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1 In the format provided by the authors and unedited. DOI: /NPHYS4186 Stripes Developed at the Strong Limit of Nematicity in FeSe film Wei Li 1,2,3*, Yan Zhang 2,3,4,5, Peng Deng 1, Zhilin Xu 1, S.-K. Mo 4, Ming Yi 3, Hao Ding 1, M. Hashimoto 6, R. G. Moore 3, D.-H. Lu 6, Xi Chen 1,2*, Z.-X. Shen 3,7*, and Qi-Kun Xue 1,2 1 State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing , China 2 Collaborative Innovation Center of Quantum Matter, Beijing , China 3 Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA 4 Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, California 94720, USA 5 International Center for Quantum Materials, School of Physics, Peking University, Beijing , China 6 Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA 7 Departments of Physics and Applied Physics, and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA *To whom correspondence should be addressed: weili83@mail.tsinghua.edu.cn, zxshen@stanford.edu and xc@mail.tsinghua.edu.cn NATURE PHYSICS 1

2 Contents Supplementary Note 1. Width of the C 2 domain wall and its apparent height. Supplementary Note 2. QPI and static stripes near the Fermi energy. Supplementary Note 3. Orientation of the stripes. Supplementary Note 4. Correlation length of the stripes. Supplementary Note 5. Impurity-states and STSs near the Fe-vacancy. Supplementary Note 6. Stripes induced by the C 2 domain walls. NATURE PHYSICS 2

3 1. Width of the C 2 domain wall and its apparent height. The apparent height and contrast of the C 2 domain wall is bias voltage dependent in STM topographic image. As shown in Fig. S1, the domain wall is brighter around 50 mv. To highlight the domain walls in Fig. 1b and Fig. 4a-d, bias voltages of -50 mv and -60 mv are applied, respectively. The domain wall is darker over the bias voltage range from 50mV to 100 mv, therefore the stripes features are highlighted within such an energy range. The Gaussian curve fitting of the profile of the domain wall is shown in Fig. S1. The estimated width of the domain wall is ~ 4 nm, which is the full width at half maximum of the fitting curve. Figure S1 STM topographic image of a nematic domain wall. Bias voltages are changed during the scan, therefore, the domain wall in the upper half part looks brighter and looks darker in the lower half part. The tunneling current is set at 100 pa. NATURE PHYSICS 3

4 2. QPI and static stripes near the Fermi energy. The periodicity of the stripes is bias voltage independent, which is in sharp contrast to the QPI features near the Fermi energy. QPIs are induced in the vicinity of impurities as shown in Fig. S2 and Fig. S3, in which four iron-vacancies are introduced as the scattering centers. As shown in those real-space di/dv maps, indicated by the arrows, the interference patterns near the impurities are sensitive to changes of the bias voltages. The evolution of the QPIs can be more easily observed in Movie S1 and Movie S2. Figure S2 di/dv maps at positive energies (above E F ). Set point: 200 mv, 0.4 na. The QPIs originate from the quasiparticles intra- and inter-bands scatterings. At positive energies, the QPIs are along the stripes (Fig. S2). Unidirectional interferences are marked by the green and blue arrows, and the two colors indicate two scatterings from two different bands, respectively. Both of the two QPI patterns move towards NATURE PHYSICS 4

5 the scattering center with higher energies, which indicates decreasing scattering wave lengths in real space, corresponding to intra-band scatterings from two electron-like bands in momentum space above the E F. At negative energies, the unidirectional QPI patterns (see the red arrows in Fig. S3), perpendicular to the stripes, move far away from the center of the defects with energies closer to E F, indicating a larger scattering wave length (a smaller wave vector q in momentum space) at E F. Contrast to the behaviors of the interferences at positive energies, such an evolution of QPI reveals a hole-like band below E F. Figure S3 di/dv maps at negtive energies (below E F ). Set point: 200 mv, 0.4 na. In the maps both in Fig. S2 and Fig. S3, the stripes are static with respect to the defects. The distances between the four impurities are only ~ 10 nm, and act as ideal references/landmarks to check the behaviors of the stripes. NATURE PHYSICS 5

6 Fast Fourier transform (FFT) is also carried out to extract the periodicity of the stripes. The bottom right images of Fig. S2 and Fig. S3 are the FFT images of Fig. 3d and Fig. 3o, from which the extracted wave length is 1.89 nm and 1.86 nm, respectively. Therefore, the charge ordering origin of the stripes is further supported. Movie S1 Evolution of QPI at positive energies (above E F ). Movie S2 Evolution of QPI at negative energies (below E F ). NATURE PHYSICS 6

7 3. Orientation of the stripes. The FeSe film is terminated with Se plane. In principle, the Se-Se lattice is rhombic rather than tetragonal, due to the tetragonal to orthorhombic structural phase transition in Fe-Fe plane (the lattice along a-axis direction is longer than that along b-axis direction). However, given the widespread tensile strain as well as the nematic domain walls in FeSe films, cautions should be considered to distinguish the directions of a and b by directly measuring the angles of the Se-Se lattice. Alternatively, the direction can be determined by the QPI features in Fig. S3, in which the dispersive QPI at the negative bias voltages arise from the quasiparticle scattering of a hole-like band. At the E F, the scattering wave vector still exists (the unidirectional patterns denoted by the red arrow in di/dv map at 0 mev), indicating that the hole-like band crosses the Fermi level. By Investigating the band structure of FeSe in nematic phase, the only matched band is the hole-like band (the green band in Fig. S4.) along the a-axis direction 1 (x direction in ref. S1). Therefore, the charge ordering propagates along the b-axis direction, and is localized as stripes along the a-axis direction. This is further supported by the temperature-dependent band width evolution in ref. S1. The band width of the red band (along the b-axis direction) becomes wider (itinerant) while green band becomes narrower (local) with larger strength of nematicity. Figure S4 a, schematic of the splitting of d yz and d xz bands below the nematic phase transition temperature T *. Along cut 1, the green hole-like band crosses the E F and its intra-band scattering contributes the QPI features in Fig. S3. b, the photoemission spectrum of the band splitting at the M point. NATURE PHYSICS 7

8 4. Correlation length of the stripes. To determine the correlation length ξ of the stripes, the profile of a stripe is fitted with a formula shown in the lower panel of Fig. S5. The obtained ξ is ~ 2.1 nm. Figure S5 Determination of the correlation length of the stripes. NATURE PHYSICS 8

9 5. Impurity-states and STSs near the Fe-vacancy. The impurity states are observed in the STS taken just above the defect, as shown in Fig. S6a. The peaks positions are marked with red arrows and the corresponding energies are -30 mev, 14 mev and 30 mev, respectively. The right panel of Fig. S6b shows the real space distribution (di/dv maps) of those impurity states, in which the dumbbell-shaped structure is presented. Fig. S6a and c show the STSs on and off the stripes over a wide energy range (from -500 mv to 500 mv), in which no gap feature has been observed. The absence of CDW gap in STS is possible and has been reported 2 in NbSe 2. Single-point STS detects the local convolution of the density of states without momentum information. CDW gap may be only opened at certain parts (of strong momentum dependence) of a band, which may barely affect the whole density of states and can not be observed in STS. In addition, due to the multiband nature of FeSe, the influence of partially opened gap to the average DOS could be even smaller. Figure S6 a, di/dv spectra on, near and off an impurity. c, di/dv spectra on and off the stripes. No gap feature is observed. Set point for a: V = 60 mv, I t = 0.1 na; for c: 500 mv, 0.2 na. b, the di/dv maps of the impurity states. Set point: 150 mv, 0.4 na. NATURE PHYSICS 9

10 6. Stripes induced by the C 2 domain walls. The stripes are induced by the wide spread C 2 domain walls as well (indicated by the red arrows in Fig. S7), which may suppress the superconductivity in FeSe/STO by breaking the long range coherence of the cooper pairs. Figure S7 Stripes induced by C 2 domain walls. The dashed yellow lines indicate two domain walls and the red arrows denote the stripes induced by them. Set point for the topographic image: V = 60 mv, I t = 100 pa. References S1. Zhang, Y. et al. Distinctive orbital anisotropy observed in the nematic state of a FeSe thin film. Phys. Rev. B 94, (2016). S2. Arguello, C. J. et al. Visualizing the charge density wave transition in 2H-NbSe 2 in real space. Phys. Rev. B 89, (2014). NATURE PHYSICS 10