Observation and control of the weak topological insulator state in ZrTe5

A quantum spin Hall (QSH) insulator hosts topological states at the one-dimensional (1D) edge, along which backscattering by nonmagnetic impurities is strictly prohibited. Its 3D analogue, a weak topological insulator (WTI), possesses similar quasi-1D topological states confined at side surfaces. The enhanced confinement could provide a route for dissipationless current and better advantages for applications relative to strong topological insulators (STIs). However, the topological side surface is usually not cleavable and is thus hard to observe. Here, we visualize the topological states of the WTI candidate ZrTe5 by spin and angle-resolved photoemission spectroscopy (ARPES): a quasi-1D band with spin-momentum locking was revealed on the side surface. We further demonstrate that the bulk band gap is controlled by external strain, realizing a more stable WTI state or an ideal Dirac semimetal (DS) state. The highly directional spin-current and the tunable band gap in ZrTe5 will provide an excellent platform for applications.


Supplementary Note 1: Band shift with time in low vacuum
The data in Fig. 1 was taken from an ARPES system with a vacuum better than 1 × 10 −11 Torr. No band shift at the same temperature was observed. However, we also carried out experiments at an ARPES system with lower vacuum (∼ 7 × 10 −11 Torr). With this system, we noticed a band shift with time, even at the same temperature. In Supplementary Fig. 1a -1d, we displayed a data sequence taken at different time but under the same experimental conditions. The band shift is summarized in Supplementary Fig. 1e. It is obvious that the band shifts toward lower binding energy, showing a hole doping effect. We observed the same phenomenon for different samples. The raw data divided by Fermi function at 200K is shown in Supplementary Fig. 2b -2c. The density of states (DOS, integration of EDCs over k a ) of Supplementary Fig. 2c roughly shows a linear decrease toward the conical point ( Supplementary Fig. 2d), which is very different from the behavior of an ideal linear dispersion. For a linear dispersion at specific k b0 and k c0 , E(k a , k b0 , k c0 ) ∼ ak a + b, in calculation the integration over k a gives a constant (ρ(E) = dN/dE ∼ dk a /dE ∼ constant), as shown in Supplementary Fig. 2g -2h. The decreased intensity in experimental data should come from the matrix element effect. As the intensity near the conical point is rather weak, the decreased intensity makes it very difficult to obtain the conical points of the valence and conduction bands. To remove such intensity change induced by matrix element effect, the raw data is normalized by its DOS. The resulting constant intensity will be similar to that from the calculation. The result is shown in Supplementary Fig. 2e. The gap size obtained from this data should be more precise.
Furthermore, the feature of the EDC at k a = 0 from Supplementary Fig. 2e is more consistent with the calculations than that from Supplementary Fig. 2c. As shown in Supplementary Fig. 2h, the peak of the EDC at k a = 0 is pronounced and indicates the position the conical point. In Supplementary Fig. 2f we compared the EDCs at k a = 0 from Supplementary Fig. 2c and 2e. The EDC from the data divided by Fermi function shows no peak feature, different from the calculation in Supplementary Fig. 2h. Instead, the EDC from the data normalized by DOS has a well-defined peak, similar to the calculations. Thus, we use this peak as the band bottom of the conduction band. The gap size obtained by this method is comparable with the data reported in Ref. [1,2].   Our measurements with the synchrotron-based nano-ARPES revealed that the successfully cleaved areas with high photoelectron intensities are very small (∼50 µm in width) in the a − b plane. Here we demonstrate that the electronic states within such small cleavage areas are rather homogenous. This fact is particularly important to justify the reliability of our data taken by laser-ARPES with a relatively large photon beam (∼ 50 µm).
Supplementary Figure 3 exhibits the band dispersions measured by nano-ARPES at many different points on the cleaved areas with high intensities from two pieces of the sample. For the sample S1, the ARPES measurements were carried out on five different points marked by the red solid dots in Supplementary Fig. 3a , and the corresponding band structures are shown in Supplementary Fig. 3c -3g. We also got signal from another piece of the sample (sample S2), and display its band structure in Supplementary Fig. 3h. Significantly, all these measurements give basically the same band structure, indicating that the electronic states are homogenous within the successfully cleaved areas. This justifies that the intrinsic electronic structure for the side surface of ZrTe 5 can be also obtained by laser-ARPES with laser spot of 50 µm in size, which is similar to the typical width of the successfully cleaved areas with homogenous electronic states. Here we discuss the details of the analysis on the spin-resolved data in Fig. 2f -2i. We measured two pairs of EDCs ( Supplementary Fig. 4a) by spin-resolved ARPES from three different samples. The k a locations are also shown in Supplementary Fig. 4b. The spin polarization curves along the b, a and c directions are displayed in Supplementary  Fig. 4c -4e. In each panel of Supplementary Fig. 4c -4e, the five curves with the same color (blue or red) are taken at two different k b (k b ∼ 0 and 10, indicated in Supplementary Fig. 4a) from three samples (one sample at only k b ∼ 0, in total 6 -1 = 5 curves). These five curves show no obvious difference, confirming the repeatability of the measurements. We notice that the spin polarization curves in the background range (< -0.15 eV) are not zero but have offsets. Such constant polarization in the background may come from the asymmetry of the spin + and spin -channels, or may come from the matrix element effect in the photoemission process, which is often observed in spin-resolved ARPES [3,4]. We averaged the five polarization curves with the same color in Supplementary Fig.  4c -4e, and subtracted the resulting curves by a constant to remove the background polarization. The results are displayed in Supplementary Fig. 4f -4h. The spin is polarized along b direction, consistent with the calculations in Fig. 2j.

Supplementary Note 5: Measurements of tensile strain
The tensile strain of the sample was controlled by applying tensile strain to the substrate on which the sample was mounted. We separately measured the actual values of tensile stain applied to the substrate and the sample, and found consistency between the two. Most importantly, the strain values directly determined agree with that estimated from the band gap measured by ARPES.
We measured the tensile strain applied to the BeCu substrate with strain gauges (KFGS series from Kyowa Electronic Instruments, which can only be used for tensile strain). The strain was induced by increasing the torque on the screw in our device, which was monitored by a digital torque screwdriver. The obtained strain-torque curve is plotted in Supplementary Fig. 5a; we did two tests, and confirmed the two curves to be similar. The maximum torque we can apply is limited by the strength of Torr Seal used to fix the substrate to our strain device; in our setup, Torr Seal generally breaks at an applied torque between 0.2 and 0.3 N·m. This value may be slightly different, depending on the condition of Torr Seal, which is daubed onto the device by hand. In test 1, Torr Seal broke when torque > 0.195 N·m, whereas it broke when torque > 0.25 N·m in test 2. In the experiment shown in Fig. 3, we applied ∼ 0.2 N·m torque to the screw, which corresponds to a tensile strain of about 0.36%, according to the strain curve in Supplementary  Fig. 5a. This value is basically consistent with the value 0.3% estimated from the band gap in ARPES (see the main text).
We also prepared one sample on the tensile strain device, applied 0.21 N·m torque to the screw, and measured the X-ray diffraction (XRD) peaks of the sample. The (080) and (170) peaks are obtained for the sample without and with strain, and these are displayed in Supplementary Fig. 5b. The peak positions and the corresponding lattice parameters are listed in Supplementary Table I. We found the strain of 0.42% is applied along the chain (a direction) on the sample; very importantly, this result agrees not only with the strain of the substrate measured by strain-gauge, but also with that estimated from the band gap in ARPES, all of which give ∼ 0.3 -0.4 %, when applying the torque of ∼ 0.2 N·m to the screw in our strain device.  The thin flakes we measured are too thin to cleave twice. Thus, to check if the band structure is reversible after the strain was released, we need a strain device tunable in-situ. Due to the limitation of our ARPES setup (location of a screw driver and the torque we can apply with it), the device shown in Fig. 3a was not suitable for such purpose. Hence, we used another strain device adjustable in-situ to check whether or not the tensile strain effect on the band structure of ZrTe 5 is reversible (Details of the strain device can be found in Ref. [5]).
In Supplementary Fig. 6a and 6c, we show the band structure obtained by strain cycle measurements for two samples: left to right panels each plot the data with no strain, ∼ 0.5% tensile strain, and strain released, following the experiment sequence. With ∼ 0.5% tensile strain (middle panels in Supplementary Fig. 6a and 6c), the band gap is enlarged (62 -66 meV) from the original values (∼ 30 meV), and then the band gap restores to its original value when the strain is released (right panels). This reversible behavior is clearly demonstrated in Supplementary Fig. 6b and 6d by plotting the EDC peaks on the horizontal axis which is the relative energy to the top of the valence band; the peak shift with strain and the restoring of it to the original position is clearly shown. Therefore, we conclude that the strain effect on the band gap is reversible. In passing, the spectra got weaker in intensity and broader than the original ones after releasing strain because of the surface aging of the samples: we transferred the samples to a chamber with a worse vacuum to release the strain and the vacuum became even worse when adjusting the screws to release the strain.