Introduction

Recently, a new class of topological phase, called a higher-order topological insulator (HOTI), is proposed based on the generalized bulk-boundary correspondence, covering d−2 or lower-dimensional topological boundaries in d-dimensional systems1,2,3. For instance, time-reversal invariant three-dimensional (3D) HOTIs exhibit gapless hinge states, where the gapped surfaces are facing each other with a reversed sign of the mass. Such a phenomenon can be understood based on the fact that the gapped surface states host a doubly inverted electronic band and the strong spin-orbit coupling (SOC)2,4,5,6. With these physical grounds, the band structure and the corresponding topological features of HOTIs have been predicted by well-established methods such as a multi-orbital tight-binding model, first principle calculation, and Wilson loop calculation1,2,3,4,5,6. To date, there exist only a few condensed matter systems predicted to be HOTIs, such as bismuth7,8, topological crystalline insulator SnTe2,4,9, twisted bilayer graphene10,11,12, and some artificial lattices13,14.

Among such candidates, WTe2 has recently attracted much interest in investigating the electronic correlations as well as exploring the topologically protected quantum phenomena15,16. With an orthorhombic 3D structure, it was first known as a type-II Weyl semimetal with electron and hole pockets around the Weyl points5,17,18; resolving the Weyl points, however, remains challenging because angle-resolved photoemission spectroscopy (ARPES) cannot provide sufficient momentum resolution to resolve the small separation of Weyl points of WTe219,20. In a monolayer limit, the thickness-dependent studies on the crystal symmetry and electronic band structure have revealed the quantum spin Hall insulating phase for 1 T′-WTe2 crystals21,22. After recent proposals on the higher-order topology, the large arc-like surface states of the bulk WTe2, which were initially considered topologically trivial, started to be understood as gapped fourfold Dirac surface states4. Spatially resolved measurements using a Josephson junction were then used to identify the hinge states as a clue for the higher-order topology7, and subsequent experiments have reported anisotropic confinement of 1D conducting hinge channels in few-layer Td-WTe223,24. However, experimental evidence for the symmetry-protected topological nature of the observed 1D hinge state is still lacking. Moreover, even in a broader sense, a time-reversal invariant spinful feature of the helical HOTI in a natural solid-state system has not been investigated25.

In this work, we experimentally show that atomically thin Td-WTe2 is indeed a time-reversal invariant HOTI hosting the helical spinful hinge states. To investigate the spin orientation of the hinge states, we have performed the spatially resolved polar magneto-optic Kerr-rotation measurements on WTe2-graphene heterostructure devices. Our results agree with the previous spin-resolved observation of WTe2, implying the possible gapless nature of the spin-polarized states26,27. In our measurements, the bulk- (or gapped surface-) and hinge-originated spin polarization can be distinguished by the Fermi level dependence of the Kerr rotation signals. Furthermore, we examine the time-reversal invariance of the spinful hinge states by opening the mass gap via external magnetic fields.

Results

Multilayer Td-WTe2 has a noncentrosymmetric orthorhombic structure belonging to the SG 31 (Pmn21) space group with two perpendicular axes (a- and b-axis) and one mirror line along the b-axis (Fig. 1a). Together with the time-reversal symmetry, this spatial mirror symmetry satisfies necessary prerequisites to support the topologically non-trivial spin-polarized helical hinges26,28. In our experiments, multilayer WTe2 is placed on monolayer graphene to detect the spinful 1D hinge state by observing the spin polarization of electrons in graphene injected from WTe2. The experiment schematic is illustrated in Fig. 1b. The bias voltage applied to the graphene channel forms a potential gradient to the bottom of the multilayer WTe2, so the conducting electrons of WTe2 are injected into the graphene. The spatial distribution of the spin-polarized electrons is recorded by the Kerr rotation microscopy with a submicrometer-scale resolution. Because the spin diffusion length is sufficiently long in single-layer graphene29,30, we infer that the spin-polarized electrons in graphene contain the necessary spin information of WTe2. Therefore, we interpret the differential Kerr rotation (ΔθK) in the scanning area, obtained by subtracting the Kerr rotation (θK) at each spatial point with and without the bias voltage, as a manifestation of the electron spin polarization originated from WTe2. Our device employs a tunable gate voltage (VG) that enables us to distinguish the bulk and the hinge contribution by inspecting the Fermi-level-dependent ΔθK. An optical microscopy image 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 measurements along both axes. The crystal axes were verified by measuring the polarization-dependent absorption, as shown in Fig. 1d.

Fig. 1: Crystal structure of multilayer Td-WTe2 and experimental design.
figure 1

a The Td structure of multilayer WTe2 is non-centrosymmetric with a mirror plane Ma (red dashed line). b Schematic experimental design for detecting the spin-polarized electronic states in WTe2. The electrical bias voltage makes electrons flow through WTe2, while the spin polarization of the electrons is optically recorded as the Kerr rotation induced in the linearly polarized pump (980 nm, 1,415 W/cm2). The pump laser with a spot size of 1.5 μm sweeps through a 6 μm × 10 μm region at graphene near the edge of WTe2 by scanning mirrors to obtain the spatially resolved Kerr rotation data. c An optical microscopy image of the device is shown. The multilayer WTe2 (yellow) and monolayer graphene (black) are highlighted. Electrodes are labeled as contact numbers 1, 2, 3, and 4. d A normalized polar plot of the polarization-dependent absorption of the multilayer WTe2 is shown. The absorption was measured at the center of the WTe2 flake in the device while varying the polarization of 980 nm laser light. The anisotropy of the absorption indicates that the crystal axes are placed as shown in c (black arrows).

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We start by presenting the VG-dependent Kerr-rotation signals to investigate the spinful characteristics of the anisotropic WTe2 hinge states. Figure 2a shows the transfer curve between contact 1 and 3, i.e., parallel to the a-axis referring to Fig. 1c. The observed two conductance deeps at VG = 0.5 and 0.95 V correspond to the charge neutrality point of the graphene and the multilayer WTe2, respectively, as illustrated in the inset of Fig. 2a. Two-dimensional (2D) contour plots in Fig. 2b display the spatially resolved ΔθK near the WTe2 edge with varying VG (VG = −1, 0, 1, 2 V) in the absence of the external magnetic field. At VG = 0 and 1 V, a substantial amount of the spin-polarized electrons is concentrated near y = ±1.85 μm, while ΔθK is evenly distributed throughout \(|y|\le 1.85\) μm at VG = -1 and 2 V. Considering the VG-tuned Fermi level and the spatial arrangement of ΔθK, the observed ΔθK distributions at VG = 0 and 1 V match the spin-polarized in-gap states localized in the hinge, while those of VG = -1 and 2 V represent the electrons from the spin-split bulk bands. The opposite sign of ΔθK seen near the two parallel hinges indicates the spinful and helical nature of the 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 range of VG (Fig. 2c, top panel), |ΔθK | localized at y = 1.85 μm decreases monotonically with increasing VG, and ΔθK changes the sign abruptly when VG reaches 1 V. This change is consistent with Fig. 2a, where VG = 1 V is above the charge neutral point. On the other hand, when WTe2 is degenerately doped, i.e., VG ≥ 2 V or VG ≤ -1 V (Fig. 2c, bottom panel), ΔθK evenly spreads across \(|y|\le 1.85\) μm, and no sign change of ΔθK across the y position was observed. Note that the sign of ΔθK implies the orientation of spin-polarized electrons, and | ΔθK | denotes the concentration of the conducting electrons (or the density of state at the Fermi level, equivalently) with the corresponding spin. These results strongly suggest that although the spin configuration of helical hinge states of the bottom surface of multilayer WTe2 resembles that of the spin-momentum-locked helical edge states of the 2D quantum spin Hall insulator. Note that the multilayer WTe2 is not simply a stack of weak 2D topological insulator layers as proven previously23.

Fig. 2: Gate voltage dependence of the spatially resolved differential Kerr rotation.
figure 2

a The VG-dependent drain current parallel to the a-axis of WTe2 is shown. The measurements were performed at 1.6 K. The longitudinal bias voltage was 0.5 V between 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 (black dashed line) and another at VG = 0.95 V is for WTe2 (black line). The illustration in the inset shows the schematic band alignment of graphene and WTe2. Representative VG and the corresponding Fermi level change \(\triangle {E}_{F}\) are marked as the black dashed lines. b Spatially resolved contour plots of the VG-dependent ΔθK. The colors represent the spatially resolved ΔθK at VG = -1, 0, 1, 2 V. The bias voltage of 0.5 V is applied between contact 1 and 3 to form a longitudinal electric field in +x direction (parallel to the a-axis; see Fig. 1c for the contact number). The black rectangle in each plot denotes the left end part of the WTe2 flake. c, Line-cut plots of ΔθK at x = 0.75 μm are shown. The VG-dependent ΔθK in the top panel (0 V ≤ VG ≤ 1 V) shows the localized ΔθK near y = \(\pm\)1.85 μm; these y positions correspond to the WTe2 hinge location (black dashed lines). The VG-dependent ΔθK for VG = −1.5, −1, 2, 3 V are displayed in the bottom panel.

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As for the HOTI characteristics, we note that the band topology of the multilayer WTe2 should be protected by the time-reversal symmetry. One method to examine such topological protection, which is associated with the gapless band with degenerated Dirac points, is to perform the magnetic-field dependent θK measurements. Figure 3a–c show the line-cut plots of the VG-dependent ΔθK under external magnetic field Bz of 0.5, 1, and 2 T, applied perpendicular to the device xy plane. In Fig. 3a, where Bz is 0.5 T, we see that the ΔθK near the hinges vanishes as VG approaches the charge neutrality. With increasing Bz of 1 T (Fig. 3b), the localized ΔθK survives only when VG is pushed further below (0 V) and above (1.5 V) the charge neutrality point. When Bz is sufficiently large, Fig. 3c shows the vanishing ΔθK signals, which imply that no spin-polarized electrons are present; this can be readily understood as the mass gap opening due to the broken time-reversal symmetry31,32. The schematic diagrams in Fig. 3d show how Bz is expected to affect the gapless dispersion of the helical hinge states. Without Bz, the hinge states remain gapless because the degeneracy of the Dirac point is protected by time-reversal symmetry. In the case of relatively weak Bz (= 0.5, 1 T), the hinge opens a bandgap while preserving its spin texture (Fig. 3a, b). On the other hand, when a relatively strong Bz of 2 T is applied (Fig. 3c), the trace of the hinge disappears. Such disappearance of ΔθK characteristics when Bz = 2 T may originate from either the hinge states being merged into the bulk while maintaining the HOTI phase (Fig. 3d)33 or WTe2 exhibits no HOTI phases with increasing external magnetic fields. A further theoretical investigation is necessary to elucidate the correlation between the spin texture and the band configuration under strong Bz.

Fig. 3: Gap opening of the multilayer WTe2 due to broken time-reversal symmetry.
figure 3

a–c The line-cut plots show ΔθK at x = 0.75 μm with varying VG under Bz = 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 in a–c at y = ±1.85 μm indicate the y position of the WTe2 hinges in the real space. d, Schematic band structures representing the effect of Bz on the spin-polarized hinge states (black lines) and spin-split bulk bands (colored lines). Because Bz breaks the time-reversal symmetry, Dirac fermions at the topological hinge states gain an effective mass. This opens a finite energy gap, which is proportional to the magnitude of Bz. The gap opening appears as a flat ΔθK along y since the Fermi level falls within the gap. The dashed lines in the diagram indicate the Fermi levels when VG is 0, 1, and 1.5 V. For the case when Bz = 2 T (d), the schematic represents one possibility that the hinge states are merged into the bulk band due to the induced gap in the hinge states.

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There might exist alternative scenarios on the role of Bz other than the mass gap opening. First, one plausible explanation would be the formation of quantum Hall states accompanied by the chiral boundary. However, Bz used in our experiment is not strong enough to generate such an effect18,34, and the observed VG-dependent counterpropagating hinge modes are not consistent with the chiral state characteristics. Second, the effect of Bz on the graphene channel may cause a similar VG dependence of ΔθK, such as opening a gap or causing transverse spin (or valley) flow in graphene. However, existing studies show that Bz of 10 T is the lower boundary to observe such effects, which is far larger compared to our Bz35,36,37. Lastly, the broken time-reversal symmetry can be associated with the spatial split of the hinge modes rather than the bandgap opening32. In our experiment regime, the applied Bz makes the hinge a boundary between one parallel to Bz and another perpendicular to Bz. Thus, considering the non-zero mass and Zeeman contribution to the position away from the hinge, such spatially shifted hinge modes cannot occur between the two surface states.

The transverse spin accumulation originated from the WTe2 bulk, i.e., spin Hall effect (SHE), might be an alternative to explain the observed ΔθK. To further substantiate that observed ΔθK features arise from the spinful hinge state exclusively, we investigated the spatially resolved ΔθK using a device with a modified structure (device #4). Figure 4a shows the corresponding optical microscopy image. The graphene layer below the multilayer WTe2 has a 1.5 μm wide gap along the a-axis of the multilayer WTe2 (see Supplementary Note 1-3 for details). If ΔθK originates from the hinge states, the localized ΔθK should arise only near the WTe2 hinge (Fig. 4b). On the other hand, if the observed ΔθK originates from the bulk spin transport in WTe2, the spin-polarized electrons injected into graphene are expected to be spread out to the left as well as to the right of the graphene area in a transverse direction to the applied electric field (Fig. 4c). Therefore, the presence of a gap in graphene would 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. Here we measured the spatially resolved ΔθK at different VG with and without an external magnetic field (Bz = 1 T) (see Supplementary Note 4 and Figs. S15, 16 for spatially resolved ΔθK with Bz). We first note that no accumulation of the spin-polarized electrons was seen on either side of the graphene gap, regardless of VG. Secondly, with varying VG (see Supplementary 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 the Dirac point of the hinge states. Third, ΔθK under the magnetic field (Figs. S15, 16) shows the gap opening of the hinge states. Under the external magnetic field Bz of 1 T, the localized ΔθK at the y-position of the 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 lifted degeneracy of hinge eigenstates due to the broken time-reversal symmetry. To summarize, the VG- and Bz-dependent ΔθK distribution in device #4 is essentially identical to the devices without the graphene gap (see Fig. 2 and Figs. S6–11). These data provide additional evidence that SHE is not likely the origin of our observation.

Fig. 4: Spatially resolved differential Kerr rotation on a device with a spatial gap in graphene.
figure 4

a An optical microscopy image is shown. Two monolayer graphene flakes are separated by a 1.5 μm gap. This device scheme is almost identical to the other devices, except the presence of a gap in graphene. The graphene layer for the electron transport measurement is located below WTe2. b, c Schematic diagrams of the expected ΔθK when the spin-polarized electrons are injected in graphene from the hinges (b) and when they originate from the bulk (c). Dashed rectangles indicate the window of spatially resolved measurement, and black arrows indicate electron transport. d, e Contour plots of ΔθK observed in device #4 when VG = 0 (d), 1 V (e) are shown. The VG-dependent transport measurements are shown in Fig. S4. The distribution of ΔθK is as expected in b, meaning there was no spin accumulation at the edge of graphene, and the spin-polarized electrons are originated from the hinges of multilayer WTe2. Dashed lines mark the edge of each graphene layer, and the black rectangles indicate the location of the multilayer WTe2 flake.

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In conclusion, we experimentally have shown that the multilayer Td-WTe2 is a time-reversal invariant helical HOTI possessing the spinful hinge states. The spin polarization of electrons originating from the 1D hinge state of the multilayer WTe2 was investigated by the spatially resolved magneto-optical Kerr rotation measurement in the WTe2-graphene heterostructure device. The VG- and Bz-dependent data provide strong evidence that the helical spin-polarized states are within the bulk bandgap while they are localized at the geometric hinge of the multilayer WTe2, whose energy degeneracy is protected by the time-reversal symmetry. Because the topologically protected spinful mode is highly confined in the 1D channel, the hinge state of the HOTI may open up a new arena to study the strong correlation and topology in other higher-order topological materials.

Methods

The detailed information about the device fabrication, experimental setup and full dataset with further discussion are available in Supplementary Information.