The realization of high-T_c superconductivity is one of the holy grails of condensed matter physics. As one idea to achieve this, P. W. Anderson proposed a possible pathway to the glory in 1987 just after the discovery of the high-T_c cuprates [1]. Strong geometric frustration of magnetically interacting spins suppresses magnetic orders, resulting in a quantum spin liquid (QSL) state. Sufficient carrier doping into a QSL yields mobility of the electrons keeping the correlated spin correlations, which perhaps lead to high-T_c charged superconducting pairs using the spin fluctuations. Nevertheless, it has been challenging to make superconductivity in a doped QSL stable in actual materials, and thus, the experimental understanding of the frustration effect on superconductivity has been less well developed.

Recently, several papers [2,3] reported that the organic superconductor, κ-(BEDT-TTF)₄Hg_2.89Br₈ (κ-HgBr), is one of the most plausible candidates for doped QSLs hosting superconductivity. This salt is classified into the strongly correlated dimer-Mott system and has the almost regular triangular lattice of the dimers, as shown in Fig. 1. Indeed, its magnetism can be described by antiferromagnetically interacting spins on a triangular lattice and does not exhibit any magnetic orders even at low temperatures. Thanks to the carrier doping by the nonstoichiometric ratio of the HgBr counter anions, the electronic state is an 11% hole-doped state from the half-filled Mott insulator, leading to metallic conductivity as well the superconductivity.

Fig. 1. (a) Molecular arrangement of the organic molecules in the two-dimensional organic layers in κ-HgBr. The dotted circles denote the molecular dimers forming the triangular lattice. (b) Schematic of the dimer lattice. The arrows represent spins of π-electrons.

In this work [4], using various high-field measurements, we revealed that the superconductivity that emerged from the doped QSL exhibits unique field-temperature superconducting phase diagrams, as shown in Fig. 2. The red area represents the region of bulk superconductivity (SC) while the blue area indicates the region of fluctuating superconductivity (FSC). In a magnetic field, superconductivity is suppressed by the paramagnetic pair breaking effect and the orbital pair breaking effect, which yields limits of the upper critical field H_c2 known as the Pauli limit H_P and orbital limit H_orb. When applying magnetic fields parallel to the superconducting plane for two-dimensional superconductivity, the orbital pair breaking effect is quenched and H_P governs H_c2. As H_P is proportional to the amplitude of the superconducting energy gap, the coupling strength of the superconductivity can be roughly estimated by the ratio H_c2/T_c. As shown in Fig. 2(a), amazingly, H_c2/T_c for κ-HgBr exceeds 6 TK^-1, which is much larger than not only 1.84 TK^-1 expected in the conventional BCS framework, but also ~3 TK^-1 observed in other strong-coupling organic superconductors. Besides, H_c2/T_c in perpendicular fields (Fig. 2(b)) reaches about 3 TK^-1, which is also much larger than those of other superconductors. Considering the results including the orbital limit in perpendicular fields, the superconductivity in κ-HgBr is realized by the extremely strong pairing of the anomalously heavy π-electrons. We discuss the origin of these anomalous features of the superconductivity and elucidate that these originate from quantum critical behavior developed near a quantum critical point of the QSL insulating phase.

Fig. 2. Field-temperature superconducting phase diagrams in parallel (a) and perpendicular (b) fields. The blue and red shaded areas highlight the regions of the fluctuating superconductivity (FSC) and bulk superconductivity, respectively. The circles denote T_c whereas the boxes signify temperatures where FSC appears.

In addition, we find that FSC appears even much above T_c (see the blue area in Fig. 2) compared to other organic superconductors. It is not clear at present why the fluctuation region appears in the wide temperature range above T_c, however, given the characteristic of the geometrical frustration to hinder long-range orders of spin-singlet pairing, this nature may be attributed to a characteristic of the superconductivity appearing in doped QSLs.

References

• [1] P. W. Anderson, Science 235, 1196 (1987).
• [2] H. Oike, K. Miyagawa, H. Taniguchi, and K. Kanoda, Phys. Rev. Lett. 114, 067002 (2015).
• [3] H. Oike, Y. Suzuki, H. Taniguchi, Y. Seki, K. Miyagawa, and K. Kanoda, Nature Commun. 8, 756 (2017).
• [4] S. Imajo, S. Sugiura, H. Akutsu, Y. Kohama, T. Isono, T. Terashima, K. Kindo, S. Uji, and Y. Nakazawa, Phys. Rev. Research 3, 033026 (2021).

Authors

• S. Imajo, S. Sugiura^a, H. Akutsu^b, Y. Kohama, T. Isonoc, T. Terashima^c, K. Kindo, S. Uji^c, and Y. Nakazawa^b
• ^aTohoku University
• ^bOsaka University
• ^cNational Institute for Materials Science