Supplementary Materials for

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1 advances.sciencemag.org/cgi/content/full/4/5/eaar6419/dc1 Supplementary Materials for Two distinct superconducting pairing states divided by the nematic end point in FeSe1 xsx Tetsuo Hanaguri, Katsuya Iwaya, Yuhki Kohsaka, Tadashi Machida, Tatsuya Watashige, Shigeru Kasahara, Takasada Shibauchi, Yuji Matsuda This PDF file includes: Published 25 May 2018, Sci. Adv. 4, eaar6419 (2018) DOI: /sciadv.aar6419 Supplementary Text fig. S1. Evolution of the histogram of the apparent heights at the lattice points in FeSe1 xsx single crystals. fig. S2. Analysis of orthorhombic lattice distortion using the twin boundary. fig. S3. Extended and localized electronic modulations in the spectroscopic maps of FeSe. fig. S4. A complete set of the in-plane QPI patterns of FeSe1 xsx. References (48, 49)

2 Sample characterizations by topographic imaging We determined sulfur contents and orthorhombic lattice distortions of FeSe 1 x S x single crystals by analyzing the topographic images. Since sulfur has smaller atomic radius than selenium, sulfur atoms are imaged as depressions in a regular selenium lattice of the STM images (Fig. 1, A to E, in the main text). Therefore a histogram of the apparent heights at the lattice points may exhibit two peaks; the lower and higher ones correspond to sulfur and selenium, respectively. The sulfur concentration can be calculated from the weights of these two peaks. For this analysis, we took constant-current STM images over 100 nm 100 nm fields of view with pixel resolution. Figures 1, A to E, in the main text are the parts of these images. The precise locations of the lattice points were determined by the Lawler-Fujita algorithm [ 48]. The apparent heights at the lattice points were taken from the STM images in which extrinsic long-wave-length height modulations brought by the strains in the crystals etc. were removed by Fourier-filtering out the small q signals. The obtained histograms shown in Fig. S1, A to E exhibit two peaks as expected. We repeated the same analysis for all of the samples we measured and fitted the peaks to obtain the weights. Since the selenium peak consists of a few sub-peaks caused by the randomly-distributed sub-surface sulfur atoms, multiple Gaussian and/or Lorentzian peaks were used for the fitting. The estimated sulfur contents reasonably agree with the results of the energy dispersive X-ray spectroscopy [20]. Orthorhombic lattice distortions can be estimated from the analyses of the twin boundaries (TB s) [ 49]. The model of the crystal structure near the TB is illustrated in Fig. S2A. The orthorhombic lattice distortion (b Fe a Fe )/(b Fe + a Fe ) can be calculated from the displacement u associated with the flipping of a Fe and b Fe axes across the TB. We found TB s in three samples and evaluated u s by the Lawler-Fujita algorithm [ 48 ] as described in Ref. [ 49 ] (Fig. S2B). As shown in Fig. S2C, (b Fe a Fe )/(b Fe +a Fe ) decreases by a few tens of percent with increasing x, in accord with the decreasing anisotropy in the band structure. Energy non-dispersive features in the Fourier maps As shown in Fig. 3 in the main text, there are energy non-dispersive features at high energies E 25 mev near q 0.05(2π/a Fe ) in L q (q, E), which are more obvious for smaller x samples. In order to argue the origin of these features, we examine real-space normalized conductance maps L(r, E) of FeSe (Fig. S3). At low energies where the dispersive QPI signals are clearly observed, conductance modulations are observed not only near the defects but also spread over extended areas as wavy patterns (Fig. S3, A to D). By contrast, at higher energies where the non-dispersive features dominate in q space, conductance modulations occur only near the defects (Fig. S3, E to H). This suggests that the non-dispersive features reflect the shape of the defect-localized state rather than the wave-like band quasiparticles. Energy and sulfur-content evolutions of in-plane QPI patterns A complete set of energy and sulfur-content evolutions of in-plane QPI patterns is shown in Fig. S3. No anomalies are detected at the nematic end point.

3 fig. S1. Evolution of the histogram of the apparent heights at the lattice points in FeSe 1 x S x single crystals. Black circles represent the experimental data. Filled red and blue curves are the fitted results for the sulfur and selenium peaks, respectively. Because the exact shapes of the tip apex may be different from run to run, ranges of the horizontal axes are not the same.

4 fig. S2. Analysis of orthorhombic lattice distortion using the twin boundary. A, Model crystal structure near the twin boundary of FeSe 1 x S x. B, Displacement u defined in A. C, Estimated orthorhombic lattice distortion as a function of x. Dashed line is the guide for the eyes.

5 fig. S3. Extended and localized electronic modulations in the spectroscopic maps of FeSe. ( A to H) Normalized conductance maps L(r, E). (I) A topographic image. Measurement conditions were V s = +50 mv, I s = 100 pa and the modulation amplitude for the lock-in detection V mod = 0.85 mv rms.

6 fig. S4. A complete set of the in-plane QPI patterns of FeSe 1 x Sx. Fourier-transformed normalized conductance Lq (q, E) maps are shown. Evolutions of the QPI patterns are smooth across the NEP at x = 0.17.