# Fileset

[s41467-023-37482-0.pdf](https://mdr.nims.go.jp/filesets/2353be6a-ab5b-4fa7-ac4f-7fae4f1ee3be/download)

## Creator

Jekwan Lee, Jaehyeon Kwon, Eunho Lee, Jiwon Park, Soonyoung Cha, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Moon-Ho Jo, Hyunyong Choi

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Spinful hinge states in the higher-order topological insulators WTe2](https://mdr.nims.go.jp/datasets/1c668f84-24e0-4478-a2e5-1210d2cee6ca)

## Fulltext

Spinful hinge states in the higher-order topological insulators WTe2Article https://doi.org/10.1038/s41467-023-37482-0Spinful hinge states in the higher-ordertopological insulators WTe2Jekwan Lee1,2, Jaehyeon Kwon1,2, Eunho Lee1,2, Jiwon Park1,2, Soonyoung Cha3,4,Kenji Watanabe 5, Takashi Taniguchi 5, Moon-Ho Jo 3,4 &Hyunyong Choi 1,2Higher-order topological insulators are recently discovered quantum materi-als exhibiting distinct topological phases with the generalized bulk-boundarycorrespondence. Td-WTe2 is a promising candidate to reveal topological hingeexcitation in an atomically thin regime. However, with initial theories andexperiments focusing on localized one-dimensional conductance only, noexperimental reports exist on how the spin orientations are distributed overthe helical hinges—this is critical, yet one missing puzzle. Here, we employ themagneto-optic Kerr effect to visualize the spinful characteristics of the hingestates in a few-layer Td-WTe2. By examining the spin polarization of electronsinjected from WTe2 to graphene under external electric and magnetic fields,we conclude that WTe2 hosts a spinful and helical topological hinge stateprotected by the time-reversal symmetry. Our experiment provides a fertilediagnosis to investigate the topologically protected gapless hinge states, andmay call for new theoretical studies to extend the previous spinless model.Recently, a new class of topological phase, called a higher-ordertopological insulator (HOTI), is proposed based on the generalizedbulk-boundary correspondence, covering d−2 or lower-dimensionaltopological boundaries in d-dimensional systems1–3. For instance, time-reversal invariant three-dimensional (3D) HOTIs exhibit gapless hingestates,where the gapped surfaces are facing eachotherwith a reversedsign of themass. Such a phenomenon can be understood based on thefact that the gapped surface states host a doubly inverted electronicband and the strong spin-orbit coupling (SOC)2,4–6. With these physicalgrounds, the band structure and the corresponding topological fea-tures of HOTIs have been predicted by well-established methods suchas a multi-orbital tight-binding model, first principle calculation, andWilson loop calculation1–6. To date, there exist only a few condensedmatter systems predicted to be HOTIs, such as bismuth7,8, topologicalcrystalline insulator SnTe2,4,9, twisted bilayer graphene10–12, and someartificial lattices13,14.Among such candidates, WTe2 has recently attracted muchinterest in investigating the electronic correlations aswell as exploringthe topologically protected quantum phenomena15,16. With an orthor-hombic 3D structure, it was first known as a type-II Weyl semimetalwith electron and hole pockets around the Weyl points5,17,18; resolvingtheWeyl points, however, remains challenging because angle-resolvedphotoemission spectroscopy (ARPES) cannot provide sufficientmomentum resolution to resolve the small separation of Weyl pointsof WTe219,20. In a monolayer limit, the thickness-dependent studies onthe crystal symmetry and electronic band structure have revealed thequantum spin Hall insulating phase for 1 T′-WTe2 crystals21,22. Afterrecent proposals on the higher-order topology, the large arc-like sur-face states of the bulk WTe2, which were initially considered topolo-gically trivial, started to be understood as gapped fourfold Diracsurface states4. Spatially resolved measurements using a Josephsonjunction were then used to identify the hinge states as a clue for thehigher-order topology7, and subsequent experiments have reportedanisotropic confinement of 1D conducting hinge channels in few-layerTd-WTe223,24. However, experimental evidence for the symmetry-protected topological nature of the observed 1D hinge state is stillReceived: 5 January 2022Accepted: 20 March 2023Check for updates1Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea. 2Institute of Applied Physics, Seoul National University, Seoul 08826,Korea. 3Center for Epitaxial van der Waals Quantum Solids, Institute for Basic Science, Pohang 37673, Korea. 4Department of Materials Science andEngineering, Pohang University of Science and Technoloagy, Pohang 37673, Korea. 5AdvancedMaterials Laboratory, National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, Japan. e-mail: hy.choi@snu.ac.krNature Communications |         (2023) 14:1801 11234567890():,;1234567890():,;http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37482-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37482-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37482-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37482-0&domain=pdfmailto:hy.choi@snu.ac.krlacking. Moreover, even in a broader sense, a time-reversal invariantspinful feature of the helical HOTI in a natural solid-state system hasnot been investigated25.In this work, we experimentally show that atomically thinTd-WTe2is indeed a time-reversal invariant HOTI hosting the helical spinfulhinge states. To investigate the spin orientation of the hinge states, wehave performed the spatially resolved polar magneto-optic Kerr-rota-tion measurements on WTe2-graphene heterostructure devices. Ourresults agree with the previous spin-resolved observation of WTe2,implying the possible gapless nature of the spin-polarized states26,27. Inour measurements, the bulk- (or gapped surface-) and hinge-originated spin polarization can be distinguished by the Fermi leveldependence of the Kerr rotation signals. Furthermore, we examine thetime-reversal invariance of the spinful hinge states by opening themass gap via external magnetic fields.ResultsMultilayer Td-WTe2 has a noncentrosymmetric orthorhombic struc-ture belonging to the SG 31 (Pmn21) space group with two perpendi-cular axes (a- and b-axis) and one mirror line along the b-axis (Fig. 1a).Together with the time-reversal symmetry, this spatial mirror sym-metry satisfies necessary prerequisites to support the topologicallynon-trivial spin-polarized helical hinges26,28. In our experiments, mul-tilayer WTe2 is placed onmonolayer graphene to detect the spinful 1Dhinge state by observing the spin polarization of electrons in grapheneinjected fromWTe2. The experiment schematic is illustrated in Fig. 1b.The bias voltage applied to the graphene channel forms a potentialgradient to the bottom of the multilayer WTe2, so the conductingelectrons of WTe2 are injected into the graphene. The spatial dis-tribution of the spin-polarized electrons is recorded by the Kerr rota-tion microscopy with a submicrometer-scale resolution. Because thespindiffusion length is sufficiently long in single-layer graphene29,30, weinfer that the spin-polarized electrons in graphene contain the neces-sary spin information of WTe2. Therefore, we interpret the differentialKerr rotation (ΔθK) in the scanning area, obtained by subtracting theKerr rotation (θK) at each spatial point with and without the bias vol-tage, as a manifestation of the electron spin polarization originatedfrom WTe2. Our device employs a tunable gate voltage (VG) thatenables us to distinguish the bulk and the hinge contribution byinspecting the Fermi-level-dependent ΔθK. An optical microscopyimage of a complete device is shown in Fig. 1c with the crystal a- and b-axis, where it is designed to perform the electrical and optical mea-surements along both axes. The crystal axes were verified by measur-ing the polarization-dependent absorption, as shown in Fig. 1d.We start by presenting the VG-dependent Kerr-rotation signals toinvestigate the spinful characteristics of the anisotropic WTe2 hingestates. Figure 2a shows the transfer curve between contact 1 and 3, i.e.,parallel to the a-axis referring to Fig. 1c. The observed twoa c b d W Te b c a b  1 3 2 4 WTe2 Graphene a b  10 μmθFig. 1 | Crystal structure ofmultilayer Td-WTe2 and experimental design. a TheTd structure ofmultilayerWTe2 is non-centrosymmetric with amirror planeMa (reddashed line). b Schematic experimental design for detecting the spin-polarizedelectronic states in WTe2. The electrical bias voltage makes electrons flow throughWTe2, while the spin polarization of the electrons is optically recorded as the Kerrrotation induced in the linearly polarized pump (980 nm, 1,415W/cm2). The pumplaser with a spot size of 1.5μm sweeps through a 6μm × 10μm region at graphenenear the edge of WTe2 by scanning mirrors to obtain the spatially resolved Kerrrotation data. cAnopticalmicroscopy image of the device is shown. ThemultilayerWTe2 (yellow) and monolayer graphene (black) are highlighted. Electrodes arelabeled as contact numbers 1, 2, 3, and 4. d A normalized polar plot of thepolarization-dependent absorption of the multilayer WTe2 is shown. The absorp-tion was measured at the center of the WTe2 flake in the device while varying thepolarization of 980 nm laser light. The anisotropy of the absorption indicates thatthe crystal axes are placed as shown in c (black arrows).Article https://doi.org/10.1038/s41467-023-37482-0Nature Communications |         (2023) 14:1801 2conductance deeps at VG = 0.5 and 0.95 V correspond to the chargeneutrality point of the graphene and themultilayerWTe2, respectively,as illustrated in the inset of Fig. 2a. Two-dimensional (2D) contourplots in Fig. 2b display the spatially resolved ΔθK near the WTe2 edgewith varying VG (VG = −1, 0, 1, 2 V) in the absence of the external mag-netic field. At VG = 0 and 1 V, a substantial amount of the spin-polarizedelectrons is concentrated near y = ±1.85μm, while ΔθK is evenly dis-tributed throughout ∣y∣≤ 1:85 μmatVG = -1 and 2 V. Considering theVG-tuned Fermi level and the spatial arrangement of ΔθK, the observedΔθK distributions at VG =0 and 1 V match the spin-polarized in-gapstates localized in thehinge,while thoseofVG = -1 and 2 V represent theelectrons from the spin-split bulk bands. The opposite sign ofΔθK seennear the two parallel hinges indicates the spinful and helical nature ofthe localized electron states. To elucidate the bulk- and hinge-originated ΔθK in detail, we show in Fig. 2c the line-cut plots of y-dependent ΔθK measured at different VG. In the bulk-insulating rangeof VG (Fig. 2c, top panel), |ΔθK | localized at y = 1.85μm decreasesmonotonically with increasing VG, and ΔθK changes the sign abruptlywhen VG reaches 1 V. This change is consistent with Fig. 2a, whereVG = 1 V is above the charge neutral point. On the other hand, whenWTe2 is degenerately doped, i.e., VG ≥ 2 V or VG ≤ -1 V (Fig. 2c, bottompanel), ΔθK evenly spreads across ∣y∣≤ 1:85 μm, and no sign change ofΔθK across the y position was observed. Note that the sign of ΔθKimplies the orientation of spin-polarized electrons, and |ΔθK | denotesthe concentration of the conducting electrons (or the density of stateat the Fermi level, equivalently) with the corresponding spin. Theseresults strongly suggest that although the spin configuration of helicalhinge states of the bottom surface of multilayer WTe2 resembles thatof the spin-momentum-locked helical edge states of the 2D quantumspin Hall insulator. Note that the multilayer WTe2 is not simply a stackof weak 2D topological insulator layers as proven previously23.As for the HOTI characteristics, we note that the band topology ofthe multilayer WTe2 should be protected by the time-reversal sym-metry. One method to examine such topological protection, which isassociated with the gapless band with degenerated Dirac points, is toperform the magnetic-field dependent θK measurements. Figure 3a–cshow the line-cut plots of the VG-dependent ΔθK under external mag-netic field Bz of 0.5, 1, and 2 T, applied perpendicular to the device xyplane. In Fig. 3a, where Bz is 0.5 T, we see that the ΔθK near the hingesvanishes as VG approaches the charge neutrality. With increasing Bz of1 T (Fig. 3b), the localized ΔθK survives only when VG is pushed furtherbelow (0 V) and above (1.5 V) the charge neutrality point. When Bz issufficiently large, Fig. 3c shows the vanishing ΔθK signals, which implythat no spin-polarized electrons are present; this can be readilyab-1 VWTe20 VWTe21 VWTe22 VWTe2WTe2 Graphene0 V  (0 meV)1 V  (10 meV)2 V  (20 meV)-1 V  (-10 meV)VG (ΔEF)cFig. 2 | Gate voltage dependence of the spatially resolved differential Kerrrotation. a The VG-dependent drain current parallel to the a-axis ofWTe2 is shown.Themeasurements were performed at 1.6 K. The longitudinal bias voltagewas 0.5 Vbetween contact 1 and 3 (parallel to the a-axis; see Fig. 1c for the contact number).Two charge neutral points were observed; one at VG = 0.5 V is for graphene (blackdashed line) and another at VG = 0.95 V is for WTe2 (black line). The illustration inthe inset shows the schematic band alignment of graphene and WTe2. Repre-sentativeVG and the correspondingFermi level change4EF aremarked as the blackdashed lines. b Spatially resolved contour plots of the VG-dependent ΔθK. Thecolors represent the spatially resolved ΔθK at VG = -1, 0, 1, 2 V. The bias voltage of0.5 V is applied between contact 1 and 3 to form a longitudinal electric field in +xdirection (parallel to the a-axis; see Fig. 1c for the contact number). The blackrectangle ineachplotdenotes the left endpartof theWTe2flake.c, Line-cut plots ofΔθK atx =0.75μmare shown. TheVG-dependentΔθK in the toppanel (0V ≤VG ≤ 1 V)shows the localized ΔθK near y = ± 1.85μm; these y positions correspond to theWTe2 hinge location (black dashed lines). The VG-dependentΔθK for VG = −1.5,−1, 2,3 V are displayed in the bottom panel.Article https://doi.org/10.1038/s41467-023-37482-0Nature Communications |         (2023) 14:1801 3understood as the mass gap opening due to the broken time-reversalsymmetry31,32. The schematic diagrams in Fig. 3d show how Bz isexpected to affect the gapless dispersion of the helical hinge states.Without Bz, the hinge states remain gapless because the degeneracy ofthe Dirac point is protected by time-reversal symmetry. In the case ofrelatively weak Bz (= 0.5, 1 T), the hinge opens a bandgap while pre-serving its spin texture (Fig. 3a, b). On the other hand, when a relativelystrong Bz of 2 T is applied (Fig. 3c), the trace of the hinge disappears.Such disappearance of ΔθK characteristics when Bz = 2 Tmay originatefrom either the hinge states being merged into the bulk while main-taining the HOTI phase (Fig. 3d)33 or WTe2 exhibits no HOTI phaseswith increasing external magnetic fields. A further theoretical investi-gation is necessary to elucidate the correlation between the spin tex-ture and the band configuration under strong Bz.Theremight exist alternative scenarioson the roleofBzother thanthe mass gap opening. First, one plausible explanation would be theformationofquantumHall states accompaniedby the chiral boundary.However, Bz used in our experiment is not strong enough to generatesuch an effect18,34, and the observed VG-dependent counter-propagating hinge modes are not consistent with the chiral statecharacteristics. Second, the effect of Bz on the graphene channel maycause a similarVGdependenceofΔθK, suchas opening a gapor causingtransverse spin (or valley) flow in graphene. However, existing studiesshow that Bz of 10 T is the lower boundary to observe such effects,which is far larger compared to our Bz35–37. Lastly, the broken time-reversal symmetry can be associated with the spatial split of the hingemodes rather than the bandgap opening32. In our experiment regime,the applied Bz makes the hinge a boundary between one parallel to Bzand another perpendicular to Bz. Thus, considering the non-zeromassand Zeeman contribution to the position away from the hinge, suchspatially shifted hinge modes cannot occur between the two surfacestates.The transverse spin accumulation originated from theWTe2 bulk,i.e., spin Hall effect (SHE), might be an alternative to explain theobserved ΔθK. To further substantiate that observedΔθK features arisefrom the spinful hinge state exclusively, we investigated the spatiallyresolved ΔθK using a device with a modified structure (device #4).Figure 4a shows the corresponding optical microscopy image. Thegraphene layer below themultilayer WTe2 has a 1.5μmwide gap alongthe a-axis of the multilayer WTe2 (see Supplementary Note 1-3 fordetails). If ΔθK originates from the hinge states, the localized ΔθKshould arise only near the WTe2 hinge (Fig. 4b). On the other hand, ifthe observed ΔθK originates from the bulk spin transport in WTe2, thespin-polarized electrons injected into graphene are expected to bespread out to the left as well as to the right of the graphene area in atransverse direction to the applied electric field (Fig. 4c). Therefore,the presence of a gap in graphenewould collect the accumulated spin-polarized electrons at the edge of graphene on both sides of the gap(Fig. 4c). To check the above idea, we have investigated the magneto-optic Kerr effect on device #4. The results are shown in Fig. 4d, e. Herewe measured the spatially resolved ΔθK at different VG with and with-out an externalmagneticfield (Bz = 1 T) (see SupplementaryNote 4 andFigs. S15, 16 for spatially resolved ΔθK with Bz). We first note that noaccumulation of the spin-polarized electronswas seenon either side ofthe graphene gap, regardless of VG. Secondly, with varying VG (seeSupplementary Note 1-2 for the relationship between VG and ΔEF),Fig. 4d, e shows that ΔθK appears only in line with the WTe2 hinges.We also observed a clear sign flip of ΔθK when EF is swept across the0 V1 V1.5 VVGBz = 2 TBz = 1 TBz = 0.5 TBz = 0 TcbadFig. 3 | Gap opening of the multilayer WTe2 due to broken time-reversal sym-metry. a–c The line-cut plots show ΔθK at x =0.75 μm with varying VG underBz =0.5 T (a), 1 T (b), and 2 T (c). ΔθK is featureless only at VG = 1 V when Bz =0.5 T,while it shows no variation when the applied VG is 0.8 V ≤VG ≤ 1.2 V under Bz = 1 T.Note that no localized ΔθK behavior is seen at any VG when Bz = 2 T. Dashed lines ina–c at y = ±1.85μm indicate the y position of the WTe2 hinges in the real space.d, Schematic band structures representing the effect of Bz on the spin-polarizedhinge states (black lines) and spin-split bulk bands (colored lines). Because Bzbreaks the time-reversal symmetry, Dirac fermions at the topological hinge statesgain an effective mass. This opens a finite energy gap, which is proportional to themagnitudeofBz. The gap opening appears as a flatΔθK along y since the Fermi levelfalls within the gap. The dashed lines in the diagram indicate the Fermi levels whenVG is 0, 1, and 1.5 V. For the case when Bz = 2 T (d), the schematic represents onepossibility that the hinge states are merged into the bulk band due to the inducedgap in the hinge states.Article https://doi.org/10.1038/s41467-023-37482-0Nature Communications |         (2023) 14:1801 4Dirac point of the hinge states. Third, ΔθK under the magnetic field(Figs. S15, 16) shows the gap opening of the hinge states. Under theexternal magnetic field Bz of 1 T, the localized ΔθK at the y-position ofthe hinges disappears when the Fermi level is close to the Dirac point(i.e., VG near 0.88 V in the case of device #4), demonstrating the lifteddegeneracy of hinge eigenstates due to the broken time-reversalsymmetry. To summarize, theVG- andBz-dependentΔθKdistribution indevice #4 is essentially identical to the devices without the graphenegap (see Fig. 2 and Figs. S6–11). Thesedata provide additional evidencethat SHE is not likely the origin of our observation.In conclusion, we experimentally have shown that the multi-layer Td-WTe2 is a time-reversal invariant helical HOTI possessingthe spinful hinge states. The spin polarization of electrons origi-nating from the 1D hinge state of the multilayer WTe2 was investi-gated by the spatially resolved magneto-optical Kerr rotationmeasurement in the WTe2-graphene heterostructure device. TheVG- and Bz-dependent data provide strong evidence that the helicalspin-polarized states are within the bulk bandgap while they arelocalized at the geometric hinge of the multilayer WTe2, whoseenergy degeneracy is protected by the time-reversal symmetry.Because the topologically protected spinful mode is highly confinedin the 1D channel, the hinge state of the HOTI may open up a newarena to study the strong correlation and topology in other higher-order topological materials.MethodsThe detailed information about the device fabrication, experimentalsetup and full dataset with further discussion are available in Supple-mentary Information.Data availabilityThe data that support the findings of this study are available from thecorresponding author on reasonable request.References1. Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L. Quantized electricmultipole insulators. Science 357, 61–66 (2017).2. Schindler, F. et al. Higher-order topological insulators. Sci. Adv. 4,eaat0346 (2018).3. Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L. Electric multipolemoments, topological multipole moment pumping, and chiralhinge states in crystalline insulators. Phys. Rev. B 96, 245115 (2017).4. Wang, Z., Wieder, B. J., Li, J., Yan, B. & Bernevig, B. A. Higher-ordertopology, monopole nodal lines, and the origin of large Fermi arcsin transitionmetal dichalcogenides XTe2 (X=Mo,W). Phys. Rev. Lett.123, 186401 (2019).5. Armitage, N., Mele, E. & Vishwanath, A. Weyl and Dirac semimetalsin three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).6. Ezawa, M. Second-order topological insulators and loop-nodalsemimetals in Transition Metal Dichalcogenides XTe2 (X= Mo, W).Sci. Rep. 9, 5286 (2019).7. Schindler, F. et al. Higher-order topology in bismuth. Nat. Phys. 14,918–924 (2018).8. Noguchi, R. et al. Evidence for a higher-order topological insulatorin a three-dimensional material built from van derWaals stacking ofbismuth-halide chains. Nat. Mater. 20, 473–479 (2021).9. Tang, F., Po, H. C., Vishwanath, A. & Wan, X. Efficient topologicalmaterials discovery using symmetry indicators. Nat. Phys. 15,470–476 (2019).0 V 1 VaMultilayer WTe2GrapheneExGrapheneExMultilayer WTe2baGrapheneGrapheneWTe210 μμmdbceFig. 4 | Spatially resolved differential Kerr rotation on a device with a spatialgap in graphene. a An optical microscopy image is shown. Two monolayer gra-phene flakes are separated by a 1.5μm gap. This device scheme is almost identicalto the other devices, except the presence of a gap in graphene. The graphene layerfor the electron transport measurement is located below WTe2. b, c Schematicdiagrams of the expected ΔθK when the spin-polarized electrons are injected ingraphene from the hinges (b) and when they originate from the bulk (c). Dashedrectangles indicate the window of spatially resolved measurement, and blackarrows indicate electron transport. d, e Contour plots ofΔθK observed in device #4when VG = 0 (d), 1 V (e) are shown. The VG-dependent transport measurements areshown in Fig. S4. The distribution of ΔθK is as expected in b, meaning there was nospin accumulation at the edge of graphene, and the spin-polarized electrons areoriginated from the hinges of multilayerWTe2. Dashed lines mark the edge of eachgraphene layer, and the black rectangles indicate the location of the multilayerWTe2 flake.Article https://doi.org/10.1038/s41467-023-37482-0Nature Communications |         (2023) 14:1801 510. Park, M. J., Kim, Y., Cho, G. Y. & Lee, S. Higher-order topologicalinsulator in twisted bilayer graphene. Phy. Rev. Lett. 123,216803 (2019).11. Ahn, J., Park, S. & Yang, B.-J. Failure of Nielsen-Ninomiya theoremand fragile topology in two-dimensional systems with space-timeinversion symmetry: Application to twisted bilayer graphene atmagic angle. Phys. Rev. X 9, 021013 (2019).12. Liu, B. et al. Higher-order band topology in twisted moiré super-lattice. Phys. Rev. Lett. 126, 066401 (2021).13. Kempkes, S. et al. Robust zero-energy modes in an electronichigher-order topological insulator. Nat. Mater. 18,1292–1297 (2019).14. Ezawa, M. Higher-order topological insulators and semimetals onthe breathing kagome and pyrochlore lattices. Phys. Rev. Lett. 120,026801 (2018).15. Sun, B. et al. Evidence for equilibrium exciton condensation inmonolayer WTe2. Nat. Phys. 18, 94–99 (2022).16. Wang, P. et al. One-dimensional Luttinger liquids in a two-dimensional moiré lattice. Nature 605, 57–62 (2022).17. Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527,495–498 (2015).18. Li, P. et al. Evidence for topological type-II Weyl semimetal WTe2.Nat. Commun. 8, 2150 (2017).19. Deng, K. et al. Experimental observation of topological Fermiarcs in type-II Weyl semimetal MoTe2. Nat. Phys. 12,1105–1110 (2016).20. Wang, C. et al. Observation of Fermi arc and its connection withbulk states in the candidate type-IIWeyl semimetalWTe2.Phys. Rev.B 94, 241119(R) (2016).21. Tang, S. et al. Quantum spin Hall state in monolayer 1T’-WTe2. Nat.Phys. 13, 683–687 (2017).22. Fei, Z. et al. Edge conduction in monolayer WTe2. Nat. Phys. 13,677–682 (2017).23. Choi, Y.-B. et al. Evidence of higher-order topology in multilayerWTe2 from Josephson coupling through anisotropic hinge states.Nat. Mater. 19, 974–979 (2020).24. Kononov, A. et al. One-dimensional edge transport in few-layerWTe2. Nano Lett. 20, 4228–4233 (2020).25. Xie, B. et al. Higher-order band topology. Nat. Rev. Phys. 3,520–532 (2021).26. Das, P. K. et al. Layer-dependent quantum cooperation of electronand hole states in the anomalous semimetalWTe2.Nat. Commun. 7,10847 (2016).27. Fanciulli, M. et al. Spin, time, and angle resolved photoemissionspectroscopy on WTe2. Phys. Rev. Res. 2, 013261 (2020).28. Das, P. et al. Electronic properties of candidate type-II Weyl semi-metal WTe2. A review perspective. Electron. Struct. 1,014003 (2019).29. Han,W. & Kawakami, R. K. Spin relaxation in single-layer and bilayergraphene. Phys. Rev. Lett. 107, 047207 (2011).30. Drögeler, M. et al. Spin lifetimes exceeding 12 ns in graphenenonlocal spin valve devices. Nano Lett. 16, 3533–3539 (2016).31. Rosenberg, G. & Franz,M. Surfacemagnetic ordering in topologicalinsulators with bulk magnetic dopants. Phys. Rev. B 85,195119 (2012).32. Queiroz, R. & Stern, A. Splitting the hinge mode of higher-ordertopological insulators. Phys. Rev. Lett. 123, 036802 (2019).33. Otaki, Y. & Fukui, T. Higher-order topological insulators in a mag-netic field. Phys. Rev. B 100, 245108 (2019).34. Wang, P. et al. Landauquantization andhighlymobile fermions in aninsulator. Nature 589, 225–229 (2021).35. Neto, A. C., Guinea, F., Peres, N. M., Novoselov, K. S. & Geim, A. K.The electronic properties of graphene. Rev. Mod. Phys. 81,109 (2009).36. Sarma, S. D., Adam, S., Hwang, E. & Rossi, E. Electronic transport intwo-dimensional graphene. Rev. Mod. Phys. 83, 407 (2011).37. Settnes, M., Garcia, J. H. & Roche, S. Valley-polarized quantumtransport generated by gauge fields in graphene. 2D Mater. 4,031006 (2017).AcknowledgementsJ.L., J.K., J.P., and H.C. were supported by the National Research Foun-dation of Korea (NRF) through the government of Korea (Grant No. NRF-2021R1A2C3005905,NRF-2020M3F3A2A03082472),CreativematerialsDiscovery program (Grant No. 2017M3D1A1040828), Scalable QuantumComputer Technology Platform Center (Grant No. 2019R1A5A1027055),the Ministry of Education through the core center program(2021R1A6C101B418), and the Institute for Basic Science (IBS), Korea,under Project Code IBS-R014-G1-2018-A1. SCandM.-H.Jwere supportedby the IBS, Korea, under Project Code IBS-R014-A1. Part of this study hasbeen performed using facilities at IBS Center for Correlated ElectronSystems, Seoul National University.Author contributionsJ.L., J.K., E.L. fabricated samples. J.L., J.P., S.C. performed the devicecharacteristics examination. K.W. and T.T. provided high-quality hBNcrystal. J.L., M.-H.J., and H.C. performed data analysis and discussed theresults. H.C. supervised the project. J.L. and H.C. wrote the manuscriptwith input from all co-authors.Competing interestsCorrespondence and requests formaterials shouldbe addressed toH.C.(hy.choi@snu.ac.kr). Authors declare no competing interests. Reprintsand permissions information is available at www.nature.com/reprints.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-37482-0.Correspondence and requests for materials should be addressed toHyunyong Choi.Peer review information Nature Communications thanks the anon-ymous reviewer(s) for their contribution to the peer review of thiswork. Peer reviewer reports are available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons license, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons license and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-37482-0Nature Communications |         (2023) 14:1801 6http://www.nature.com/reprintshttps://doi.org/10.1038/s41467-023-37482-0http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Spinful hinge states in the higher-order topological insulators WTe2 Results Methods Data availability References Acknowledgements Author contributions Competing interests Additional information