A weak topological insulator state in quasi-one-dimensional superconductor TaSe 3
Jounghoon Hyun, Min Yong Jeong, Sunghun Kim, Myung-Chul Jung, Yeonghoon Lee, Chan-young Lim, Jaehun Cha, Gyubin Lee, Yeojin An, Makoto Hashimoto, Donghui Lu, Jonathan D. Denlinger, Myung Joon Han, Yeongkwan Kim
AA weak topological insulator state in quasi-one-dimensional superconductor TaSe Jounghoon Hyun † , Min Yong Jeong † , Sunghun Kim , Myung-Chul Jung ,Yeonghoon Lee , Chan-young Lim , Jaehun Cha , Gyubin Lee , Yeojin An ,Makoto Hashimoto , Donghui Lu , Jonathan D. Denlinger , Myung Joon Han ∗ and Yeongkwan Kim , ∗ Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea. Stanford Synchrotron Radiation Lightsource, Stanford Linear Accelerator Center, Menlo Park, CA 94025, USA. Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. and Graduate School of Nanoscience and Technology,Korea Advanced Institute of Science and Technology, Daejeon 34141, South Korea.
A well-established way to find novel Majoranaparticles in a solid-state system is to have su-perconductivity arising from the topological elec-tronic structure. To this end, the heterostruc-ture systems that consist of normal supercon-ductor and topological material have been ac-tively explored in the past decade. However, asearch for the single material system that si-multaneously exhibits intrinsic superconductiv-ity and topological phase has been largely lim-ited, although such a system is far more favorableespecially for the quantum device applications.Here, we report the electronic structure studyof a quasi-one-dimensional (q1D) superconductorTaSe . Our results of angle-resolved photoemis-sion spectroscopy (ARPES) and first-principlescalculation clearly show that TaSe is a topologi-cal superconductor. The characteristic bulk inver-sion gap, in-gap state and its shape of non-Diracdispersion concurrently point to the topologicallynontrivial nature of this material. The further in-vestigations of the Z indices and the topologi-cally distinctive surface band crossings disclosethat it belongs to the weak topological insulator(WTI) class. Hereby, TaSe becomes the first ver-ified example of an intrinsic 1D topological super-conductor. It hopefully provides a promising plat-form for future applications utilizing Majoranabound states localized at the end of 1D intrinsictopological superconductors. Topological superconductors are recently attractinggreat research attention due to their fundamental impor-tance and potential application to the quantum compu-tation based on the Majorana bound states . A popu-lar approach is to make use of superconducting proxim-ity effect with which Cooper pairs are injected into thetopological surface state as theoretically suggested by Fuand Kane . Following this idea, several heterostructureshave been fabricated and indeed shown to host the Majo-rana quasiparticles . From the point of view of the ap-plication, however, the heterostructure systems can likelybring technical difficulties in the device fabrication. It istherefore highly desirable to have a material that intrin-sically hosts topological superconductivity, although notmany systems have been experimentally confirmed to bethe case. One promising candidate is Fe(Te,Se) where superconductivity is encoded into the topological surfacestate on the two-dimensional (2D) surface . In this ma-terial, the topological superconductivity can certainly beintrinsic. However, the location of the Majorana state canbe at the center of the vortex or anywhere on the edgeof 2D surface; namely, it is not pre-determined locally.In this regard, an important research direction, thathas not been well explored so far, is to search for in-trinsic topological superconductivity in one-dimensional(1D) systems. Different from the 2D or three-dimensional(3D) case, Majorana states exist at both ends of the 1Dtopological superconductor , thus making its manip-ulation much easier. It would be useful for circuit deviceapplications by securing the Majorana states at certaindesired positions. Here we note a recent theoretical studysuggesting that TaSe is a strong topological insulator(STI) . Also, the previous experiment seem to indicatethe unusual superconductivity in this material by show-ing the absence of a diamagnetic response below the crit-ical temperature T C14 . To be the first confirmed exam-ple of 1D intrinsic topological superconductivity, how-ever, further investigations of its topological propertiesare strongly requested from both experimental and the-oretical sides.In this Communication, we report our detailed studyof the electronic structure of TaSe by using angle-resolved photoemission spectroscopy (ARPES) andfirst-principles density functional theory (DFT) calcula-tion. The band inversion by spin-orbit coupling (SOC)and the additional in-gap surface state with non-Diracdispersion clearly indicate the nontrivial topology ofits band structure. Further analyses of Z indices andthe number of Dirac points depending on the surfacetype clearly show that TaSe is a weak topologicalinsulator (WTI). Our results establish TaSe as thefirst experimentally verified example of an intrinsic 1Dtopological superconductor. ResultsCrystal and electronic structure.
TaSe consists ofelongated prismatic chains with monoclinic P2 /m spacegroup symmetry (Fig. 1a), which gives rise to thequasi-one-dimensional (q1D) electronic properties. Thechains are stacked via van-der-Waals interaction andthe weak potential modulation along with the chain-perpendicular direction results in the finite band dis- a r X i v : . [ c ond - m a t . s up r- c on ] S e p a ac TaSe(101) cleavage planeb b AEΓ~ BΓ YBZ DΓ k a Z C Y~ k (010) hv k z D c (101) S~X~ k || k c k b E - E F ( e V ) DOS (states/eV)
Ta- d Se- p TotalSe- p Ta- d FIG. 1.
Crystal structure and calculated bulk band structure of TaSe . a , Crystal structure of TaSe . Ta and Seatoms are depicted by yellow and violet spheres, respectively. The black solid parallelogram and blue dashed line shows the unitcell and the practical cleavage plane (10¯1). b , 3D and surface-projected BZs. The planes colored by blue and yellow representthe surface BZs of (10¯1) and (010) planes, respectively. k (cid:107) and k ⊥ indicate projected reciprocal lattice vectors on the (10¯1)surface BZ. c , Calculated bulk band structure (left) and projected density of states (PDOS, right). The projected weights ofTa-5 d and Se-4 p orbitals are presented in red and blue colors, respectively. The band inversions are clearly observed aroundthe high-symmetry points of B, Z, and D. For the calculated band structure without SOC, see Supplementary Fig. 2. persion within 3D Brillouin zone (BZ) (Fig. 1b). Dueto the different bonding strengths between interchainSe ions, (10¯1) plane becomes a natural cleavage planeon which ARPES measurements are conducted. Figure1b shows the eight time-reversal invariant momentum(TRIM) points and their projections onto the surfaceBZs. Hereafter, we will use the notations of the high-symmetry points in the surface-projected BZ and in 3DBZ for describing ARPES data and bulk band calcula-tions, respectively.Figure 1c presents the calculated bulk band structureof TaSe . The low-energy states are governed by Ta-5 d and Se-4 p orbital characters and their relative weightsare depicted by red and blue color, respectively. Thesizable hybridization between these two orbitals areclearly noted in the projected density of states (PDOS;right panel of Fig. 1c). The orbital-weighted bandstructure shows the band inversions around B, Z, andD points, which indicates its topological nature. Itbecomes clearer in comparison to the calculated bandstructure without SOC (see Supplementary Fig. 2). TheSOC removes the band crossings and induces the gapopenings accompanied by band inversion; see the bandstructure changes along e.g., D–E, B–A and Z–C line. ARPES electronic structure and an in-gap state.
In order to examine the electronic structure and its topo-logical nature, we carried out ARPES measurement onhigh-quality single crystals of TaSe . Figure 2 presentsthe ARPES spectra measured on the cleaved (10¯1) sur- face. A constant energy contour plot at Fermi level ( E F )(Fig. 2a) shows an elongated Fermi surface along k ⊥ , re-flecting the overall 1D character of this material ( x - and y -axis corresponds to k (cid:107) and k ⊥ direction in Fig. 1b, re-spectively). The band dispersions were measured alongtwo projected high-symmetry lines, namely, ˜Γ– ˜Y (cut 1)and ˜X–˜S (cut 2). These two lines are particularly inter-esting because the characteristic band inversions are ob-served (see Fig. 1b, c) and the Dirac cone, a hallmark of atopological insulator, has been predicted by the previouscalculation .In taking the ARPES spectra, we utilized both linearvertically (LV) and horizontally (LH) polarized incidentlight to avoid missing of the spectral weight caused bymatrix element effect. Note that each spectrum takenwith different polarizations highlights different bands andis therefore complementary to each other. For instance,two hole bands with different band-top energies near E F are well identified in the cut 1 taken with LV (Fig. 2b)while only the lower one is seen by LH (Fig. 2c). Alongcut 2, LV clearly reveals a hole band near E F (Fig. 2d)whereas LH proves the relatively large electron-like bandtogether with additional two tiny electron bands whichbarely cross the E F (Fig. 2e). To analyze the compli-cated band dispersion of TaSe more clearly, the curva-ture method is applied (Figs. 2f-i) which enables us tomake more direct comparisons with calculation results.As shown in Fig. 2b-i, the overall band structure ofARPES spectra is in good agreement with our theoret-ical result. The calculated bulk bands along Γ–Y (Z–C) a -0.2 0.0 0.2 k || (Å -1 )0.40.20.0-0.2 k ⊥ ( Å - ) cut 2cut 1 -0.6-0.4-0.20.0-0.4 0.0 0.4-0.8 k || (Å -1 ) c cut 1 -0.6-0.4-0.20.0-0.4 0.0 0.4-0.8 k || (Å -1 ) d cut 2 -0.6-0.4-0.20.0-0.4 0.0 0.4-0.8 k || (Å -1 ) e cut 2 b cut 1 k || (Å -1 ) f k || (Å -1 ) cut 1 g -0.6-0.4-0.20.0-0.4 0.0 0.4-0.8 k || (Å -1 ) cut 1 h -0.6-0.4-0.20.0-0.4 0.0 0.4-0.8 k || (Å -1 ) cut 2 i -0.6-0.4-0.2-0.4 0.0 0.4-0.8 k || (Å -1 ) cut 2 LH S~Y~
LHLVLVLHLHLVLV E - E F ( e V ) E - E F ( e V ) (101) FIG. 2.
ARPES results of TaSe in comparison to the calculated bulk band structure. a , Fermi surface measuredat (10¯1) plane. k (cid:107) ( k ⊥ ) refers to the direction parallel (perpendicular) to the chain. Gray solid lines with arrows indicate twohigh symmetry lines, ‘cut 1’ ( ˜Y–˜Γ– ˜Y) and ‘cut 2’ (˜S- ˜X-˜S), along which further investigations were carried out. b-c , ARPESspectra along cut 1, obtained by utilizing LV and LH polarized light. d-e , ARPES spectra along cut 2, obtained by utilizingLV and LH polarized light. f-i , Curvature plots of (b-e) . The calculated bulk band structures are superimposed on the righthalf of the plots for comparison. Black solid lines (gray solid lines) indicate the visible (invisible) bands in each polarization.The red arrows in (g,i) indicate the bands which are observed by ARPES but not found in the bulk band calculation. are presented as solid lines and overlaid on the curva-ture plots of cut 1 (cut 2) in Fig. 2f-i where the black(gray) lines represent the calculated bands that are ob-served (not observed) in the corresponding polarizationlight of ARPES data. From the point of view of topol-ogy, most intriguing is the tiny electronic bands whosebottom is located just below E F ; see the small parabolicband (solid black line) in Fig. 2i (it is not visible with LVpolarization and depicted by the gray line in Fig. 2h).This band is symmetric with respect to k (cid:107) = 0 ( ˜X) asseen in our curvature plot; see the left half of Fig. 2h-i(not overlaid with the calculation result of a solid line).Note that the bottom of this band is not located at ˜X.This characteristic feature caused by band inversion re-flects its topological nature as discussed recently by Tang et al. . Thus, our result provides the first experimentalsignature of nontrivial topology of this q1D superconduc-tor.Importantly, some noticeable band features in ARPESspectra are not observed in the calculation. See, inparticular, two bands near E F indicated by red arrows inFigs. 2g and 2i. The first one is the two hole bands in cut1 (Fig. 2g). While the upper-hole band is well identifiedin our calculation (see the uppermost black solid linein Fig. 2h), the lower is only observed in ARPES. Thesecond is a small piece of the electron-like band in cut 2locating in between the lower-lying large hole bands andthe upper tiny electron bands; see Fig. 2i. Once again, the spectrum of this band is large enough in ARPES butnot seen in DFT result. Understanding the discrepancybetween theory and experiment, particularly for thecase of this second band, is of key importance because itlocates in the band inversion gap and thus is likely tobe involved with the topological nature of this material.In the below, we will show that this ‘in-gap state’ has infact the surface origin and its dispersion feature can beregarded as an indication of WTI state rather than STI . Surface electronic structure and band topology:DFT calculation.
To further elucidate the nature ofband dispersion including the in-gap state, we performedthe slab calculation by using iterative Green’s functionmethod based on maximally localized Wannier func-tions (MLWFs) generated from DFT bands (seeMethods for more details). In Fig. 3, the results are pre-sented and compared with experimental spectra wheretwo ARPES spectra taken from both polarizations areadded up. Besides the overall good agreement in betweencalculation and experiment, we first take a special noteon the broad continuum states (indicated by white arrowsin Figs. 3a, e). This continuum is well identified also inthe calculation being attributed to the surface projectionof bulk states at a range of k z values (see Fig. 1b). InARPES measurement, on the other hand, the broaden-ing of photoelectron momentum along k z direction is dueto the finite probing depth of incident light in real space. -0.2-0.10.0-0.2 cut 2 -0.2-0.10.0-0.2 cut 1 a be f g c hd -0.6-0.4-0.20.0-0.4 0.0 0.4-0.8 k || (Å -1 ) -0.6-0.4-0.20.0-0.4 0.0 0.4-0.8 k || (Å -1 )-0.6-0.4-0.20.0-0.4 0.0 0.4-0.8 k || (Å -1 ) -0.6-0.4-0.20.0-0.4 0.0 0.4-0.8 k || (Å -1 ) cut 1 cut 1cut 2 cut 2 -0.2-0.10.0-0.2 0.0 0.2 k || (Å -1 ) cut 1 -0.2-0.10.0-0.2 0.0 0.2 k || (Å -1 ) cut 2 E - E F ( e V ) E - E F ( e V ) k || (Å -1 )0.0 0.2 k || (Å -1 ) BSSS BSSSSS SSSSSS
FIG. 3.
The (10¯1) surface states revealed by ARPES and the slab calculation. a-d , ARPES spectra along cut 1( ˜Y–˜Γ– ˜Y) and its curvature plot in comparison with the corresponding slab band calculation. a , ARPES spectra along cut 1obtained by adding up the LV and LH data (Figs. 2b, c). The slab calculation results are overlaid in the right half of thefigures. The white arrow indicates the broad continuum state, which is consistently found in both experiment and calculation. b , Curvature plot of (a) overlaid by the same slab calculation. The black dashed line shows the surface-originate state (‘SS’). c , Zoomed-in ARPES image of (a) (left) and (b) (right). d , Zoomed-in image of (b) . The black dashed line (‘BS’) representsthe band from the bulk band calculation (guide to the eye) and the red dashed line (‘SS’) indicates the band not observed inthe bulk calculations. The surface band spectra are well separated from the nearby bands. e-h , The same with (a-d) alongcut 2 (˜S- ˜X-˜S). h , Overlaid red dashed line represents the in-gap state observed in ARPES spectra which is missing in the bulkband calculation. It is also clearly observed in the left half of the panel as indicated by the red arrow. Therefore, this consistency between theory and experi-ment confirms that our slab calculation sufficiently welldescribes the states near the surface.Interestingly, Fig. 3 clearly shows that the two afore-mentioned bands (which are present in ARPES but notobserved in the bulk calculation) are originated from sur-face states. For clearer comparisons, see Fig. 3b and 3ffor the case of hole-like (in cut 1; ˜Γ– ˜Y line) and electron-like band (in cut 2; ˜X–˜S line), respectively, as denoted bythe black-dashed lines and the red arrows. From the factthat these bands are only reproduced by surface bandcalculations (and not found in 3D bulk calculations), weconclude that they are the surface states. Another factthat these bands are well separated from the nearby bulkspectra also supports this conclusion.From the point of view of band topology, important isthe unambiguous identification of the second band (i.e.,the electron-like band indicated by ‘SS’ in Figs. 3f, h)as being originated from the surface. As is well known,a hallmark of topological insulator is the characteristicsurface state with Dirac crossing, which is located insidethe inversion gap . The absence of Dirac cone at (10¯1)surface leads us to conclude that TaSe is not STIcontrary to the previous theoretical suggestion , andto require further investigation regarding its topologicalnature. DiscussionZ topological indices and weak topological insu-lator. According to Fu et al. , STI has surface Diraccones on its surface. On the other hand, WTI has Diracsurface state only on a certain type of surfaces. The othertype of surface is called topologically ‘dark’. Here it is im-portant to note that the cleaving surface of TaSe is infact a dark surface. Therefore, our observation of no Diracpoint in ARPES spectra does not exclude the intriguingpossibility for TaSe to be the first confirmed exampleof q1D topological superconductor. In order to examinethe possibility of WTI, we calculated Z topological in-dices, and found that TaSe is indeed a WTI; ( ν ; ν , ν , ν )=(0;101). Figure 4a shows the products of the occu-pied band parities at the eight TRIM points from which( ν ; ν , ν , ν ) are defined . As is well established, ν =0 and ν , (cid:54) = 0 are a clear signature of WTI .In order to further confirm the WTI nature of TaSe ,we explored the other surfaces than (10¯1), namely the‘non-dark’ surfaces on which the surface Dirac cones areexpected to appear. The dark surface of WTI is definedby the Miller indices of the given surfaces. That is, thesurfaces defined by ( ν , ν , ν ) and ( ν , ν , ν ) + 2 (cid:126)G ( (cid:126)G :the reciprocal lattice vector) are topologically dark . Asis already mentioned, our cleaving surface is therefore a Z = (0;101)A E Γ Y k c k a k b Z CDB δ = +1 δ = –1 a cd E - E F ( e V ) b (101) hv (100) ac b (010) DPDP
Γ~Y~ S~ X~ Y~BDΓ Z D (010)Z DΓ BYΓ~~ S~X~(101) E - E F ( e V ) FIG. 4.
The calculated Z topological invariants and the surface Dirac points. a , The products of band parities forall occupied bands ( δ ) at eight bulk TRIM points. The red and blue dots represent δ = +1 and −
1, respectively. b , Schematicpicture for the TaSe surfaces and their topological nature. According to the Z classification , the (10¯1) surface (blue colored)should be topologically dark while two other side surfaces, (010) and (100), are expected to have two Dirac points on each planeand to host topologically protected helical surface states (depicted by blue and red arrow). c , The calculated (010) surfaceband structure. The inset shows the surface-projected BZ and the relevant high-symmetry points. Two Dirac points are foundas expected at ¯B and ¯Z points. The topological surface states are indicated by the black (connecting to the conduction band)and the green dashed lines (connecting to the valence band) with arrows. The color bar represents the intensity strength. d The same as in (c) , for the (10¯1) surface. As expected, no Dirac cone is found. dark surface, and no Dirac cone found in our ARPESdata is consistent with the WTI nature. The calcula-tion result of the other type (010) surface is presented inFig. 4c, and two Dirac points are clearly noticed; see thepoints indicated by ‘DP’. The dashed lines with arrowsdemonstrate that both Dirac points are indeed the pointsmade by the crossings of the surface bands connectingvalence and conduction bands, and the band inversionchanges the band parity. For another allowed (i.e., non-dark) surface of (100), we found Dirac points as well; seeSupplementary Fig. 6. While some Dirac points are em-bedded in the bulk bands, the Dirac nature of their cross-ings can always be checked straightforwardly. Hereby, weestablish that TaSe has a WTI nature.It should be noted that the experimental verificationof WTI nature can be challenging due to the two dis-tinctive types of topological surfaces and the limited ca-pability of choosing cleaving surface . Further, addi-tional subtleties are also involved in the computation sidearising from the notorious issue of exchange-correlationfunctionals . Our effort of resolving this issue for thecurrent case of TaSe can be found in SupplementaryInformation. To the best of our knowledge, the only ex-ample of the experimentally reported 1D WTI is β -Bi I and its WTI nature has still been debated until very re- cently. Our case of TaSe is the second, if not the first,example of 1D WTI, and it is the first example of 1Dtopological superconductor.In summary, we provide the convincing evidence ofWTI nature in TaSe by means of ARPES experimentsand first-principles calculations. Topological features ofband inversion and surface in-gap state are clearly iden-tified. The calculated Z indices as well as the absenceand the presence of Dirac cones respectively on the darkand the non-dark surfaces confirm our conclusion of WTInature. With this, this material is suggested to be thefirst experimentally confirmed example of q1D topolog-ical superconductor in an intrinsic as-is form. Unveilingthe relation between the superconductivity and topologycan also be an exciting future direction. MethodsSample growth and characterization.
Single crystalsof TaSe were grown via the chemical vapor transport(CVT) method . Ta (99.99%) and Se (99.999%) powderof molar ratio 1 : 3.3 were loaded into one end-side(source zone) of the quartz tube. The additional amountof Se is intended to prevent Se deficiency , and towork as a transport agent. Then the quartz tube wasevacuated, sealed and loaded into the two-zone furnacewith the temperature of the zones set by 720 ◦ C and680 ◦ C, and maintained for 14 days. Whisker-like singlecrystals of typical dimensions of 10 × × wereachieved. The structural and electrical properties ofTaSe single crystals were characterized using energydispersive spectroscopy (EDS), X-ray diffraction (XRD),and electrical resistivity measurement (see Supplemen-tary Fig. 1). ARPES measurements.
ARPES measurements wereperformed at beamline 5-4 of Stanford Synchrotron Ra-diation Lightsource (SSRL), SLAC National Laboratoryand beamline 4.0.3 of Advanced Light Source (ALS),Lawrence Berkeley National Laboratory. ARPES spectrawere acquired with Scienta R4000 (R8000) electron ana-lyzer at SSRL (ALS). A clean surface of the sample wasobtained by in-situ cleaving of single crystals of TaSe .Samples were cleaved to reveal the natural cleavageplane of (10¯1) at 10K under ultra-high vacuum pressurebetter than 5 × − torr. Measurements were carriedout maintaining sample temperature at 10K at bothbeamlines. At SSRL, linearly polarized light of photonenergy hν = 20 eV was used for the measurements. AtALS, linearly polarized light of photon energy hν = 56eV was used. The total energy resolution and angularresolution was set to be better than 10 meV and 0.3 ◦ ,respectively, for the measurements at both beamlines. DFT band structure calculations.
Our DFT calcula-tions were performed with ‘Vienna Ab initio SimulationPackage (VASP)’ based on the projector augmented-wave pseudopotential . We used the experimentallattice parameters , and the internal atomic coordinateswere optimized with a force criterion of 0.001 eV/˚A.The 7 × × . Our main resultswere double-checked by using GGA-PBEsol andlocal density approximation (LDA) as parameterizedby Perdew and Zunger . We also double-checkedthe results by using all-electron full-potential code,‘Wien2k’ for which R mt K max = 7 and 7 × × d and Se p orbitals ,and ‘WannierTools’ code to analyze the topologicalproperty and surface state. The parities at TRIM pointswere calculated directly from DFT wave-functions byusing ‘vasp2trace’ . For comparison with ARPES data,the E F was shifted by 39 meV in the calculated bandstructure for both bulk and slab case. As reported inprevious studies , it likely reflects the presence of acertain amount of defects in crystals. Acknowledgements
Y.K. acknowledge helpful discus-sion with S.-K. Mo and J. S. Kim. M. Y. J. and M.-C.J. thank to S. Nie and Z. Wang for helpful comments.This research was supported by National R&D Pro-gram (No.2018K1A3A7A09056310), Creative MaterialsDiscovery Program (No.2015M3D1A1070672), BasicScience Resource Program (No.2017R1A4A1015426,No.2018R1D1A1B07050869) through the NationalResearch Foundation of Korea (NRF) funded by theMinistry of Science, ICT and Future Planning, Basic Sci-ence Research Program (No. 2019R1A6A1A10073887)through the NRF funded by the Ministry of Educationand by the Internal R&D Program at KAERI funded bythe Ministry of Science and ICT (MSIT) of the Republicof Korea (525350-19). M. Y. J., M.-C. J. and M. J.H. were supported by Basic Science Research Program(2018R1A2B2005204), and Creative Materials DiscoveryProgram through NRF (2018M3D1A1058754) funded bythe MSIT of Korea, and the KAIST Grand Challenge 30Project (KC30) in 2019 funded by the MSIT of Koreaand KAIST.
Author contributions
Y.K. and M.J.H. conceived thework. J.H. synthesized and characterized the TaSe singlecrystals. J.H., S.K., Y.L., C.L., J.C., G.L., Y.A., and Y.K.performed the ARPES measurements with support fromM.H., D.L. and J.D.D. J.H., S.K. and Y.K. analyzed theARPES data. M.Y.J., M.-C.J. and M.J.H. carried outtheoretical calculations. All authors discussed the results.J.H., M.Y.J., M.J.H. and Y.K. wrote the manuscript withcontribution from all authors. References Kitaev, A. Y. Unpaired Majorana fermions in quantumwires.
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