Investigation of isotope effects on superconducting transition temperature (Tc) is one of the useful methods to examine whether electron–phonon interaction is essential for pairing mechanisms. The layered BiCh2-based (Ch: S, Se) superconductor family is a candidate for unconventional superconductors, because unconventional isotope effects have previously been observed in La(O,F)BiSSe and Bi4O4S3. In this study, we investigated the isotope effects of 32S and 34S in the high-pressure phase of (Sr,La)FBiS2, which has a monoclinic crystal structure and a higher Tc of ~ 10 K under high pressures, and observed conventional-type isotope shifts in Tc. The conventional-type isotope effects in the monoclinic phase of (Sr,La)FBiS2 are different from the unconventional isotope effects observed in La(O,F)BiSSe and Bi4O4S3, which have a tetragonal structure. The obtained results suggest that the pairing mechanisms of BiCh2-based superconductors could be switched by a structural-symmetry change in the superconducting layers induced by pressure effects.
In conventional superconductors, electron–phonon interactions are essential for the formation of Cooper pairs1. According to BCS (Bardeen-Cooper-Schrieffer) theory1, the transition temperature (Tc) of a phonon-mediated superconductor is proportional to its phonon energy ħω, where ħ and ω are the Planck constant and the phonon frequency, respectively. Therefore, Tc of conventional superconductors is sensitive to the phonon frequency, and modifications of the isotope mass (M) of the constituent elements, the so-called isotope effect, have been used to investigate the importance of electron–phonon interactions in the pairing of various superconductors. The isotope exponent α is defined by Tc ~ M−α, and α ~ 0.5 is expected according to BCS theory1. For instance, α values close to 0.5 have been detected in (Ba,K)BiO3 (αO ~ 0.5)2, MgB2 (αB ~ 0.3)3, and borocarbides (αB ~ 0.3)4. In addition, the hydrides (H3S and LaH10) high-Tc superconductors also showed a conventional shift in Tc with αH = 0.3–0.5 in isotope effect investigations5,6. In contrast, in superconductors with unconventional mechanisms, the isotope effect is not consistent with the BCS theory, and α values deviated from 0.57,8.
The target system of this study, layered BiCh2-based (Ch: S, Se) superconductors, has been extensively studied since its discovery in 20129,10,11. Because of its layered structure composed of alternate stacking of a superconducting layer and a blocking (insulating) layer, which resembles those of high-Tc superconductors12,13, many studies have been performed on material development and on pairing mechanisms11. Although non-doped (parent) BiCh2-based compounds are semiconductors with a band gap, electron doping of the BiCh2 layers makes the system metallic, and superconductivity is induced. An example of this is F substitution in REOBiCh2 (RE: rare earth)9,10,11. In addition, the superconducting properties of BiCh2-based systems are very sensitive to the effects of external (physical) and/or chemical pressures14,15,16,17. When external pressures are applied, the crystal structures of REOBiCh2-based systems tend to distort into a monoclinic (P21/m) structure, and a higher-Tc phase (Tc > 10 K) is induced16. Instead, by applying in-plane chemical pressure (shrinkage of the Bi-Ch conducting plane) via isovalent-element substitutions at the RE and/or Ch sites, a tetragonal (P4/nmm) phase is maintained, and bulk superconductivity is induced in the tetragonal phase. The emergence of bulk superconductivity due to chemical pressure effects can be explained by the suppression of local structural disorder, which is caused by the presence of Bi lone pair electrons18,19,20.
Regarding the mechanisms of superconductivity in the BiCh2-based family, the pairing mechanisms of the BiCh2-based superconductor family are still controversial19, owing to superconducting properties that are tunable by external and/or chemical pressure effects, which sometimes causes scattered results. Although earlier theoretical and experimental studies suggested conventional mechanisms with fully gapped s-wave pairing states21,22,23, recent theoretical calculations of Tc indicated that a Tc of an order of several K to 10 K in BiS2-based superconductors with a tetragonal structure cannot be explained within phonon-mediated models24. Furthermore, angle-resolved photoemission spectroscopy (ARPES) proposed unconventional pairing mechanisms owing to the observation of a highly anisotropic superconducting gap in NdO0.71F0.29BiS225. In addition, a study on the Se isotope effect with 76Se and 80Se in LaO0.6F0.4BiSSe (Fig. 1f) indicated the possibility of unconventional (non-phonon) mechanisms with αSe close to 0 (− 0.04 < αSe < 0.04)26. In addition, we have recently reported on an unconventional isotope effect with 32S and 34S in Bi4O4S3 (− 0.1 < αS < 0.1) (Fig. 1g)27. These two superconductors have a tetragonal crystal structure and show a relatively low Tc of 3.8 K for LaO0.6F0.4BiSSe and 4.7 K for Bi4O4S3. As mentioned above, the BiS2-based superconductor has a high-pressure (high-P) phase, which exhibits a higher Tc of over 10 K16. Therefore, this background encouraged us to plan an isotope effect study for a high-P (monoclinic) phase with a higher Tc, in order to find a way to design new BiCh2-based superconductors with a higher Tc and to elucidate the mechanisms of superconductivity in the system.
Herein, we show experimental evidence of phonon-mediated superconductivity in a high-P phase of BiS2-based superconductors (Sr,La)FBiS2. We have investigated the sulphur isotope effects (32S and 34S) on Tc for a high-P phase of (Sr,La)FBiS2 with Tc ~ 10 K28,29,30. Conventional shifts in Tc between samples synthesised with 32S and 34S were observed, which suggests the importance of phonons for the pairing mechanisms in the compound. The conventional isotope effects in (Sr,La)FBiS, which has a monoclinic structure, are in contrast to the unconventional isotope effects observed in La(O,F)BiSSe and Bi4O4S3, which have a tetragonal structure26,27. Based on a combination of the discussion of previous and present isotope studies, we suggest that the structural difference between the tetragonal and monoclinic structures could be a switch of the pairing mechanisms in BiCh2-based superconductors.
Characterisation of isotope samples
In general, the shift in Tc due to isotope effects is very small, even with α ~ 0.5 for low-Tc superconductors. Therefore, examining the isotope effects with sets of samples with comparable superconducting properties is important to reach a reliable conclusion. However, precise control of the superconducting characteristics of BiCh2-based compounds is the challenge of this study, because the Tc of BiCh2-based superconductors depends on the carrier concentration. From among the BiCh2-based compounds, we selected the Sr1−xLaxFBiS2 system, because the carrier concentration in this system is essentially determined by the La concentration (x), and x can easily be analysed by compositional analysis, such as energy dispersive X-ray spectroscopy (EDX). Here, we synthesised polycrystalline samples of Sr1−xLaxFBiS2 using 32S and 34S isotope chemicals for the investigation of sulphur isotope effects. We confirmed that the structural characteristics (particularly lattice constants) of the examined samples are comparable on the basis of powder X-ray diffraction (XRD) analyses (Fig. 1a,b). Detailed Rietveld analysis results are summarised in the Supplementary file. Although small impurity peaks of Bi and LaF3 were observed, the lattice constants for the examined samples were comparable as shown in Fig. 1b. The La concentration (x) analysed by EDX was x = 0.36–0.38, which is plotted in Fig. 1c. Among these samples, the carrier concentrations of samples #32-2, #34-1, and #34-2 were comparable, and that of #32-1 was slightly higher, where the sample labels indicate isotope mass (32 or 34) and batch number (1 or 2).
Magnetisation measurements under high pressure
As reported in a recent pressure study30, (Sr,La)FBiS2 shows a dramatic increase in Tc from ~ 3 K for the low-pressure (low-P) phase to ~ 10 K for the high-P phase on application of external pressure of about 1 GPa. The crystal structure of the high-P phase can be regarded as monoclinic, whereas that for the low-P phase is tetragonal, as shown in Fig. 1d,e, which is similar to the structural evolution of LaO0.5F0.5BiS2 under pressures16,30. Figure 2a–d show the temperature dependences of magnetisation measured at 10 Oe after zero-field cooling (ZFC). All samples of #32-1, #32-2, #34-1, and #34-2 show the transition from a low-P phase to a high-P phase, as plotted in Fig. 2e. Notably, in the high-P phase after the Tc jump, Tc does not change by an increase in applied pressure below 1.4 GPa. A similar behaviour was reported for EuFBiS2; the pressure dependence of Tc of EuFBiS2 showed a plateau under pressures above the critical pressure31. The appearance of the Tc plateau would be related to the structural characteristics of BiS2-based superconductors composed of fluoride-type blocking layers. This trend enabled us to examine the S isotope effect for the high-P phase of the samples. Figure 3a shows selected data of the temperature dependence of magnetisation for high-P phases of #32-1, #32-2, #34-1, and #34-2. Zoomed plots near the onset temperature of the superconducting transition (Tc) are shown in Fig. 3b. To estimate Tc, the temperature differential of magnetisation (dM/dT) was calculated and plotted as a function of temperature (Fig. 3c–f). Tc was estimated to be the temperature at which linear fitting lines for just below the transition temperature within a range of 0.5 K, as indicated by the red lines in those figures. The estimated Tc are 10.42, 10.16, 9.94, and 9.73 K for the high-P phases of #32-1, #32-2, #34-1, and #34-2, respectively (see Table 1 for the error). The highest Tc was observed for #32-1 with a higher La concentration (electron doping amount). For the two samples with 34S, x for #34-1 is slightly higher than x for #34-2, while the difference is within the error bars shown in Fig. 1c. The difference in Tc, however, can be seen in Fig. 3e,f. The trend that a higher Tc is observed for a sample with higher x is consistent with the trend seen for #32-1 and #32-2. Although the Tc is sensitive to the La concentration, we can reach a conclusion by comparing the Tc based on the analysed La concentrations. When comparing the Tc between #32-2 and #34-1, a different trend was observed; the Tc estimated for #32-2 was higher than that of #34-1 with x slightly higher than x for #32-2. This fact implies that the isotope effect in the high-P phase of Sr1−xLaxFBiS2 is conventionally present.
As La concentrations for #32-2 and #34-2 are very close, estimation of their αS may be essential, which gives αS ~ 0.7. This value is slightly larger than the conventional α = 0.5 expected from BCS theory, but it suggests the importance of phonon-mediated pairing in the high-P phase of (Sr,La)FBiS2. There are uncertainties in the determination of the essential αS for the high-P phase of (Sr,La)FBiS2 because Tc depends on the carrier concentration in this system, and the expected difference in Tc between samples with 32S and 34S is not large. However, with the results shown here and the systematic analyses of αS, we can reach the conclusion that phonons are essential for the superconductivity pairing mechanisms in the high-P phase of (Sr,La)FBiS2. This is in contrast to the unconventional isotope effects observed in La(O,F)BiSSe26 and Bi4O4S327. We discuss the possible differences in the structural and electronic characteristics of (Sr,La)FBiS2 (αS ~ 0.7) and La(O,F)BiSSe (− 0.04 < αSe < 0.04)26 in the following section.
As summarised in Fig. 1, isotope effect suggesting the importance of phonon was observed for the high-P phase of (Sr,La)FBiS2, whereas unconventional isotope effects were observed in La(O,F)BiSSe and Bi4O4S326,27. Although there are some possible factors, which could affect isotope effect, other than pairing states32, we consider that the observed difference in isotope effect is essentially caused by the different pairing states between those systems. The reason for proposing the scenario is the recent observation of nematic superconductivity in La(O,F)BiSSe33,34; nematic superconductivity has been observed in unconventional superconductors like Fe-based and Bi2Se3-based superconductors35,36. Since nematic superconductivity emerges in both LaO0.9F0.1BiSSe (tetragonal) and LaO0.5F0.5BiSSe (tetragonal) with different carrier concentrations but with comparable structures of the BiSSe conducting layer, unconventional pairing states would commonly present in tetragonal BiCh2-based superconductors with a tetragonal symmetry without structural distortion or local disorder. In contrast, nematic superconductivity was not observed in Nd(O,F)BiS237, which is also tetragonal but has larger local structural disorder than La(O,F)BiSSe11,17,19. These facts suggest the importance of structural symmetry in the conducting layers and would support our scenario suggested in this article. Here, we discuss the possible differences in electronic states and pairing states between tetragonal and monoclinic phases.
The high-P phase of (Sr,La)FBiS2 has a monoclinic structure and a distorted in-plane structure in the BiS2 layers30. In contrast, La(O,F)BiSSe and Bi4O4S3 have tetragonal structures, in which the square Bi-Ch network forms a superconducting plane. Although the low-P phase of (Sr,La)FBiS2 is tetragonal, same as for La(O,F)BiSSe and Bi4O4S3, bulk superconductivity is not observed at ambient pressure because of insufficient in-plane chemical pressure17,18,19,30. In the low pressure range, bulk superconductivity is induced, but the determination of Tc is difficult because there are two possible superconducting transitions of the manometer (Pb) and the high-P phase. Based on the isotope effects in the high-P phase of (Sr,La)FBiS2, La(O,F)BiSSe, and Bi4O4S3, we suggest that structural symmetry breaking in the superconducting BiCh2 layer is an essential factor in the switching of the isotope effect from unconventional to conventional.
We calculated the band structures of (Sr,La)FBiS2 and La(O,F)BiSSe (see Supplementary file). Note that the calculated results for (Sr,La)FBiS2 are based on the tetragonal structure of the low-P phase, because structural parameters for the high-P phase have not been experimentally obtained for (Sr,La)FBiS2, and the structural relaxation was not successful for the high-P phase in this work. One can determine that the shape of the Fermi surface is similar between (Sr,La)FBiS2 and La(O,F)BiSSe, because the expected carrier doping amount is comparable. Therefore, we consider that the different isotope effects were due to the modifications of electronic and/or phonon characteristics induced by structural symmetry breaking in the monoclinic phase. According to previous theoretical calculations for the tetragonal and monoclinic phases of La(O,F)BiS2, band splitting results from a structural transition from tetragonal (low-P phase) to monoclinic (high-P phase)38. In addition, the impact of interlayer coupling between two BiS2 layers, caused by the structural symmetry breaking, on the electronic states was suggested as a possibility. The switching of isotope effects between the tetragonal and monoclinic phases may be linked to the formation of the Bi–Bi bonding in the high-P phase in the present system. Let us remind that the theoretical study on the calculation of Tc for LaO0.5F0.5BiS2 by Morice et al.24 was performed on a tetragonal unit cell. Their conclusion is consistent with the unconventional isotope effects observed in tetragonal La(O,F)BiSSe and Bi4O4S3. If the same calculation of Tc could be performed on a monoclinic unit cell, a Tc of 10 K may be reproduced. For that, high-resolution structural analyses of the high-P phase of (Sr,La)FBiS2 are needed.
In conclusion, we synthesised (Sr,La)FBiS2 polycrystalline samples with 32S and 34S isotope chemicals. With magnetisation measurements under high pressure, we investigated the sulphur isotope effects on Tc for a high-P phase of (Sr,La)FBiS2. As a conventional shift in Tc was observed, we suggested the importance of phonons for the pairing mechanisms for the high-P phase. Based on comparisons with isotope effects in La(O,F)BiSSe and Bi4O4S3, in which unconventional isotope effects have been observed, we suggest that structural symmetry breaking from tetragonal to monoclinic is a key factor for the switch of the isotope effects in the BiCh2-based superconductor family.
Polycrystalline samples of (Sr,La)FBiS2 were prepared by a solid-state reaction method in an evacuated quartz tube. Powders of La (99.9%), SrF2 (99%), and Bi (99.999%) were mixed with powders of 32S (ISOFLEX: 99.99%) or 34S (ISOFLEX: 99.26%) with a nominal composition of Sr0.5La0.5FBiS2 in an Ar-filled glove box. The mixed powder was pelletised, and sintered in an evacuated quartz tube at 700 °C for 20 h, followed by furnace cooling to room temperature. The obtained compounds were thoroughly mixed, ground, and sintered under the same conditions as the first sintering. Except for the starting materials, the synthesis method was the same as our recent study on (Sr,La)FBiS230.
The phase purity and crystal structure of the (Sr,La)FBiS2 samples were examined by laboratory X-ray diffraction (XRD) by the θ-2θ method with Cu-Kα1 radiation on a SmartLab (RIGAKU) diffractometer. The schematic images of crystal structures were drawn by VESTA39 using structural data refined by Rietveld refinement using RIETAN-FP40. Through the XRD analyses, Bi and LaF3 impurity phases were detected. The actual compositions of the examined samples were analysed using energy dispersive X-ray spectroscopy (EDX) on a TM-3030 instrument (Hitachi). The average value of xEDX was calculated using the data obtained for five points on the sample surface. Standard deviation was estimated and shown in Table 1. Through the XRD analyses, small spots with La-rich compositions were found. The impurity phase will be LaF3, since a LaF3 phase was found in XRD.
The temperature dependence of the magnetisation at ambient pressure and under high pressures was measured using a superconducting quantum interference device (SQUID) on MPMS-3 (Quantum Design) after zero-field cooling (ZFC). Hydrostatic pressures were generated by the MPMS high-pressure capsule cell made of nonmagnetic Cu-Be, as described in our recent high pressure study on (Sr,RE)FBiS230. The sample was immersed in a pressure transmitting medium (Daphene 7373) and covered with a Teflon cell. The pressure at low temperature was calibrated based on the superconducting transition temperature of the Pb manometer. The magnetisation data shown in this paper contains background magnetisation. For sample #32-1, the maximum pressure was lower than that for other samples, which is due to the setup of high-pressure cell with a shorter piston stroke.
All relevant data are available from the corresponding authors upon reasonable request.
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The authors thank R. Jha and O. Miura for their assistance with the experiments. This work was partly supported by JSPS KAKENHI (Grant Nos. 18KK0076, 15H05886 and 19K15291) and the Advanced Research Program under the Human Resources Funds of Tokyo (Grant No. H31-1).
The authors declare no competing interests.
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Yamashita, A., Usui, H., Hoshi, K. et al. Possible pairing mechanism switching driven by structural symmetry breaking in BiS2-based layered superconductors. Sci Rep 11, 230 (2021). https://doi.org/10.1038/s41598-020-80544-2
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