Experimental observation of conductive edge states in weak topological insulator candidate HfTe₅

Quantum Spin Hall (QSH) insulators are quantum materials with a bulk insulating gap and helical transport channels at the edge protected by time reversal symmetry (TRS) without backscattering,^1–4 making them good candidates for dissipationless transport. Starting from HgTe/CdTe and InAs/GaSb heterostructures^2,4–6 to monolayer stanene^7–10 and 1T’-transition metal chalcogenides,^11–14 tremendous efforts have been made on obtaining QSH compounds with large bandgap, good stability, and ease of fabrication, which are all desirable properties for high-temperature low-dissipation device applications. Among all the theoretical proposals on QSH insulator candidates, XTe₅ materials (X = Zr or Hf) have attracted extensive attention due to their simple stoichiometry, large bandgap size, and layered nature,¹⁵ making them ideal candidates for potential applications.

In the past few years, most of the studies are focusing on the topological properties in bulk ZrTe₅,^16–25 which are rather controversial because they are predicted to be located near the boundary of the strong topological insulator (STI) phase and the weak topological insulator (WTI) phase, depending on the strength of interlayer coupling.^15,26 Moreover, its band topology is also predicted to be very sensitive to the lattice constants, which can be tuned by many factors such as the doping level, strain, or growth conditions.^27,28 Till now, the topological nature of these bulk materials is still an issue under debate. Various angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy/scanning tunneling spectroscopy (STM/STS) experiments on ZrTe₅ seem to draw different conclusions on the existence of a bulk gap and topological surface states.^{17–21,23–25} On the one hand, a circularly dichroic ARPES report reveals the presence of spin polarized states near the Fermi energy,²³ and a subsequent ARPES study reports on the topological surface states,¹⁸ both suggesting the STI character of ZrTe₅. On the other hand, several high resolution laser ARPES measurements report on the existence of the bandgap which supports the WTI nature of ZrTe₅.^24,25 In addition, transport experiments report on the chiral magnetic effect in ZrTe₅ and point to its being as a topological Dirac semimetal (boundary phase between the STI and WTI).^16,22 Notably, two recent STM/STS studies have reported on the existence of the bandgap and topological edge states in ZrTe₅,^17,21 suggesting that it is a WTI rather than a STI.

Meanwhile, so far there have been much fewer reports on the isostructural compound HfTe₅²⁹ with stronger spin-orbit interaction strength comparing to ZrTe₅, partially due to the inferior sample quality of HfTe₅.³⁰ The investigation of the electronic structure of HfTe₅ (especially the topological non-trivial electronic states) would help us understand the topological nature of the whole family.

In this work, by the combination of ARPES and STM/STS experiments, we systematically investigated the electronic structure of bulk HfTe₅ to address its topological nature. Using ARPES, we directly visualized the complete band structure of HfTe₅. Specifically, our photon energy dependent experiments clearly reveal the bulk nature of the band dispersions without seeing any surface related electronic states. Additionally, our STM/STS measurements not only reveal the electronic structure of HfTe₅ in consistent with the ARPES results but also provide clear evidence in support of the WTI nature of this material by observation of the bulk bandgap and the in-gap states near the HfTe₅ step edges. Interestingly, the STM/STS results further demonstrate the development of the edge states in concomitance with the bulk band bending near the step edges and the spatial evolution of both the edge states and the bulk bands at the sample boundary with a broken symmetry.

HfTe₅ polycrystalline, prepared by the direct stoichiometric solid-state reaction of Hf (99.999%) with Te powder (99.999%), is mixed with a transportation agent (I₂) and then loaded into an evacuated quartz ampoule to grow HfTe₅ crystals with a temperature profile of 500 ∼ 400 °C. After a growth period over 10 days, the centimeter-sized strip single crystals with metallic luster are obtained.

Both ARPES and STM/STS measurements were carried out in an ultra-high vacuum (UHV) environment. HfTe₅ samples were all cleaved in situ along its natural cleavage plane (010) to obtain fresh and clean surfaces. ARPES experiments were performed at the Stanford Synchrotron Radiation Lightsource (SSRL), USA, and beamline I05 in the Diamond Light Source (DLS), UK. Experimental data were collected at 10 K by using Scienta R4000 analyzers with a total convolved energy and angle resolution of 20 meV and 0.2°, respectively. In STM/STS experiments, cleaved samples were transferred in situ to the cryostat kept at 4.2 K or 77 K. Chemically etched tungsten (W) tips were used for both imaging and tunneling spectroscopy. The tips for the measurement were all decorated and calibrated on the surface of silver islands grown on the p-type Si (111)-7 × 7 to avoid any artificial tip effects. Lock-in technique was employed to obtain dI/dV curves with an extra 5 mV modulation at 991 Hz alongside the normal DC sample biases.

HfTe₅ has a base-centered orthorhombic crystal structure, and its space group is Cmcm (No. 63). Each unit cell comprises two stacking Hf-Te layers constituted by trigonal prismatic Hf-Te3 chains (along the a axis) and connecting Te zig-zag chains (along the c axis) in the (010) plane (a-c plane) [Fig. 1(a)]. Therefore, HfTe₅ is easily cleavable along the a-c plane, which is confirmed by the atomic resolved STM images, where the Te-Te dimers in the parallel Hf-Te3 chains can be clearly seen, forming the stripe-like topography, as seen in Fig. 1(b) and more clearly in Fig. 1(c) (other Te atoms below could also be observed as spots with weaker intensity). From the atom-resolved topography image, we found that the quality of HfTe₅ single crystal is not as good as the previously reported ZrTe₅ single crystal²⁰ as we constantly observe defects seen as the bright points in Fig. 1(b) (more details can be found in supplementary material). From the STM topography image, we could measure the distance between two parallel Hf-Te3 chains and inter-dimer spacing of Te atoms to be 13.29 Å and 3.84 Å (measured at T = 4.2 K), respectively, smaller than the measured lattice constant c = 13.68 Å and a = 3.96 Å in previous experimental values³¹ (these results are consistent since the discrepancy, which is about 3% of the previously reported values, may come from the imperfect piezo calibration in STM measurement). The core-level photoemission spectrum of HfTe₅ is shown in Fig. 1(d), where the characteristic peaks of Hf_4d and Te_5f are clearly observed. The 3D Brillouin zone (BZ) and the projected surface BZ in the (010) plane are given in Fig. 1(e). Broad Fermi surface (FS) mapping covering more than 10 BZs is shown in Fig. 1(f), which confirms the cleavage surface as the (010) surface.

We performed high-resolution ARPES measurements to investigate the detailed electronic structures of bulk HfTe₅. In Fig. 2(a), we show the 3D intensity plot of the photoemission spectra to provide an overview of band structures. The only observed feature on the FS is the hole pocket around the $Γ¯$ point in the surface BZ, revealing the p-type nature of our sample. The constant-energy contours (CECs) become more complex at higher binding energies [see the stacked plot in Fig. 2(b)], reflecting the multi-band and anisotropic nature of the dispersions. The dispersions along the high symmetry directions are plotted in Fig. 2(c), which show good agreement with the previous first-principle calculations.¹⁵ In addition, we performed systematic photon energy dependence measurement to track the k_z evolution of the band at the $Γ¯$ point. With 65 eV photons (corresponding to Γ point), only a simple hole-like dispersion is observed [Fig. 2(d–i)]. However, with 55 eV photons (corresponding to Z point), an additional feature is found at Z, most likely due to the M shape of the band top [Fig. 2(d–ii)]. Such observation reveals the strong k_z dispersions of the bulk band along $Γ$-Z, similar to the previous calculations and ARPES results in ZrTe₅.^15,19,23,24 Because the surface states are two dimensional and do not have k_z dispersions, we claim that the hole-like dispersion near the $Γ¯$ point is originated from the bulk electronic states and no surface related bands are observed (more details can be found in Fig. S1 of the supplementary material).

Given the p-type nature of the HfTe₅ samples (in agreement with the transport measurement³²), ARPES measurement could not retrieve further information about the conduction band and whether a bulk gap is formed. In order to clarify its topological properties in HfTe₅, we carried out comprehensive STM/STS measurements focusing on the density of states (DOS) on the cleaved HfTe₅. Figure 3(a) shows a large scale STM topographic image in the (010) plane with a clear stripe-like structure and a terrace step in the middle of the image. The measured step height is about 1.40 nm [see the line-profile in the lower panel of Fig. 3(a)], slightly less than the lattice constant b = 1.44 nm.³¹ We measured STS at three different locations [A, B, and C points, labeled as green, blue, and red dots in Fig. 3(a), respectively], with the bias range from −100 mV to +150 mV. Positions A, B, and C are located at the lower layer far away from the step, the upper layer far away from and in the vicinity of the step, respectively. From the stack plots of the STS results [Fig. 3(b)], we could clearly observe gaps of ∼50 meV size in both spectra at A [green curve in Fig. 3(b)] and B (blue curve). By contrast, the spectrum at C (red curve) shows a non-zero DOS/metallic states within the same bias range. We measured the uniformity of the gap by conducting the STS measurement on sequential dots as labeled by the dotted line crossing A in Fig. 3(a). The result dI/dV curves are displayed as an intensity map in Fig. 3(c). Across the measurement distance over 50 nm, all the spectra show a ∼50 meV bandgap, with the valance band maximum (VBM) and conduction band minimum (CBM) located at ∼0 and ∼50 mV, respectively. We note that there is a less-than-20 meV rigid shift between the lower layer (spectra A) and upper layer (spectra B) [Fig. 3(b)], whereas the gap size remains unchanged, which may be a result of the inhomogeneity of the sample.

Apart from the universal ∼50 meV gap observed in HfTe₅, the other significant feature detected by STS is the non-zero DOS/metallic states discovered at the step edge of the top layer, which breaks the translation symmetry along the c direction. To better visualize the edge states, we measured the dI/dV mapping at 23 meV [lower panel of Fig. 3(d), the corresponding feature was marked with a black arrow in the red curve in Fig. 3(b).] and compare it with the topographic image in the same region [upper panel of Fig. 3(d)]. From the color mapping, we find that the intensity near the step edge is dramatically enhanced, while kept low and rather uniform away from the step edge as expected, providing clear evidence for the existence of edge states. The edge states persist all the way along the step edge and extend about 10 nm from the edge on the upper layer, proving its 1D nature (more discussions later). The edge state does not have any contribution to the electronic state in the adjacent region in the lower layer, most likely due to the weak inter-layer interaction in HfTe₅. Therefore, based on the measurement of the ∼50 meV bandgap in the bulk and 1D electronic state in the step edge, we propose that HfTe₅ is a WTI in 3D, similar to the ZrTe₅ proposed by several previous ARPES/STM measurements.^17,21,24,25

To illustrate the evolution of the 1D edge state and bulk bandgap when approaching the step edge, we carried out more detailed STM/STS study on another sample. We did STS measurements across a sharp step edge with height 0.696 nm [half the b lattice constant, see Fig. 4(a)]. The evolution of the bulk gap across this step is plotted as an intensity map in Fig. 4(b), where the edge electronic states is well distinguished, similar to the situation of step edge height 1.40 nm. When approaching the step edge, we observed clear band bending behavior of the VBM and CBM in both the upper and lower layers toward higher positive energy when the edge state appears in the bandgap [Figs. 4(b) and 4(c)]. Interestingly, while the edge states are mostly localized in the upper layer, the effective region of bulk band bending distributes much more broadly in both the upper and lower layers. Detailed fitting shows that while the edge state develops within ∼10 nm adjacent to the step edge [∼7 unit cells, see the fitting result in Fig. 4(d)], the bulk band bending takes place within ∼40 nm of the step edge [∼28 unit cells, see the fitting result in Fig. 4(e)]. Clearly, the band bending and edge states have different spatial scales, indicating that the edge state is not coming from bulk DOS. Such observation provides important information of the low dimension electronic states near the edge and illustrates the different behavior of the bulk and edge states in a WTI candidate.

Here, we note that the energy position of the VBMs and CBMs as well as the bandgaps shown in Fig. 4 is uniform in the upper and lower layers, at places far away from the step. The measured band positions are slightly shifted from the other sample measured in Fig. 3. This may results from the sample inhomogeneity and the rather localized probing size in the STM experiment. On the other hand, ARPES measures spatial averaged electronic structures across many adjacent needle-like pieces (HfTe₅ single crystal has a quasi-one-dimensional structure, and the bulk crystals are needle-like pieces) or domains (typical ARPES beam spot size is ∼100 µm) and provides a spatially averaged band structure. Therefore, the observed p-type band structure from ARPES reflects the large ratio of the p-type sample pieces although the VBMs and CBMs in Fig. 4 are all located at ∼−50 mV and ∼0 mV, respectively, in the measured sample positions.

Compared to the previous reports on ZrTe₅, our ARPES and STM/STS measurements provide a more systematic description of the electronic structure of HfTe₅. Compared to ZrTe₅, the overall electronic band structure of HfTe₅ is very much similar. Given the larger spin orbit coupling of Hf compared to Zr, the bulk bandgap in ZrTe₅ should be smaller than HfTe₅ (∼50 meV), suggesting an overestimate of the gap size (∼80 meV) in the previous reports.^17,21 Furthermore, our reports provide new important information on the edge state in XTe₅. The conductive state can be detected both on the edge of the monolayer (with step height b/2) and bilayer (with step height b) steps. There is bulk band bending on the step edge in accompany with the development of the 1D edge state, suggesting their different origins. Moreover, the edge state is not affected by the potential field causing the band bending, and it remains robust inside the bandgap, making HfTe₅ a good candidate for device applications if the Fermi level could be tuned into the bulk gap. At last, although the topological nature of the observed edge states in our experiments needs further experimental and theoretical support, our experiment suggests a WTI phase in bulk HfTe₅ and proposes HfTe₅ as a good material candidate for studying the QSH effect and other novel quantum phenomena emerged during topological quantum phase transitions.

See supplementary material for detailed experimental data of HfTe₅.

This work was supported by a grant from the National Key R&D Program of China (Grant No. 2017YFA0305400) and the Chinese Academy of Science-Shanghai Science Research Center (Grant No. CAS-SSRC-YH-2015-01). Y.L.C. acknowledges the support from the Engineering and Physical Sciences Research Council Platform Grant (Grant No. EP/M020517/1). Z.K.L. acknowledges the support from the National Natural Science Foundation of China (Grant No. 11674229). M.X.W. acknowledges the support from the Shanghai Sailing Program (Grant No. 16YF1407800), the Shanghai Natural Science Foundation (Grant No. 16ZR1447500), and the National Natural Science Foundation of China (Grant No. 11604207). C.C. acknowledges the support of the China Scholarship Council—University of Oxford Scholarship. All authors contributed to the scientific planning and discussions. The authors declare no competing financial interest.