Abstract Body

Quasi two-dimensional organic superconductor, λ-(BETS)₂GaCl₄ where BETS stands for bis(ethyleneditio)tetraselenafulvalene, have been actively studied regarding the electronic properties [1] and attracted much attention because they shows interesting superconducting phenomena, such as the existence of FFLO state (Fulde-Ferrel-Larkin-Ovchinnkov) that has been reported experimentally by thermodynamical measurement [2], the distorted of the nodal line compared to the d-wave SC gap symmetry which is similar to that found in cuprates superconductor [3], spin fluctuation that exist close to the superconducting state [4] and the deviation from normal Fermi liquid in the metallic state [5]. Furthermore, by changing the central atom of the tetrahedral GaCl₄, λ-(BETS)₂Fe_1-yGa_yCl₄, and changing the halogen atom ones,λ-(BETS)₂GaBr_xCl_4-x, x< 2, does not have serious effect on the crystal structure, nonetheless, they provide a large variety of electronic properties [6].

As for the Fermi liquidity studied the temperature dependence of the resistivity of unconventional superconductors shows n = 1, i.e., non-Fermi liquid (non-FL), where n defined as the power value of ρ=ρ₀+ATⁿ, while normal Fermi liquid (FL) will show n = 2 [7-8]. The change from n=1 to 2, can be observed by doping in the cuprates system [7] or applying pressure in the organic κ-(ET)₄Hg_2.89Br₈ system [9]. Our recent studied on the metallic state in λ-(BETS)₂GaCl₄ (abbreviated as λ-Ga) under physical pressure showed that just above the superconducting transition, the metallic state has the n value around 1.38(2). Furthermore, by applying pressure, it gradually increases to n = 2.4 at P = 0.28 GPa, then stabilized at n = 2 for the higher-pressure region. This behavior of n differs with that of cuprates and κ-(ET)₄Hg_2.89Br_8, although there is a deviation from n = 2 [5]. Furthermore, we found an upturn anomaly in the resistivity data under pressure of 0.13 and 0.28 GPa as shown in the inset of Fig.1(a). The results of magnetic susceptibility revealed that the superconducting volume fraction decreases by applying small pressure at P = 0.13 GPa. This implies the superconducting phase lost to the magnetic one [5,12]. The results of resistivity and magnetic susceptibility measurements under pressure suggest the formation of a dome of superconducting state. We aim to reveal whether the n value keeps decreasing towards n = 1 in the region of negative pressure. It becomes necessary to see the whole picture of non-Fermi liquidity in λ-(BETS)₂GaCl₄ by checking the chemical pressure effect giving the negative pressure region of the phase diagram of λ-(BETS)₂GaCl₄. It can be achieved by measuring the λ-(BETS)₂GaBr_xCl_4-x, x< 2 system.

Previous research on electrical properties of λ-(BETS)₂GaBr_xCl_4-x at ambient pressure revealed the superconducting transition can be observed when x < 0.75 [10]. The magnetic susceptibility measurement for the compound with x = 0.7 confirmed the anomaly which correspond to metal-to-insulator transition. By further research, it reveals that the insulating state correspond to the spin density wave (SDW) phase [6,11]. Our resistivity result at x = 0.2, shows the upturn toward lower temperatures suggesting the metal-insulating transition, then it vanished at x = 0.4 as shown in Figure 1(b) and (c) in which different with previous study [6]. In correlation with λ-Ga studied under physical pressure, the spin fluctuation which correspond to SDW phase observed at ambient pressure [8] and the metal-insulator transition appear by low pressure, P=0.13 GPa. Thus we suggest this relates to the upturn anomaly in x~0.2 although it not as sharp [12]. Furthermore, the superconducting transition, T_c, increase at x=0.4 followed with the decrease of n value. This behavior is similar to that of λ-Ga under physical pressure below 0.3 GPa, which shows the increase of T_c toward P_c = 0.13 GPa followed with deviation of n value from the normal metal [5]. The existence of insulating state at x=0.75 after vanishing at x=0.4 from resistivity measurement [11], indicates the competition between magnetic and superconducting phase in the λ-(BETS)₂GaBr_xCl_4-x. Furthermore, the superconducting transition temperature decreases under magnetic fields as shown in Fig 1. (a-c). For the compound x= 0, 0.2, and 0.4 under magnetic field, we confirmed that the n value hardly changes compared to the zero field. We will discuss the detail of the chemical pressure dependence of Fermi liquidity and how it behaves under the magnetic field to establish the general phase diagram of λ-(BETS)₂GaBr_xCl_4-x and give a hint in the field-induced superconductivity in this system.

References

[1] H. Aizawa, et al., J. Phys. Soc. Jpn 87, 9 (2018).

[2] S. Imajo et.al., Phys. Rev. B. 103, 22 (2021)

[3] D. P. Sari et al., Phys. Rev. B 104, 224506 (2021).

[4] Kobayashi et al., Phys. Rev. B 96, 12 (2017).

[5] M. Ueno, et al., Interactions 245, 71 (2024).

[6] H.Tanaka et.al., J. Am. Chem. Soc 121, 4 (1999).

[7] C. Proust and L. Taillefer, Annu. Rev. Condens. Matter Phys. 10, 409-429 (2019).

[8] H. Oike et.al., J. Phys. Soc. Jpn. 93, 4 (2024).

[9] H. Taniguchi, et.al., J. Phys. Soc. Jpn. 76, 11379 (2007)

[10] H. Kobayashi, H. Cui, and A. Kobayashi., Chem. Rev. 104 11 (2004).

[11] T. Kobayashi, et al., Phys. Rev. Res. 2, 2 (2020).

[12] A. A. Firdaus, et al., submitted (2024).

Acknowledgment

This work is supported by Grant JSPS KAKENHI Grant Number JP20H04463, JP21K13885.

Figure 1. The normalized resistivity in λ-(BETS)₂GaBr_xCl_4-x at (a) x=0, resulting λ-(BETS)₂GaCl₄ with the range 8-24 K, (b) at x=0.2 with the range 17-30 K, and (c) x=0.4 with the range 10-17 K under various magnetic field including the error bar of n using the fitting function ρ/ρ_rt=ρ₀+ATⁿ.  The dashed line is the fitting result. The inset of the left figure is the physical pressure dependence in the case of λ-(BETS)₂GaCl₄.

Keywords: organic superconductor, negative pressure, insulating phase, non-Fermi liquid, spin fluctuation