Spin fluctuations from Bogoliubov Fermi Surfaces in the Superconducting State of S-substituted FeSe
PI of Joint-use project: N. Fujiwawra
Host lab:Uwatoko Group
Host lab:Uwatoko Group
The study of the iron-based superconductor, FeSe1-xSx, has resulted in various topics. Recently, topologically protected nodal Fermi surfaces, referred to as Bogoliubov Fermi surfaces (BFSs), have garnered much attention [1,2]. A theoretical model for FeSe1-xSx demonstrated that BFSs can manifest under the conditions of spin-orbit coupling, multi-band systems, and superconductivity with time-reversal symmetry breaking [1]. Here we report the observation of spin fluctuations originating from BFSs via 77Se-nuclear magnetic resonance (NMR) measurements to 100 mK [3]. We found an anomalous enhancement of low-energy spin fluctuations deep in the superconducting (SC) state for x = 0.18, which gives evidence for strong Bogoliubov quasiparticles interactions in addition to the presence of BFSs.
We performed 77Se-NMR measurements using a single crystal for each S-substitution level. Typical size is approximately 1.0 × 1.0 × 0.5 mm. We applied a magnetic field of 6.0 T parallel to the FeSe planes. Figure 1 shows 1/T1T below Tc for several S-substitution levels crossing the nematic quantum critical point, xc ~ 0.17. As seen from 77Se-NMR spectra in Fig. 2, the double-peaks structure observed in the nematic phase disappears above xc. 1/T1T provides a measure of low-energy spin fluctuations and is expressed as 1/T1T∝∑qlmχ(q), where χ(q) is the wave-number (q)-dependent susceptibility. The decrease in 1/T1T just below Tc is due to the opening of the SC gap. In conventional clean superconductors, 1/T1T should decrease to zero with decreasing temperature. However, 1/T1T for x = 0.05 and 0.10 became constant at low temperatures. With further substitution over xc, 1/T1T exhibited an upturn with decreasing temperature and the values became significantly larger than those for x = 0.05 and 0.10. Upturns of 1/T1T observed below and above Tc are exceedingly rare in SC systems. The behavior of 1/T1T = constant suggests a residual DOS. In most cases, the following effects may be expected: (1) the impurity effect, (2) the Volovik effect, and (3) the coexistence of SC and normal states. However, the first two cases are ruled out because the values of 1/T1T change almost one order of magnitude between x = 0.05 and 0.10, and the last case is also ruled out considering the high sample quality. Furthermore, the upturn of 1/T1T is difficult to be explained by these possibilities. Instead of the coexistence in real space, the coexistence in momentum space such as the formation of BFSs would be promising as shown in Fig. 3. The appearance of BFSs with two-hold rotational symmetry has been observed by laser ARPES measurements [4] and time-reversal-symmetry breaking required for the appearance of BFSs has been suggested from recent μSR measurements [5].
Recently, Y. Cao et al. theoretically calculated χ(q) and 1/T1T for the ultranodal states in a minimal two-band model, where the interband non-unitary spin-triplet pairing is responsible for BFSs [6]. In this model, they assumed double hole pockets at the Γ point and BFSs with two-fold rotational symmetry like the schematic diagram shown in Fig. 3. By adding a Hubbard interaction in the particle-hole channel, they found that an enhancement of χ(q) at low temperatures at q~(0.4π, 0) connecting coherent segments/spots on the BFSs when the interaction is strong. This leads to an upturn of 1/T1T at low temperatures like experimental results of Tc = 0.18. In this model, the upturn can be derived based on the minimal two-band model at the Γ point, while the T dependence of 1/T1T below Tc is similar to that above Tc, implying that the nesting between the hole and electron pockets would be responsible for the upturn of 1/T1T below Tc [3]. It remains a future problem whether the nesting contributes to the upturn of 1/T1T.
The presence of BFSs below xc makes it easy to comprehend 1/T1T =constant. The values of 1/T1T for x = 0.05 or 0.10 are one or two orders of magnitude smaller than those for x = 0.18, implying that the BFSs should be much smaller and the interactions should be suppressed. In such case, the upturn of 1/T1T is hardly expected and 1/T1T =constant is attributed to the scattering between a nucleus and almost free Bogoliubov quasiparticles like the Korringa relation in conventional metals. It should be noted that such relaxation process is realized not in the normal state but in the SC state. In the Korringa relation, 1/T1T is proportional to square of the DOS. The difference of 1/T1T in one order of magnitude between x = 0.05 and 0.10 implies that the quasiparticle DOS differs almost three times between them. Our results suggest that BFSs exist even below xc ~ 0.17 and expand with increasing S-substitution level.
In conclusion, we have observed the upturn of 1/T1T deep in the SC state from 77Se-NMR measurements down to 100 mK. The upturn can be explained by the minimal two-band model, where the interband spin-triplet pairing is responsible for BFSs. The appearance of the upturn of 1/T1T gives evidence for strong Bogoliubov quasiparticles interactions in addition to the presence of BFSs.
References
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