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1 Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family Z. K. Liu 1,2,3, L. X. Yang 4,5,6, Y. Sun 7, T. Zhang 4,5, H. Peng 5, H. F. Yang 5,8, C. Chen 5, Y. Zhang 6, Y. F. Guo 1,2,5, D. Prabhakaran 5, M. Schmidt 7, Z. Hussain 6, S.-K. Mo 6, C. Felser 7, B. Yan 1,2,7 and Y. L. Chen 1,2,3,4,5* 1 School of Physical Science and Technology, ShanghaiTech University, Shanghai , China 2 CAS-Shanghai Science Research Center, 239 Zhang Heng Road, Shanghai , China 3 Diamond Light Source, Didcot, Oxfordshire, OX11 0QX, UK 4 State Key Laboratory of Low Dimensional Quantum Physics, Collaborative Innovation Center of Quantum Matter and Department of Physics, Tsinghua University, Beijing , P. R. China 5 Physics Department, Oxford University, Oxford, OX1 3PU, UK 6 Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 7 Max Planck Institute for Chemical Physics of Solids, D Dresden, Germany 8 State Key Laboratory of Functional Materials for Informatics, SIMIT, Chinese Academy of Sciences, Shanghai , China These authors contributed equally to this work * yulin.chen@physics.ox.ac.uk This file includes: SI A: Cleavage surface and the electronic structures of NbP SI B: Detailed band structures of NbP, TaP, TaAs and comparison to theory SI C: Photon energy dependent measurements of the electronic structures of NbP and TaP SI D: SI E: SI F: Further evidence for the existence of Fermi arc on the surface of NbP and TaP Bulk electronic states and Weyl fermions in TaP Polarization dependent measurement of the electronic structure of NbP SI G: Spin-orbit coupling dependent separation of Weyl pairs and band splitting Figs. S1 to S13 NATURE MATERIALS 1

2 SI A: Cleavage surface and the electronic structures in NbP Each unit cell of NbP consists of 4 NbP layers with the same interlayer distance (0.167c or Å), nearly twice the distance between the Nb and P planes (0.083c or 0.944Å) within a NbP layer. The crystal would naturally get cleaved between any two adjacent NbP layers with equal possibility (Fig. S1a). After cleavage the broken Nb-P bonds dangling on the adjacent NbP layers are aligned along orthogonal directions (Fig. S1b-c), leading to the rotation of the corresponding surface electronic structure by 90 degrees between adjacent layers (Fig. S1d). Considering the two-fold crystal symmetry, 4 different types of NbP layers would host two kinds of surface electronic structures which are orthogonal to each other (Fig. S1d). Consequently, if the photoemission beam spot covers adjacent cleaved surface layers (Fig. S1b), ARPES measurement would reflect the surface electronic structures of both types of cleavage surfaces (Fig. S1d). Figure S1. Cleavage dependent electronic structure of NbP. a, Unit cell of NbP. NbP1-NbP4 denote four NbP layers. Red arrows indicate the possible cleavage locations. b, Schematics of the surface formed after cleavage, where different layers are exposed for ARPES measurement. Broken Nb-P bonds are aligned in the orthogonal directions (indicated by the green arrows) between adjacent layers of NbP. c, Plot of the lattice structure and alignment of the broken Nb-P bonds (represented by the thick red shape) for four types of NbP termination layers. d, Plot of the two kinds of orthogonal electronic structures and their mixing will reflect the actual ARPES measurement. 2 NATURE MATERIALS

3 SUPPLEMENTARY INFORMATION Fig. S2 shows the measured electronic structure of NbP from two surface types. Compared with the ARPES measurements on a single type of surface (Fig. 2 in the manuscript), the number of Fermi surface pieces around XX and YY and the band dispersions along high Figure S2. ARPES results of NbP from two types of surface. a, Stacking plots of constant-energy contours at different binding energies showing the band structure evolution. Red square marks the first BZ. b, Side-by-side comparison of three constant energy contours at different binding energies between experiments (left panels) and ab initio calculations (right panels) showing overall agreements. c, 3D intensity plots of the photoemission spectra illustrating the band structure for both the bowtie- (i) and spoon-like (ii) FSs with calculated dispersions (red dotted plots) overlaid. d, Comparison of calculated (i) and experimental (ii) dispersions along high symmetry directions across the whole BZ (MM XX ΓΓ YY MM ). e, Plot of photoemission intensities at E F along the high symmetry YY ΓΓ YY direction (measurement position is marked by the red line on the FS in the lower panel) as a function of photon energy (52-130eV), showing the k z dispersion of different bands. symmetry directions are doubled (Fig. S2a-d). By comparing with Fig. 2, the measured electronic structure can be divided into two sets (rotated by 90 degrees from each other) which were labeled with different colors in the calculated band structure (Fig. S2b-d). Each set of calculated band structure shows nice agreement with the single surface type data in Fig. 2 of the main text. The photon energy dependent measurement along the YY ΓΓ YY direction (Fig. S2e) further shows negligible k z variation of the twinned band structure, indicating the surface origin of the states near the Fermi energy (E F) from both types of surfaces and consistent with the result from single surface type in Fig. 2 of the main text. Page 3 We note that the mixed electronic structure is an extrinsic effect due to the cleavage conditions and has been observed from time to time in all members of the transition metal monopnictides because of their identical crystal structure. The mixture of the electronic structures from two surface types complicates the verification of the surface Fermi arcs. For example, the counting of the Fermi crossings along a closed loop (see Fig. 3) would give an even number due to the band doubling even if the loop crosses Fermi arcs. The data we showed NATURE MATERIALS 3

4 in Fig. 2-4 of the manuscript and Fig. S3-S4, Fig. S6-S11 of the Supplementary Information, including the one used for the analysis of the Fermi arcs, are all measured from a single type of surface of NbP, TaP and TaAs. SI B: Detailed band structures of NbP, TaP, TaAs and comparison to theory The detailed band structures of three members of transition metal monopnictides (NbP, TaP and TaAs) and their comparison to theory are summarized in Fig. S3 and S4. From the constant energy contour plots at different binding energies (Fig. S3), we can see that all three compounds share similar features on the Fermi Surface, including both bowtie-like pockets near the Brillouin zone boundary (XX and YY ) and the orthogonal spoon-like pockets near the halfway of ΓΓ XX (ΓΓ YY ). At higher binding energies, the pockets enlarge and eventually form complex interconnected texture. Figure S3. Constant energy contours of NbP, TaP and TaAs and the comparison to the ab initio calculations. a-c, Left columns: constant energy contours of NbP (a), TaP (b) and TaAs (c) measured by ARPES at binding energies from 0 mev to 300 mev (top to bottom panels). Right columns: corresponding ab initio calculations for the three compounds. 4 NATURE MATERIALS

5 SUPPLEMENTARY INFORMATION In addition, the band dispersions (Fig. S4 plots those along the high symmetry directions) of the three compounds show systematic evolution from NbP to TaP and to TaAs. Again, their band structures [Fig. S4a, c, e] from experiment show nice agreement with the ab initio calculations [Fig. S4b, d, f]. The similarity between the band structures of the three compounds (Fig. S3, S4) suggests that they share common topological properties, i.e., they are all TWSs. Moreover, the systematic evolution of their band structures enables the fine-tuning of the electronic properties of TWSs in order to obtain better performance for potential future applications. Figure S4. Band structure of NbP, TaP and TaAs and the comparison to the ab initio calculations. a,c,e, Measured band structures along high symmetry directions of NbP (a), TaP (c) and TaAs (e). b,d,f, Ab initio calculations of the band structures along the corresponding high symmetry directions of NbP (b), TaP (d) and TaAs (f). SI C: Photon energy dependent measurement of the electronic structure of NbP and TaP In an ARPES measurement, the in-plane electron momentum (k //, parallel to the sample surface) can be naturally determined by the momentum conservation of photoelectrons; while determining the out-of-plane (vertical) momentum component (k z) requires a series of ARPES measurements performed at different photon energies. NATURE MATERIALS 5

6 The k z value could be derived based on the free-electron final state approximation with a potential parameter V 0 (also known as the inner potential) describing the energy difference from the bottom of the valence band to the vacuum level, kk zz = 2mm ee(ee kk cos 2 θθ + VV 0 ) ħ where θ is the emission angle and E k is the kinetic energy of the emitted electron, which satisfies: EE kk = hυυ ww EE BB where hν is the photon energy, w is the work function of the sample and E B is the electron binding energy. Therefore, ARPES measurements using different photon energies probe the Figure S5. Photon energy dependent measurements on the electronic structure of NbP with two surface types. a-n, Dispersions along the high symmetry YY -ΓΓ -YY direction (XX -ΓΓ -XX direction is the same due to the twin effect) obtained at different photon energies. o, Ab initio calculations on the band structure along the high symmetry YY -ΓΓ -YY direction. The color scale is proportional to the surface component. For both experimental and calculation data of NbP, the mixing of the two orthogonal sets of electronic structures from two surface types has been considered. electronic structure with different k z values and can be used to identify surface electronic states (which do not disperse along the k z direction) from bulk electronic states (which usually show variation along the k z direction) [S1, S2]. The k z evolution of the electronic structure of NbP has been briefly discussed in Fig. 2e, which reveals bowtie- and spoon-like FS features do not show resolvable k z evolution. To further elaborate this point, we present the band structure along the ΓΓ YY direction measured 6 NATURE MATERIALS

7 SUPPLEMENTARY INFORMATION at various photon energies from 52eV to 130eV (Fig. S5a-n). Multiple features can be identified in the band structure and show different evolution with the photon energy. Among the bands which cross the E F, SS1~SS3 can always be observed at all the photon energies and show no change in the dispersion while BVB changes in intensity and shape. In addition, SS1~SS3 show sharp dispersions while BVB is broad and fuzzy. Both findings strongly indicate the different origins of these features, and SS1~SS3 are surface-related bands while BVB are dispersions from the bulk electrons. The comparison to the ab initio calculations (Fig. S5o) proves the surface nature of the SS1~SS3 features. Meanwhile, BVB has a broad shape as they are the projection of the bulk Figure S6. Photon energy dependent measurements on the electronic structure of TaP. a-c, FS (a) and band dispersions along XX ΓΓ XX (b) and YY ΓΓ YY (c) measured with different photon energies, together with corresponding ab initio calculations of both surface and bulk projected bands. d, Plot of photoemission intensities at the E F along the high symmetry XX ΓΓ XX (i) and YY ΓΓ YY (ii) directions as a function of photon energy (45-130eV), showing the k z dispersion of different bands. NATURE MATERIALS 7

8 electronic states with strong k z dispersions. As SS1~SS2 form the spoon-like feature and SS3 forms the bowtie-like feature, we conclude these features are originated from the surface electronic states. In TaP, we have observed similar photon energy dependence in Fig. S6. The FSs obtained with different photon energies show negligible variation both in size and shape (Fig. S6a(i)-(iv)) and the bands contributing to the spoon- and bowtie-like FSs show identical dispersions under different photon energies along both XX ΓΓ XX (Fig. S6b(i)-(iv)) and YY ΓΓ YY (Fig. S6c(i)-(iv)), proving their surface origin. The surface origin of the E F-crossing bands is further supported by the ARPES intensity plots along YY ΓΓ YY and XX ΓΓ XX at the E F over a large energy range (from 45 ev to 130 ev, Fig. S6d), which show negligible variation. Moreover, we have also observed a bunch of features with weaker intensity along both XX ΓΓ XX (Fig. S6b) and YY ΓΓ YY (Fig. S6c) which show clear photon energy dependence, indicating their bulk origin. These bulk states are also well captured by the calculations which show their projection to the surface (the lighter red curves in Fig. S6b(v),c(v)). SI D: Further evidence for the existence of Fermi arc on the surface of NbP and TaP A compelling method to evidence the existence of Fermi arcs is to count the number of Fermi surface crossings along a closed reference loop in the momentum space. An odd number of FS crossings along a closed reference loop provides sufficient evidence for the existence of Fermi arcs. In Fig. 3 of the main text (also see Fig. S7a), we found such a reference loop (MM XX ΓΓ MM ) with odd number (seven) of FS crossings, thus proved the existence of Fermi-arcs in the surface BZ of TaP. Below in Fig. S7, we deliver further discussion on the counting of the FS crossings. The total seven crossing along the ΓΓ XX MM ΓΓ loop include three FS crossings along XX ΓΓ, four along XX MM and zero along ΓΓ MM, respectively (Fig. S7a). Among these crossings, #3, #6 & #7 could be individually resolved from ARPES; #1 & #2 are from two nearly 8 NATURE MATERIALS

9 SUPPLEMENTARY INFORMATION degenerate bands and #4 & #5 are very close to each other (see the momentum distribution curve (MDC) at E F drawn on the top of Fig. S7a(i)). We are able to identify them separately by fitting to the peaks in the MDC, tracing their band evolution at high energies and comparing to the ab initio calculation band structure (Fig. S7a(i)). Therefore, the FS crossing counting along the closed loop gives odd number, confirming the existence of Fermi arcs on the surface of TaP. Figure S7. Evidence for the existence of Fermi arcs on the surface of TaP and NbP from the counting of Fermi surface crossings in the closed loops in the BZ. a, (i) The band dispersions of TaP along high symmetry MM XX ΓΓ MM direction overlapped with the ab initio calculations (red curves). We can identify a total of 7 FS crossings along the loop. The momentum distribution curve at E F together with peak fitting results and numbered arrows indicating each crossing is plotted on the top of the figure. Bands with FS crossings are denoted. (ii) Schematics of the FS crossing counting along the reference loops in a (i). The Weyl points is marked by red and blue dots and FS crossings marked by green arrows as in a. The MM XX ΓΓ MM loop is highlighted by bold magenta lines. b, (i) The FS crossing counting along the MM XX ΓΓ MM closed loop for NbP, similar as a(i). We can identify a total of 5 FS crossings along the loop. The momentum distribution curve at E F together with peak fitting results and numbered arrows indicating each crossing is plotted on the top of the figure. Bands with FS crossings are denoted. (ii) Schematics of the FS crossing counting along the reference loop in b (i), similar as a (ii). Similarly, for NbP, we did the same counting of the Fermi surface crossings (Fig. S7b) along the same closed ΓΓ XX MM ΓΓ loop. We could locate three FS crossings along XX ΓΓ, two along XX MM and zero along ΓΓ MM, respectively (Fig. S7b) a total of 5 (odd) crossings. Among these crossings, #3 could be individually resolved from ARPES; #1 & #2 and #4 & #5 are from nearly degenerate bands (see the MDC at E F drawn on the top of Fig. S7b(i)), which we label them separately by fitting to MDC peaks and comparing to the ab initio calculations. NATURE MATERIALS 9

10 Therefore, the counting result also suggests the non-trivial topology in the FS pattern and proves the existence of the Fermi-arcs on the surface of NbP. We have established the existence of Fermi arcs on the FS of NbP and TaP. In the next step, we provide further evidence to identify the Fermi arc from the observed bands. We will elaborate in the following three aspects: i) Further theoretical investigations to understand the surface FS and identify the Fermi-arc: In Fig. S8, we show more detailed (and spin-resolved) plot of the spoon-like FS feature around the YY point (XX point is similar) from the ab initio calculations for NbP, TaP and TaAs. We start with TaAs to describe how each band evolves. As can be seen in Fig. S8e, three FS pieces have been observed, FS-1, 2 and 3 have different spin textures and the spin polarizations evolve smoothly along each piece of FS. The inset of Fig. S8e shows the zoomed in details of the three FS pieces around the Weyl points and how FS-1 (green) gradually vanishes. Figure S8. Detailed analysis on the ab initio calculation of the Fermi arc. a,c,e Detailed ab initio calculation results with the spin polarization of the Fermi surface around the YY point for NbP (a), TaP (c) and TaAs (e). Black arrows indicate the amplitudes and directions of the spin polarization. Different colors represent different FS pieces. For the same FS piece, spin polarizations evolve continuously. The inset of a,c,e shows the zoomed-in plot of the FS around the Weyl points. b,d,f, Photoemission spectral intensity of the Fermi surface around the YY point for NbP (b), TaP (d) and TaAs (f). Dashed line indicates the position where the band numbers are reduced. Numbers with arrows label each FS piece. 10 NATURE MATERIALS

11 SUPPLEMENTARY INFORMATION Meanwhile, the FS-2 below the dashed line is the natural continuation of FS-2 above the dashed line with continuous spin evolution and geometry extension. FS-3 shows less surface contribution compared to FS-1 and FS-2 either above or below the dashed line, as well as much weaker spin polarization (almost vanishing and hard to label). Based on the discussion above, we conclude that the change of the number of FS pieces from 3 (above the dashed line) to 2 (below the dashed line) is due to the termination of FS-1, rather than the merging of FS-1 and FS-2 in the Region 2 below the dashed line. Therefore, FS-1 is observed as the Fermi arc surface states in TaAs. As for NbP and TaP, the calculated band structure (Fig. S8a,c) shows some difference comparing to TaAs: 1) there are only two FSs above the dashed line and one FS below. The other feature shows up as filled bands with negligible surface contributions in NbP and TaP. 2) The splitting between FS-1 and 2 is much smaller in NbP and TaP comparing to TaAs. Despite these differences, all the features we have seen in TaAs is similar in NbP and TaP: FS-1 and 2 both have different spin textures; From the evolution of the spin texture we found while the FS- 2 naturally continues below the dashed line, FS-1 terminates after crossing the dashed line (details of how FS-1 terminates is shown in the inset of Fig. S8a and c.). Therefore, from the detailed analysis of the ab initio calculations we could identify FS-1 as the Fermi arc surface states in all three materials. ii) Surface doping experiments confirming the Fermi-arc nature of FS-1 in TaP: Moreover, in order to visually confirm FS-1 as the unclosed Fermi arc from the ARPES measurements, we have to slightly shift the Fermi energy up since the ab initio calculation predicts the broken of the arc is most evident at tens of mev above the E F of pristine cleaved surface (e.g. ~60meV for TaP and TaAs). To achieve this goal, we measured one TaP for an extended period of time (24 hrs) and found the residue gas in the vacuum chamber slowly electron dope TaP and shift the E F up, allowing us to clearly observe the broken FS-1 separated from other Fermi surfaces (Fig. S9a-d), in perfect agreement with the ab initio calculation (Fig. S9e-h). In addition, the constant energy contour at E F-60meV of effectively n-doped sample shows nice agreement with the Fermi surface of the pristine TaP surface, suggesting the aging effect does not change the bandstructure. NATURE MATERIALS 11

12 Figure S9. Observation of Fermi arc on the effectively n-doped surface of TaP. a-d, The constant energy contours at different binding energies on an effective electron doped surface of TaP measured 24 hours after cleavage. e-h, ab initio calculations of the corresponding surface electronic structure. The energy position of d and h roughly corresponds to the Fermi level of the pristine surface of TaP. iii) MDC line shape analysis to confirm the evolution of different FS pieces: We carefully conducted the line shape analysis of the momentum distribution curves (MDCs) for the Fermi surface of NbP, TaP and TaAs and examined the termination behavior of the Fermi arc near the Weyl points. The MDC fitting results are shown in Fig. S10, in which Lorentzian peaks are used for the fitting process. From the fitting results of all three compounds, we can see while the peak positions and intensities of FS-2 (and also FS-3 for TaAs) are continuous when crossing the Weyl point, the peak intensity of FS-1 diminishes quickly after passing the intercepting points (Fig. S10, which also agrees with the calculation in Fig. S8 above), suggesting its termination at the Weyl point. Based on the three considerations discussed above, we conclude that the Fermi-arc nature of the FS-1 is well justified. 12 NATURE MATERIALS

13 SUPPLEMENTARY INFORMATION Figure S10. Line shape analysis of the MDCs on the Fermi surface of NbP, TaP and TaAs. a,b,c, Fitting results for NbP (a), TaP (b) and TaAs (c). For each row: (i) Photoemission intensity of the Fermi surface around the YY point. Dashed line indicates the position where the band numbers are reduced. Two (three for TaAs) bands are identified and labeled. For the convenience of fitting, the plot has been symmetrized with respect to the k x=0 plane according to the crystal symmetry. (ii) Stacking plot of the MDCs of the intensity map in (i). Dots with different color represent the fitted MDC peak positions of corresponding bands. (iii-iv) Summary plot of the fitted MDC peak positions (iii) and peak intensities (iv) of the two (three for TaAs) bands as a function of k y. The black dashed lines mark the k y position of the Weyl points. SI E: Bulk electronic states and Weyl fermion in TaP In addition to the unique surface Fermi-arcs, we also carried out ARPES measurements with high photon energy to investigate the bulk band structure of TaP (Fig. S11). The bulk bands with strong k z dispersion can be clearly seen in the k y-k z spectra intensity map (the cut direction is indicated by the gray plane in Fig. S11a), showing great contrast to the surface states in Fig. S6 without k z dispersion) and agreeing well with our ab initio calculation for the bulk bands (overlapped on Fig. S11b, note that the Weyl points are not observed here as they NATURE MATERIALS 13

14 are off the k x=0 plane, see Fig. S11a). The measured dispersions along two high symmetry directions (Σ-Γ-Σ in Fig. S11c and S-Z-S in Fig. S11d) also shows rapid change of band structure at different k z values, indicating their bulk origin. The rapid k z dispersion and the excellent agreements between our experiments and calculations allow us to identify the Weyl points predicted lying at k z=±1.17 /c and k z=0 planes (Fig. S11a), which can be accessed by using 168eV (k z= 1.17π/c in the reduced BZ) and 154eV (k z=0 in the reduced BZ) photons, respectively (Fig. S11b). At each photon energy, we first carried out k x-k y FS mapping (Fig. S11e, g) to locate the in-plane momentum positions of the Weyl points, then measured the band dispersions across them (Fig. S11f, h). Indeed, the measured bulk band dispersions in both cases show clear linear dispersions that match well with our calculations (Fig. S11f, h), confirming the existence of Weyl Fermions in the bulk of TaP. Figure S11. Bulk electronic states and Weyl fermion in TaP. a, Schematic illustration of the BZ of TaP and Weyl points. The vertical grey plane indicates the measurement k y-k z plane of the intensity plot in b. b, Photoemission intensity plot in the k y-k z plane (k x=0, the grey plane in a) close to E F. Overlaid orange curves are calculated bulk bands constant energy contour at E F, showing good agreement with the experiment. Green and magenta curves indicate the (k z) momentum locations probed by 168eV and 154eV photons, respectively. The two dashed lines marked as cut1 and cut2 indicate the momentum directions of the two band dispersions shown in c and d. c, d, Bulk band dispersions along two high-symmetry directions, indicated as cut1 and cut2 in b, respectively. e, FS map of the k x-k y plane using 168eV photons, with the calculated FS overlapped (orange pockets). Black dashed line indicates the measurement direction of the band dispersion in f, and the blue solid lines indicate the k x- k y BZ at k z=1.17π/c (in the reduced BZ). f, Broad band dispersion (i) and its zoomed-in plot (ii) across the Weyl points (along the direction indicated by the dashed line in e).wp+ and WP- mark the position of the Weyl points around k z=1.17π/c. g, h, Same as e, f for photon energy of 154 ev (through the Weyl points at k z=0 in the reduced BZ). 14 NATURE MATERIALS

15 SUPPLEMENTARY INFORMATION SI F: Polarization dependent measurement of the electronic structure of NbP The measured ARPES signal intensity (I 0) is affected by the photoemission matrix element: I 0 φφ kk ff εε xx φφ kk ii 2, where φφ kk ii and φφ kk ii are the wavefunctions for the initial and final states. εε is the unit vector along the polarization vector EE and xx is the position operator. Thus different photon polarization and measurement geometries can enhance or suppress ARPES signal intensity for initial states (bands) with different symmetries [S1]. Figure S12. Polarization dependent measurement on the electronic structure of NbP with two surface types and circular dichroism. a, Measurement geometry with perpendicular (EE LV), parallel (EE LH) (with respect to the emission plane) and right circular (EE CR) polarizations of photons, indicated by the red, blue and green arrows, respectively. The blue bar on top shows the direction of the analyzer slit where measurements are performed. The labeled lobes represent electrons in the d xy orbit. b, Photoemission intensity of the high symmetry YY ΓΓ YY cut measured with left/right circular (CL/CR) and parallel/perpendicular (with respect to the emission plane, LH/LV) polarized photons. Observed surface/bulk bands are labelled (SS1-SS3 and BVB). c, The spectral intensity difference between using the left circular and right circular polarized photons show clear circular dichroism. d, Ab initio calculations on the bandstructure along the high symmetry YY -ΓΓ -YY direction. The color scale is proportional to the surface component. We performed ARPES measurements with different light polarizations. The measurement geometries for the experiment are shown in Fig. S12. Four kinds of photon polarization have been used during our measurement, including EE CL/CR (left/right circularly polarized light), EE LH (parallel to the incident plane and perpendicular to the analyser slit/yy ΓΓ YY direction) and EE LV (perpendicular to the incident plane and parallel to the analyser slit/yy ΓΓ YY direction), respectively (Fig. S12a). With all polarizations, consistent band structures are observed in the high symmetry YY ΓΓ YY dispersions (Fig. S12b), including NATURE MATERIALS 15

16 those with FS crossings (surface states SS1~SS3 and bulk bands BVB), in agreement with the ab initio calculations. However, as we change the light polarization, ARPES intensity of different bands are either suppressed or enhanced, reflecting their individual matrix elements. ARPES circular dichroism could be obtained from the difference of the spectral intensity measured with the left and right circularly polarized light (Fig. S12c). Interestingly, all the bands we observed show clear dichroic signal: as the k<0 part of SS1, SS2 are enhanced when probed with left circular polarized photons, SS3 and BVB are suppressed. The circular dichroism can provide important information on their orbital characters, final state effects and even spin polarizations as well as their interplay thus worth further investigations in the future work. SI G: Spin-orbit coupling dependent separation of Weyl pairs and band splitting In the formation of Weyl semimetals in the transition metal monopnictide family (NbP, TaP, TaAs), the strong spin-orbit coupling (SOC) in these materials plays a crucial role (besides the broken of the inversion symmetry). The SOC will cause the opening of the inversion band gap (similar to the case in topological insulators) in this family of compounds [S3, S4] and push the Weyl points with opposite chirality away from the mirror plane which has been reproduced by our ab initio calculations in Fig. S13: the splitting of the Weyl points is proportional to the strength of SOC in different compounds (Fig. S13a), and the splitting of the band dispersions (that causes the splitting of the Fermi-arcs) also increase with the SOC in different compounds (Fig. S13b). 16 NATURE MATERIALS

17 SUPPLEMENTARY INFORMATION To further confirm the SOC effect and eliminate the complexity from different compounds, in Fig. S13c, we show the evolution of the ab initio calculated band structure of TaP with (virtually) different SOC strength and kept all other calculation parameters unchanged. Using the true SOC in TaP as the unit, we carried out calculations for virtual SOC = 0, 0.3, 0.5 and 0.8. The results are summarized in Fig. S13c, which again clearly demonstrate the separation of the Weyl points and the splitting of the Fermi-arcs. Figure S13. Evolution of the Weyl point splitting and Fermi arc feature controlled by the SOC strength. a, Calculated spoon-like FS of NbP, TaP and TaAs showing the increase of splitting between the Weyl points (labelled as ΔK1) and Fermi-surfaces (labelled as ΔK2) as the SOC strength increases. b, Calculated band dispersions along the high symmetry YY ΓΓ direction in NbP, TaP and TaAs. The separation between the Fermi crossings is labeled as ΔK2. c, Calculated surface Fermi arcs of TaP using different SOC strength (the unit is the actual SOC strength in TaP). Black dots indicate the positions of the two degenerate Weyl points, while red/blue points denote the positions of a pair of Weyl points with opposite chirality (labelled as WP+ and WP-). NATURE MATERIALS 17

18 References: S1. Damascelli, A., Hussain, Z. & Shen, Z.-X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys., 75, (2003). S2. Chen, Y. Studies on the electronic structures of three-dimensional topological insulators by angle resolved photoemission spectroscopy. Front. Phys. 7, (2012). S3. Weng, H., Fang, C., Fang, Z., Bernevig, A. & Dai, X. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides. Phys. Rev. X 5, (2015). S4. Huang, S.-M. et al. A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nature Commun., 6: 7373 (2015). 18 NATURE MATERIALS