## Introduction

Two of the most prominent examples of topological insulators in three dimensions are the STIs and WTIs1,2,3,4. Among them, STIs have been widely studied in the past decades both in theories and experiments. They host 2D spin-momentum locked Dirac cones on all surfaces, in which the perfect backscattering is prohibited, while general scattering off 180° still exists5,6. On the other hand, WTIs host surface states only on particular side surfaces. They were thought to be weak (or not robust) since two adjacent layers in even-layer WTIs may couple with each other, leading to a topologically trivial phase. However, it was later found that the surface states of WTIs are actually robust owing to the delocalization of surface electrons7. The weak interlayer coupling in WTIs generally yields a topological surface state with quasi-1D dispersion; this could prohibit even general scattering off 180° to establish dissipationless spin current, which cannot be realized in STIs. Even with such advantages, theoretical proposals of WTIs are rare8,9,10,11,12,13,14,15, and experimental investigations of the topological side surfaces are very challenging; layered WTI materials are inherently cleavable only on the top surface, and thus there is difficulty in preparing a large and uniform side surface for observation. One exception is Bi4I4, where top and side planes are both naturally cleavable14. However, such crystal structures may pose obstacles in preparing a single side surface with the topological feature for applications.

The material which has been best studied from the early stage of exploring a WTI among scarce candidates is ZrTe5, which consists of a van der Waals layered structure; notably, this compound exhibits very high mobility16, thus it has been regarded as a promising platform for devices. Nonetheless, the bulk topology of ZrTe5 has not been experimentally identified to date because the observation of band structure on the side surface has not been successful so far. All the previous surface-sensitive studies were carried out on the top surface17,18,19,20, which only confirms the lack of surface states; whether or not this material is topological, therefore, has not been determined beyond speculation. Another difficulty for this study is that ZrTe5 is in proximity to multiple topological phases, whereas this feature could bring an attractive functionality of controlling bulk topology by fine-tuning a physical parameter10.

## Results

ZrTe5 has a quasi-1D crystal structure. The lattice constant a along the chain direction is ~4.0 Å. Except for the chain direction, the lattice constants for the other two directions are both large, as shown in Fig. 1a: The layer distance along the b direction is ~7.3 Å, and it is ~6.9 Å along the c direction21. As a result of the large layer distances, in principle, it should be possible to cleave both surfaces. Along the b direction, the layers are stacked by van der Waals forces, and a clean surface can be easily obtained by cleavage. Instead, Te–Te bonding exists between adjacent layers along the c direction, causing much more difficulty in cleaving the a-b surface. All the surface-sensitive studies reported so far have been carried out on the a-c surface, which is easy to cleave17,18,19,20,22,23.

### Band structure of the top surface

We observed a tiny hole-type Fermi surface on the a-c surface, as shown in Fig. 1c. The band along ka (Fig. 1d–e) shows a cone-shape dispersion, similar to that in the previous reports except for the difference on Fermi level (EF)17,19,22. We notice a splitting of the band in Fig. 1d at approximately −0.1 eV, with one branch going up and the other going down, as indicated by the dashed yellows lines in Fig. 1d. Such a feature most likely originates from a kz average effect, and it is indeed reproduced by the first-principles slab calculations plotted in Fig. 1g along $$\overline{{{\Gamma }}}\overline{X}$$, where the series of bands come from different kz (kb); this further indicates that the slab calculations are reliable to explain the ARPES data. The measurements with p-polarized light (Fig. 1e) reveal only the cone-shaped branch going up, which is thus suitable for the study of the bulk band gap.

To have a better visualization of the band structure over the whole energy range, the data in Fig. 1e is normalized by its density of states (integration of EDCs over ka), as plotted in Fig. 1f (More details can be found in Supplementary Fig. 2). A small band gap with the size of about 32 meV is observed in the data at 200 K. Our experiments over a temperature cycle of 20 K-200 K-20 K (Fig. 1h) have confirmed almost no change in the valence band at different temperatures; this result clearly differs from the previous reports demonstrating a large energy shift in the band with temperature17,19,20,24. On the other hand, we have confirmed a band shift in an ARPES system with a worse vacuum level (~7 × 10−11 Torr v. s. ~1 × 10−11 Torr for Fig. 1h); the band shift actually occurs even for the sample kept at the same temperature (See Supplementary Fig. 1 for more details). These results lead us to conclude that ZrTe5 should be in a stable phase, which is not a strong topological insulator since surface states are absent in the data, but either a normal insulator or a WTI. However, with the data merely from the top surface, it is impossible to distinguish the two phases experimentally.

### Band structure of the side surface

To identify the topological phase of ZrTe5, the observation of the side a-b surface is essential. We successfully cleaved the side surface with a top post and silver epoxy. The problem, however, is that the cleaved areas are very small and inhomogeneous. With a synchrotron-based nano-ARPES (spot size < 1 μm), we took real space maps of photoemission intensity on several samples, and found that the typical dimension of cleaved areas is around or smaller than 50 μm (Fig. 2a). Several positions of one cleaved area are measured and they all give the same band structure, as shown in Supplementary Fig. 3, indicating that the cleaved area with high photoelectron intensities is homogeneous. The selective measurements only of such a small surface area are beyond the capacity of most ARPES systems. Nevertheless, our laser-based micro-ARPES (spot size 50 μm) resolved this difficulty and clearly revealed the band structure on the side a-b surface. A quasi-1D Fermi surface (S1) is exhibited in Fig. 2c by plotting ARPES intensities about the Fermi level. The band S1 shows a hole-like dispersion along ka (Fig. 2d–e), which has a Fermi vector kF much larger than that of the band B observed near $$\overline{{{\Gamma }}}$$ on the a-c surface (Fig. 1f). The band S1 is, thus, distinct from the bulk band B located at the center of the BZ ($$\overline{{{\Gamma }}}$$). The bulk band B cannot be identified in ARPES data on the side a-b surface likely due to a much weaker intensity than that of the surface states. The synchrotron-based nano-ARPES measurements for Cut1 with a different photon energy (Fig. 2b) show similar result to the data obtained by laser-based ARPES: Only the band S1 was clearly observed, and its dispersion is almost identical to that of the laser-based ARPES data. This coincidence supports that the band S1 has a surface origin.

The spin polarization is expected for the topological surface state. To confirm this, we have used spin-resolved ARPES. In Fig. 2f, we plot EDCs (EDC 1 and EDC 2; see Fig. 2d) which are spin-resolved in the b-direction; a clear spin polarization is detected (Fig. 2g). In contrast, the spin polarization is almost zero along the a and c directions (Fig. 2h–i). Therefore, the band S1 is spin-polarized along the b-direction with spin-momentum locking, forming a typical spin-texture of WTIs with quasi-1D dispersion (see Fig. 2j).

We also carried out the first-principles slab calculations on the side a-b surface to fully understand the ARPES data. The calculated Fermi surface (Fig. 2j) displays four sheets: two open sheets (red color) and two closed sheets (black color). By comparing these calculations with our ARPES data (Fig. 2c), we ascribe the inner open sheet to the band S1, and the closed sheets to the bulk band B. The outer open sheet (S2) was not observed with either laser-based ARPES or synchrotron-based ARPES most likely due to a small photoemission cross section. In the slab calculations, the bands S1 and S2 are localized at the surface and have spin polarization indicated by the black arrows in Fig. 2j; the spin orientation of the band S1 is consistent with our data of spin-resolved ARPES (Fig. 2f–i). The slab calculations (Fig. 2k) clearly illustrate the topological nature of the bands S1 and S2, which connect the valence and conduction bands and cross with each other at two BZ boundary points, $$\overline{K}$$ and $$\overline{T}$$; The formation of two Dirac points is a typical feature of WTIs1,2. Although the Dirac points have not been directly detected, our data demonstrating the quasi-1D spin-momentum locking and its agreement with the first-principles calculations strongly support that the band S1 originates from the topological surface state of a WTI. The trivial bands (colored gray in Fig. 2k) crossing EF in the calculations are from the dangling bonds at the a-b surface, which will be removed in the calculations by proper atom absorption25 and do not appear in the surface Greens’ function calculations10,26 insensitive to the dangling bonds. They are not intrinsic, and not observed in the experiments.

### Band structure with external strain

The small bulk gap (~32 meV) we observed by ARPES indicates that the WTI state in ZrTe5 is protected only marginally from external perturbations. This is compatible with transport measurements showing semimetal behaviors in ZrTe522,27,28,29,30. Theoretical calculations proposed that the band gap changes with external strain10. Such effect could be adopted to stabilize the topological state of matter in WTI, DS, or even STI state; a relevant feature has been previously reported with the data showing a strain-dependent magneto-transport possibly caused by a band gap variation31. However, the signature of transport measurements is indirect, calling for the direct evidence of strain effect on the band structure by ARPES measurements32.

In this study, the samples are glued on Ti or BeCu substrates, to which compressive or tensile strain is applied along the chain direction of ZrTe5 (Fig. 3a; see “Methods” section for more details). The band structures under different strain are displayed in Fig. 3b. The sample with no strain shows a band gap of ~28 meV (Fig. 3b2), similar to that in Fig. 1. We have applied tensile strain to two samples, and find an increase of the band gap up to more than the double of the original value (~61 meV; Fig. 3b4), which makes a WTI state much more robust to external perturbations. In contrast, we could instead reduce the gap value by the compressive strain, even realizing a Dirac semimetal state with a gap no longer distinguishable (Fig. 3b1). We found that the cleaving process causes wrinkles in the sample under large compressive strain to relax the stress on the crystal lattice. It thus becomes harder to apply larger compressive strain to realize a STI state by ARPES, which requires the sample cleavage. We note, however, that cleavage is not necessary for most applications, thus a STI state could be easily reached by a compression method. In Supplementary Fig. 6, we further show that the band gap can be reversibly controlled by external strain.

To better understand our data, we have carried out first-principles calculations of the band structure for different lattice constants of a (Fig. 3c); In ARPES, the strain was applied to the samples along the chain direction (the a-axis). The calculations for compression by 0.25% (Fig. 3c2) obtain a DS state, which is consistent with the ARPES results under compressive strain in Fig. 3b1. On the other hand, the case of lattice expansion by 0.3% (Fig. 3c4) corresponds to our data under tensile strain in Fig. 3b3. Hence, we conclude that about 0.3% compression and stretch are reached in our experiments with a strain device. This is consistent with the strain values measured by X-ray diffraction on the sample and strain gauge on the substrate (See Supplementary Fig. 5). The band gap variation with the lattice constant a is summarized in Fig. 3d, where the experimental data roughly correspond to the solid dots. The calculations further indicate that a STI state with a gap of 18 meV can be reached with 0.7% compression (Fig. 3c1), and a WTI state with a band gap about 70 meV can be reached with 0.7% stretch. Our experimental results provide the direct evidence with ARPES on the band gap control and topological phase transition by external strain.

## Discussion

In summary, we have revealed that ZrTe5 is a WTI, as sketched in Fig. 4a, by directly observing the electronic structure not only on the top surface but also on the side surface of crystal. On the top a-c surface of ZrTe5, the band structure was confirmed to be gapped at any temperatures lower than 200 K. In contrast, the side a-b surface exhibits quasi-1D surface band with spin-momentum locked texture, which illustrates the WTI nature of ZrTe5 distinct from a STI or a normal insulator. Under external strain, the band gap increases with tensile strain and decreases with compressive strain, providing a way to control the bulk gap of the WTI state, or to realize a topological phase transition to a Dirac semimetal state, or even a STI state (Fig. 4b–d). A large band gap obtained by tensile strain can bring further protection of the 3D WTI state or monolayer QSH states in ZrTe5 from thermal fluctuations or other external perturbations33. The quasi-1D surface states yielding the highly directional dissipationless spin current and the strain-tunable bulk gap make ZrTe5 an ideal platform for 2D devices and spin engineering.

## Methods

### Sample growth

High-quality crystals of ZrTe5 were synthesized by the flux method with Te as the flux. High-purity elements (99.99999% Te and 99.9999% Zr) were loaded into a double-walled quartz ampoule and sealed under vacuum. The materials were first melted at 900 °C in a box furnace and fully rocked for 72 h to achieve a homogeneous mixture. The melt was then slowly cooled and rapidly heated between 445 and 505 °C for 21 days. Needle-like crystals were obtained.

### ARPES

Laser-based ARPES and spin-resolved ARPES measurements were performed at the Institute for Solid State Physics, the University of Tokyo, with a laser delivering 6.994-eV photons. Photoelectrons were detected with ScientaOmicron R4000 analyzer and DA30L analyzer. The angle resolution was 0.3° (0.7°) and the overall energy resolution was set to ~5 meV (30 meV) in ARPES (spin-resolved ARPES) measurements. Three-dimensional spin-polarizations of photoelectrons were detected by two VLEED-type spin detectors34. Synchrotron-based nano-ARPES measurements were performed at the 3.2L-Spectromicroscopy beamline of the Elettra Light Source. A Schwarzschild objective was used to focus the photon beam to a spot <1 μm in size. The photon energy was set to 74 eV and temperature was set to around 100 K. The overall energy resolution was set to be better than 60 meV.

### Band fitting

The band dispersions are extracted from MDC peaks. To avoid any complication, we simply used the position of the MDC maximums. Since the band dispersion highly resembles a cone structure, we used the following formula to fit the band structure:

$$f(x)\,=\,\left\{\begin{array}{ll}{c}_{1}(x\,-\,c_4)\,+\,{c}_{3}, & x\,\ge\, {c}_{4}\\ {c}_{2} (x\,-\,c_4)\,+\,{c}_{3}, & x\,<\,{c}_{4}\end{array}\right.$$
(1)

where c1, c2, c3, c4 are the fitting parameters. If the computer program returns 0 or 1 for the inequality x ≥ c4 and x < c4, the above formula can be rewritten in one line:

$$f(x)\,=\, [{c}_{1}(x\,-\,c_4)\,+\, {c}_{3}] (x\,\ge\, {c}_{4})\,+\, [{c}_{2}(x\,-\,c_4)\,+\,{c}_{3}](x{\,}< {\,}{c}_{4})$$
(2)

Since the band dispersion may not be perfectly symmetric, two independent slopes were used for a better fitting. We note this method will underestimate the gap size, as the band top is actually curved due to the band gap opening. However, since the band gap is very small and the band dispersion resembles a cone structure to the very top, the difference should be quite small. Also, we mainly compare the gap change with strain, such underestimation should not affect the comparison.

### Strain device

The strain device shown in Fig. 3a has a unibody structure made of BeCu. There are two walls on the flat plate: a thick one (left) and a thin one (right). A substrate is fixed on the top of the two walls. By reducing or increasing the space between the two walls, we can apply compressive or tensile strain to the substrate, thus to the sample. In the device to apply compressive strain, the thick wall (left) has a through hole, while the thin wall (right) has a threaded hole. Thus by tightening the screw, the space between the two walls will be reduced, and compressive strain will be applied. In the device to apply tensile strain, the thick wall has a threaded hole, while the thin wall is blinded. Thus by the tightening the screw, the space will be enlarged, and tensile strain will be applied. Due to the limited space of the sample holder, Torr Seal is used to fix the substrate on top of the walls.

The data in Fig. 3b are all taken from one thick sample. We exfoliated this thick sample with scotch tape and got different flakes. Then we mounted these different flakes to the substrates of the strain devices, and carried out the experiments. With this method, we avoided the problem that different samples may have slightly different bulk band gap.

### DFT calculations

Our calculations have been performed with the projector augmented wave method implemented in Vienna ab initio simulation package35,36. Generalized gradient approximation of Perdew-Burke-Ernzerhof type is used37. The k-point sampling grids are set to 13 × 13 × 7 and 7 × 7 × 1 for ZrTe5 bulk and ZrTe5 slab, respectively. Spin-orbit coupling is included in the calculations. Considering the fact that ZrTe5 is a strong topological insulator10 when the experimental lattice constants21 are used, we take a slightly increased interlayer distance (0.25 Å) to mimic the weak topological insulator phase, which is consistent with our experimental observations. The ionic positions are relaxed until force on each ion is less than 0.01 eV/Å.