered FeSe-Based Superconductors

B. L. Kang, M. Z. Shi, S. J. Li, H. H. Wang, Q. Zhang, D. Zhao, J. Li, D. W. Song, L. X. Zheng, L. P. Nie, T. Wu, and X. H. Chen

Phys. Rev. Lett. 125, 097003 – Published 28 August 2020

Abstract

Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while in the underdoped high- $T_{c}$ cuprate superconductors, the electron pairing occurs at higher temperature than the long-range phase coherence. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on ${SrTiO}_{3}$ substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudogap behavior below $T_{p} \sim 60 K$ in two kinds of layered FeSe-based superconductors with quasi2D nature. In the pseudogap regime, a weak diamagnetic signal and a remarkable Nernst effect are also observed, which indicates that the observed pseudogap behavior is related to superconducting fluctuations. These works confirm that strong phase fluctuation is an important character in the 2D iron-based superconductors as widely observed in high- $T_{c}$ cuprate superconductors.

Received 15 December 2019
Revised 6 June 2020
Accepted 27 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.097003

Physics Subject Headings (PhySH)

Superconducting fluctuations

Iron-based superconductors

Magnetization measurements Nuclear magnetic resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

B. L. Kang¹, M. Z. Shi¹, S. J. Li¹, H. H. Wang¹, Q. Zhang¹, D. Zhao¹, J. Li¹, D. W. Song¹, L. X. Zheng¹, L. P. Nie¹, T. Wu ^1,2,3,4,*, and X. H. Chen^1,2,3,4,†

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

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

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Vol. 125, Iss. 9 — 28 August 2020

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Images

Figure 1
Crystal structure and superconducting properties of $(TBA)_{x} FeSe$ . (a) The crystal structure of pristine FeSe with c-axis lattice constant $d_{0} \sim 5.5 Å$ and the intercalated $(TBA)_{x} FeSe$ with $d_{1} \sim 15.5 Å$ . (b) Tunneling spectrum taken on a cleaved surface of $(TBA)_{x} FeSe$ at 5 K reveals the appearance of a superconducting gap. Pronounced superconducting coherence peaks appear at $\pm 16 meV$ . Inset: Atomically flat STM image for $(TBA)_{x} FeSe$ with a bias voltage of $V_{bias} = 1 V$ and tunneling current of $I_{t} = 220 pA$ . (c) Temperature dependence of in-plane resistance under different magnetic fields applied along c axis. The $T_{c}^{onset}$ is determined by the intersection of the linear extrapolation of normal-state resistance $R_{n}$ and the sharp superconducting transition, and the $T_{c 0}$ is determined by using the one percent normal state resistance criterion. The fan-shaped broadening of resistive transition under magnetic fields indicates a strong 2D characteristic. (d) Temperature dependence of anisotropic magnetic susceptibility measured in field-cooling and zero-field-cooling modes under magnetic field of 5 Oe applied along in plane (blue) and out of plane (red), respectively. The significant difference of shielding fraction between two orientations, usually up to dozens of times, supports a strong 2D characteristic. (e) Temperature dependent FWHM of ${}^{77}{Se}$ NMR spectra under different external magnetic fields. The temperature indicated by dashed line is defined as the superconducting transition temperature ( $T_{c}$ ) in the $H − T$ phase diagram of Fig. 4.
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Figure 2
Evidence for preformed Cooper pairs above $T_{c 0}$ in $(TBA)_{x} FeSe$ . (a) Temperature dependence of Knight shift $K$ (upper panel) and its first derivative (lower panel). (b) Temperature dependence of the spin-lattice relaxation rate divided by temperature $1 / T_{1} T$ (upper panel) and its first derivative (lower panel). The external magnetic field of 120 kOe in (a) and (b) was applied within the ab plane. (c) The high-field magnetic susceptibility $χ_{ab}$ and $χ_{c}$ measured in field-cooling mode with the magnetic field of 70 kOe applied in plane (green) and out of plane (orange), respectively. The black solid lines are the extrapolation fitting curves of high-temperature behavior. The arrow indicates the onset of diamagnetism. (d) Temperature dependence of Nernst effect under a magnetic field of 135 kOe applied along c axis. A vortex-related Nernst signal is observed well above $T_{c 0}$ . The arrow shows the onset of the vortex-related Nernst effect at $\sim 65 K$ . It should be noted that the $T_{p}$ determined by Nernst effect is slightly higher than other probes, which suggests that the Nernst effect is more sensitive to detecting superconducting fluctuation.
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Figure 3
Two-dimensional electronic properties of $(TBA)_{x} FeSe$ . (a) Temperature dependence of in-plane and out-of-plane resistivity. (b) The anisotropy of resistivity ( $ρ_{c} / ρ_{ab}$ ) for $(TBA)_{x} FeSe$ and pristine FeSe. The data of FeSe is adopted from Ref. [90]. (c) $V$ ( $I$ ) curves at various temperatures plotted in a logarithmic scale. The numbers provide the measured temperature for each curve. The short black lines are fits of the data across the $T_{c 0}$ . The two long black lines correspond to $V \sim I$ and $V \sim I^{3}$ behavior, respectively. The temperature for $V \sim I^{3}$ behavior is defined as $T_{BKT} \sim 44 K$ . (d) Temperature dependence of the power-law exponent $α$ as deduced from the fits shown in (c). (e) $R − T$ dependence for the $(TBA)_{x} FeSe$ single crystal $(I = 500 μ A)$ plotted in a $[d \ln (R) / d T]^{- 2 / 3}$ scale. The solid line shows the fitting to the Halprin-Nelson formula $R (T) = R_{0} \exp [- b / (T - T_{BKT})^{1 / 2}]$ with $T_{BKT} \sim 44.7 K$ .
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Figure 4
Summarized $H − T$ phase diagram for $(TBA)_{x} FeSe$ . The external magnetic field is parallel to the c axis. $T_{c 0}$ stands for zero-resistance transition temperature, which is also consistent with the $T_{m}$ defined by NMR measurement under magnetic field. $T_{c}$ stands for the superconducting temperature defined by the onset temperature of NMR line broadening and the first derivative of resistance data. $T_{p}$ stands for the onset temperature of pseudogap behavior. Resistivity, magnetization, and NMR measurements give the same $T_{p}$ of about 60 K, while the Nernst effect gives a slightly higher $T_{p}$ of about 65 K. It suggests that Nernst effect is more sensitive than other probes to detecting superconducting fluctuations. In the vortex solid or vortex glass state, the resistivity becomes zero with highly anisotropic diamagnetism. In the vortex liquid state, the resistivity is no longer zero but there is still anisotropic diamagnetic signal. Such phase diagram for vortex is similar to that of high- $T_{c}$ cuprate superconductors [35] in which the vortex physics is strongly affected by the 2D superconducting fluctuations. Above $T_{c}$ , a remarkable pseudogap phenomenon appears up to $T_{p}$ .
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