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A Quantitative Description between Superconductivity and Strange-metal State in FeSe Revealed by Ionic-liquid Gating

Date:17-01-2023 Print

In superconductors, electrons form pairs and travel without dissipation. Although the pairing mechanism of conventional superconductors is well described by the Bardeen–Cooper–Schrieffer (BCS) theory, how electrons pair in high-temperature superconductors remains a mystery. Clues are thought to lie in the 'strange metal' behaviour of the normal state, that is, the state at temperatures above the superconducting transition temperature (Tc). Examples of such behaviour include the linear-in-temperature (T-linear) resistivity, which is unlike the quadratic temperature–resistivity relationship of conventional Fermi liquids. A quantitative description of the relationship between superconductivity and the strange-metal state is of great importance for further theoretical understandings, but so far comprehensive studies are very scarce due to the difficulties in realizing a systematic control of the superconducting states. To overcome this barrier, Kui Jin’s group from Institute of Physics, Chinese Academy of Sciences (IOP, CAS), developed an advanced composition-spread (combinatorial) film fabrication technique, and subsequently uncovered a quantitative relationship between Tc and A1 in an electron-doped cuprate, namely Tc ∝ (A1)0.5, where A1 is the coefficient of the T-linear resistivity. One key question is whether or not the scaling exponent in this equation is the same for other high-Tc superconductors. It is difficult to accumulate enough reliable data points to conclusively determine this power-law index because data obtained by conventional methods are generally scarce and have a large variability.

Recently, a research team led by Qihong Chen and Kui Jin of IOP, CAS used an ionic-liquid gating technique to tune Tc of FeSe—the structurally simplest iron-based superconductor—to investigate the interplay between the strange-metal state and superconductivity. Electron doping can be realized in FeSe through ionic-liquid induced hydrogen ion injection, which consequently enhances its superconductivity. To monitor the doping process, they designed a two-coil mutual inductance measurement device integrated with ionic-liquid gating. Using this device they achieved a uniform bulk tuning of FeSe with Tc varying from 8 K to above 45 K. By using high-field magnets, they obtained clear signatures of the strange-metal state in FeSe, namely T-linear and linear-in-field (H-linear) resistivity, and an H/T scaling of the magnetoresistance.

By continuously varying Tc of the FeSe with ionic-liquid gating, they mapped the relationship between superconductivity and the strange-metal state over a wide doping range. With A1 and Tc extracted from each doping level, a quadratic relationship between A1 and Tc emerged out of the systematic data, which indicated that the power-law index is 0.5 for FeSe. Combining this result with the relationships that have previously been reported in cuprate superconductors revealed that this quadratic dependence is universal and robust. This discovery provides strong evidence for a unified picture of the interplay between strange metallicity and unconventional superconductivity.

One mechanism for high-Tc superconductivity that has been frequently discussed is the formation of electron pairs through interactions with spin fluctuations. Superconductivity in Bechgaard salt and electron-doped cuprates is believed to be linked to antiferromagnetic spin fluctuations. Considering the highly universal behaviour observed across these systems—the T-linear and H-linear resistivity and the interplay between the strange-metal state and superconductivity—it is highly likely that the same, or similar, mechanism is also at work in iron-based superconductors. Therefore, spin fluctuations may have a common role in unconventional superconductors.

This study entitled "Interplay between superconductivity and the strange-metal state in FeSe" was published in Nature Physics on January 16th, 2023. "This paper is exciting because finding a quantitative relationship between the strange metal and superconductivity indicates that the mechanism for these might be universal to other superconductors, such as the cuprates." says by David Abergel, the chief editor of Nature Physics.

This study was initiated and supervised by Qihong Chen, Kui Jin and Zhongxian Zhao. Kun Jiang, Jiangping Hu and Tao Xiang from IOP provided theoretical support. High field measurements were performed at Wuhan National High Magnetic Field Center (pulsed) with help from Ming Yang and Junfeng Wang, and the High Magnetic field Laboratory of the Chinese Academy of Science (steady, Hefei) with help from Chuanying Xi and Zhaosheng Wang. The study was supported by the National Key Basic Research Program of China, the National Natural Science Foundation of China, Beijing Natural Science Foundation, Beijing Nova Program, the Key-Area Research and Development Program of Guangdong Province, the Strategic Priority Research Program (B) of Chinese Academy of Sciences, and CAS Project for Young Scientists in Basic Research.

Fig.1 The quantitative relationship between T-linear resistivity and superconductivity of FeSe revealed by ionic-liquid gating. A, Evolution of temperature-dependent resistivity with gating. B, Evolution of temperature-dependent diamagnetism with gating. C, Temperature-dependent resistance under high magnetic field for a gated state. D, Phase diagram showing the evolution of strange-metal and superconducting states with electron doping. E, The quadratic relationship between the T-linear coefficient A1 (A1 divided by the distance between adjacent FeSe layers) and Tc.  (Image by Institute of Physics)

Institute of Physics
CHEN Qihong

Key words:
High-temperature superconductivity; iron-based superconductors; strange metal; quantitative relationship.

In contrast to conventional Fermi liquids where resistivity decreases quadratically with temperature, unconventional superconductors usually exhibit a normal-state resistivity that varies as a linear function of temperature (T-linear) in the low-temperature limit. This phenomenon, termed the strange metal, has been extensively studied in cuprates and is thought to be intimately linked to superconductivity. A quantitative description of its relationship with superconductivity is therefore of great importance for developing further theoretical understanding, but so far comprehensive studies are scarce due to the difficulties in realizing systematic control of the superconducting state. Here, we report the observation of typical strange-metal behaviour in FeSe, namely, T-linear resistivity, linear-in-field magnetoresistance, and a universal scaling of the magnetoresistance. More importantly, when we tune the superconductivity by ionic-liquid gating, the superconducting transition temperature increases from approximately 10 to 45 K, and the T-linear resistivity coefficient exhibits a quadratic dependence on the critical temperature. This is a ubiquitous feature that describes the relation between these parameters in various systems including overdoped cuprates and Bechgaard salts. This suggests that there may be a universal mechanism underlying the T-linear resistivity and unconventional superconductivity.