⇦Chinese Physics Letters, 2019, Vol. 36, No. 11, Article code 117301 Experimental Observations Indicating the Topological Nature of the Edge States on HfTe$_{5}$ * Rui-Zhe Liu (刘睿哲)1,2,3†, Xiong Huang (黄雄)1,3†, Ling-Xiao Zhao (赵凌霄)1,3†, Li-Min Liu (刘立民)1,3, Jia-Xin Yin (殷嘉鑫)4, Rui Wu (武睿)1,2, Gen-Fu Chen (陈根富)1,3,5, Zi-Qiang Wang (汪自强)6, Shuheng H. Pan (潘庶亨)1,2,3,5,7** Affiliations 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 2Physical Science Laboratory, Huairou National Comprehensive Science Center, Huairou, Beijing 101400 3School of Physics, University of Chinese Academy of Sciences, Beijing 100190 4Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, NJ, USA 5Songshan Lake Material Laboratory, Dongguan 523808 6Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA 7CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190 Received 3 June 2019, online 21 October 2019 *Supported by the Chinese Academy of Sciences, the National Natural Science Foundation of China under Grant No 11227903, the BM-STC under Grant No Z181100004218007, the National Basic Research Program of China under Grant Nos 2015CB921300 and 2015CB921304, National Key R&D Program of China under Grant No 2017YFA0302903, the Strategic Priority Research Program B of the Chinese Academy of Sciences under Grant Nos XDB04040300 and XDB07000000, and Beijing Municipal Science & Technology Commission (Z181100004218007).
†Rui-Zhe Liu, Xiong Huang and Ling-Xiao Zhao contributed equally to this work.
**Corresponding author. Email: span@iphy.ac.cn Citation Text: Liu R Z, Huang X, Zhao L X, Liu L M and Yin J X et al 2019 Chin. Phys. Lett. 36 117301    Abstract The topological edge states of two-dimensional topological insulators with large energy gaps furnish ideal conduction channels for dissipationless current transport. Transition metal tellurides $X$Te$_{5}$ ($X$=Zr, Hf) are theoretically predicted to be large-gap two-dimensional topological insulators, and the experimental observations of their bulk insulating gap and in-gap edge states have been reported, but the topological nature of these edge states still remains to be further elucidated. Here, we report our low-temperature scanning tunneling microscopy/spectroscopy study on single crystals of HfTe$_{5}$. We demonstrate a full energy gap of $\sim$80 meV near the Fermi level on the surface monolayer of HfTe$_{5}$ and that such an insulating energy gap gets filled with finite energy states when measured at the monolayer step edges. Remarkably, such states are absent at the edges of a narrow monolayer strip of one-unit-cell in width but persist at both step edges of a unit-cell wide monolayer groove. These experimental observations strongly indicate that the edge states of HfTe$_{5}$ monolayers are not trivially caused by translational symmetry breaking, instead they are topological in nature protected by the 2D nontrivial bulk properties. DOI:10.1088/0256-307X/36/11/117301 PACS:73.20.-r, 73.22.-f, 73.43.Jn, 68.37.Ef © 2019 Chinese Physics Society Article Text A two-dimensional topological insulator (2D TI) is characterized by a full energy gap in the bulk electronic bands and conducting helical states at the one-dimensional (1D) edges. There, backscattering is forbidden because the electrons with opposite spins propagate in opposite directions. Therefore, 2D TIs are proposed to be used in fabrication of dissipationless electronic devices. As a high-resolution local probe, scanning tunneling microscopy/spectroscopy (STM/S) technique enables us to study such a promising 2D electronic system and its localized 1D edge states on a microscopic scale. In many proposed 2D topological systems,[1–11] e.g., Bi,[12] Bi$_{14}$Rh$_{3}$I$_{9}$,[13] WTe$_{2}$,[14,15] (Pb, Sn)Se[16] and $X$Te$_{5}$ ($X$=Zr, Hf),[17–19] STM/S results have already shown the insulating bulk energy gap and the existence of edge states. However, the discussions of the topological nature of these edge states observed by STM/S merely rely on the predictions of theoretical calculations. Hence, further experimental evidence closely related to their topological origin is required. In this Letter, we report our STM/S study on the electronic structures of the surface of single crystal HfTe$_{5}$. In particular, our investigations are concentrated on the monolayer step edge (i.e., the 1D boundary of a 2D bulk) and the interaction of the electronic states of two step edges with a one-unit-cell separation. We discuss the implications of our experimental observations and argue for the topological nature of the in-gap edge states. Single crystals of HfTe$_{5}$ were grown by chemical vapor transport method. Stoichiometric amounts of Hf (powder, 3 N, Zr nominal 3%) and Te (powder, 5 N) were sealed in a quartz ampoule with iodine (7 mg/mL) and placed in a two-zone furnace. Typical temperature gradient from 500$^{\circ}\!$C to 400$^{\circ}\!$C was applied. After one month, long ribbon-shaped single crystals were obtained. To obtain a high-quality surface for STM/S measurements, the HfTe$_{5}$ samples were mechanically cleaved in situ at $\sim$20 K, and inserted into the STM head immediately after cleaving. All STM measurements were performed at 4.3 K with tungsten tips fabricated by electrochemical etching followed by field emission against a single crystal gold target. STM topographies were measured in the constant current mode, and differential tunneling conductance spectra were obtained using the lock-in technique.
cpl-36-11-117301-fig1.png
Fig. 1. (a) Side view (left) and top view (right) of the schematic crystal structure of HfTe$_{5}$. (b) Topographic image of the surface of a cleaved single crystal HfTe$_{5}$ ($20 \times 20$ nm$^{2}$, $V=500$ mV, $I=0.03$ nA). Inset: Zoom-in image of the HfTe$_{3}$ chains ($V=500$ mV, $I=0.1$ nA). (c) Tunneling conductance on HfTe$_{5}$ surface ($V=500$ mV, $I=0.5$ nA).
As shown in Fig. 1(a), the HfTe$_{5}$ crystal is structured by stacking 2D HfTe$_{5}$ layers along the $b$ axis with a spacing constant of 1.45 nm, and the HfTe$_{5}$ layer is composed of HfTe$_{3}$ prismatic chains along the $a$ axis, which is bonded in the $c$-axis direction by the tellurium zigzag chains. It has an orthorhombic layered structure with the space group of $Cmcm$. The lattice constants in the $a$–$c$ plane are $a=0.39$ nm and $c=1.37$ nm. Since the coupling between the two adjacent HfTe$_{5}$ layers is van der Waals type, the cleaving process always takes place there and exposes the HfTe$_5$ layer. An STM topographic image of the HfTe$_{5}$ layer is displayed in Fig. 1(b). This demonstrates a stripy structure with a periodicity of $\sim$1.4 nm, which is consistent with the value of lattice constant $c$. The zoom-in topography in Fig. 1(b) clearly shows the topmost Te dimers of the prismatic HfTe$_{3}$ chains. The measured $\sim $0.40 nm distance between two adjacent Te dimers agrees with the lattice constant $a$. In Fig. 1(c), we display the differential tunneling conductance spectrum taken on this surface that clearly shows an energy gap of $\sim$80 meV near the Fermi level ($E_{\rm F}$). The profile of this STS curve resembles that of ZrTe$_{5}$,[17] demonstrating that these two materials have very similar electronic structure, as predicted by theoretical calculations.[20] Because of the relatively weak coupling between the adjacent HfTe$_{3}$ prismatic chains, the in-plain cleavage can take place between the chains. Thus, it is natural to expect for the occurrence of straight monolayer steps along the chain direction. Figure 2(a) shows a topographic image of such a step edge with a height of $\sim $0.7 nm, which equals half of the lattice constant $b$, indicating that this is a monolayer step edge. A sequence of tunneling spectra taken along a line perpendicularly across the step edge is listed in Fig. 2(b). For those spectra taken at the locations near the step edge, finite density of states (DOS) emerges inside the entire energy gap. To demonstrate the spatial evolution of the edge states from the edge into the 2D bulk, we show in Fig. 2(c) the values of the integrated DOS (within the energy range of 100 meV–130 meV) for the corresponding spectra in Fig. 2(b). The in-gap states exhibit an exponential decay with a characteristic length $r\sim 2.91$ nm, twice of the lattice constant $c$ (1.4 nm), demonstrating that the edge states are localized at the step edge and decay into the 2D bulk for a short distance of only a few unit-cells. All these experimental observations are very similar to that on ZrTe$_{5}$ reported previously,[17] and also consistent with the early theoretical predictions that the bulk of HfTe$_{5}$/ZrTe$_{5}$ is a weak 3D TI and its monolayer is a possible candidate for 2D topological insulator supporting topological edge states.[20]
cpl-36-11-117301-fig2.png
Fig. 2. (a) Topographic image of a monolayer step ($20 \times 20$ nm$^{2}$, $V=500$ mV, $I=0.03$ nA). (b) Spatially resolved tunneling spectra ($V=500$ mV, $I =0.5$ nA) across the step edge. Their corresponding locations are marked in (a) as colored dots. (c) Integrated conductance within the gap plotted as a function of distance away from the step edge on the upper terrace surface. The red curve is the exponential fitting with a decay length of $\sim $2.91 nm.
In general, the edge states of a 2D system can either be trivial states caused by symmetry breaking or nontrivial states protected by the 2D topological band structure. To further identify the topological nature of the edge states observed at the edges of the HfTe$_{5}$/ZrTe$_{5}$ monolayers, more experimental evidences would be much preferred. Here, we present a case of an isolated narrow HfTe$_{5}$ strip, as shown in Fig. 3(a). This narrow strip resides on the atomically flat surface of the single crystal HfTe$_{5}$ and has a height of $\sim $0.7 nm and width of one unit-cell ($\sim$1.4 nm). From the high resolution STM topography (inset of Fig. 3(a)), we can resolve the atomic structure of this narrow strip as the same as a unit-cell strip from the striped surface lying below. Notably, the spatially resolved tunneling conductance spectra in Fig. 3(b) show that the energy gap keeps open across this strip and no conducting in-gap states emerge at either its edges. Figure 3(c) compares the 'regular' tunneling spectra taken at the edge of a large 2D monolayer, at the edge of a unit-cell strip, and on the monolayer away from the edge.
cpl-36-11-117301-fig3.png
Fig. 3. (a) Topographic image showing an isolated strip ($V=500$ mV, $I=0.03$ nA). (b) Spatially resolved tunneling spectroscopic map across the strip of red arrow line in (a) showing the absence of edge states ($V=500$ mV, $I =0.5$ nA). (c) Tunneling spectra taken at (blue) and away (red) from the strip, respectively. The spectrum with edge states (green) obtained in Fig. 2(c) is presented as a reference.
The absence of in-gap states at the edges of a one-unit-cell wide monolayer strip is quite remarkable. In terms of the crystal's structure, there is no difference between the edge of a one-unit-cell monolayer strip and the one of a large monolayer. The trivial edge states due to the lateral environment change at the step edge should appear in both the cases. However, it is more consistent to argue that there is a fundamental difference between the two cases for the edge states of topological nature. In the case of the large monolayer, the topological edge states are supported and protected by the topological bands of the 2D topological insulator. However, in the case of the one-unit-cell monolayer strip, no such bands exist due to the lack of 2D translational invariance. It can also be argued that the topological edge states from the two edges of a narrow topological strip can couple, when they are close enough, and open a gap. Indeed, in our observation, the two edges are distant from each other for only a unit-cell length, while the characteristic decay length of the edge states is several unit-cells long, as shown in Fig. 2(c). Therefore, the strong coupling between the topological edge states opens a full gap as the one on a large 2D topological monolayer.
cpl-36-11-117301-fig4.png
Fig. 4. (a) Topographic image showing two adjacent step edges separated by a one-unit-cell wide monolayer groove ($V=500$ mV, $I=0.03$ nA). (b) Tunneling spectra taken at the center of the groove (blue) and at the step edges of the groove (red, green), respectively. Their corresponding locations are marked in (a) as colored dots ($V= 500$ mV, $I=0.5$ nA). (c) Corresponding tunneling conductance map at $E=100$ meV (junction set: $V=500$ mV, $I=0.3$ nA). (d) Integrated DOS within the gap along a line perpendicular to the two edges, showing the faster decay of the edge states into the groove than into the than into the 2D bulk.
The topological argument can also be further supported by the experimental observation on a one-unit-cell wide monolayer groove (Fig. 4(a)). As shown in Fig. 4(b), the conducting in-gap states still exist at both edges, though the two edges are also separated by one-unit-cell distance. For a trivial edge state, it can propagate on both top and lower terraces. The edge states from two nearby edges can couple and induce interference in the area of the groove, but this is not what we observe. While, for the case of a 2D topological insulator, its edge states will decay very sharply into the vacuum (in the groove). Therefore, the topological edge states from the sides of the one-unit-cell wide monolayer groove will not strongly couple. The measured partial gap size at the center of the groove is about 50 meV, which is smaller than the bulk gap (80 meV) of that on the 2D monolayer, indicating a much weaker coupling compared with the case of the one-unit-cell wide monolayer strip. Figure 4(c) displays the differential tunneling conductance mapping of the same region in Fig. 4(a) at the energy (100 meV) within the bulk gap. The in-gap states for both edges and their spatial evolution are well visualized. For both edges, the edge states decay faster into the vacuum (groove) than into the 2D bulk; as shown in Fig. 4(d). It should be pointed out that the actual decay of the edge states is much faster than that shown in the measurement, because of the relatively poor spatial resolution at the down step side due to the finite dimension of the STM tip. In conclusion, our study of HfTe$_5$ single crystals clearly demonstrates that the HfTe$_5$ surface monolayer has a full gap of about 80 meV and almost constant in-gap states at its edges. These observations are consistent with the theoretical predictions that the bulk of HfTe$_5$ is a weak 3D topological insulator, and that the surface monolayer of HfTe$_5$ is a 2D topological insulator. We also observe the distinct behavior of the in-gap states at two edges separated by one-unit-cell distance. They disappear at both edges of a unit-cell-wide strip and persist at both edges of a unit-cell-wide groove. This remarkable observation, although it is not a direct proof, strongly reinforces the topological arguments and undermines the trivial interpretations. Further study of the interaction of the edge states as a function of separation distance would greatly enhance the comprehensive understanding of the topological nature and provide in-depth knowledge for applications. We sincerely thank Dr. Hong-Ming Weng, Dr. Xi Dai and Dr. Si-Min Nie for in-depth discussions. References Quantum Spin Hall Effect in Inverted Type-II SemiconductorsLarge-gap two-dimensional topological insulator in oxygen functionalized MXeneQuantum Spin Hall Effect in Silicene and Two-Dimensional GermaniumLarge-Gap Quantum Spin Hall Insulators in Tin FilmsFunctionalized germanene as a prototype of large-gap two-dimensional topological insulatorsLarge-Gap Quantum Spin Hall Insulator in Single Layer Bismuth Monobromide Bi 4 Br 4Quantum spin Hall effect in two-dimensional transition metal dichalcogenidesQuantum spin Hall effect in two-dimensional transition-metal dichalcogenide haeckelitesGraphene-like Dirac states and quantum spin Hall insulators in square-octagonal M X 2 ( M = Mo , W; X = S , Se, Te) isomersTwo-dimensional oxide topological insulator with iron-pnictide superconductor LiFeAs structureQuantum spin Hall effect and topological phase transition in two-dimensional square transition-metal dichalcogenidesSpatial and Energy Distribution of Topological Edge States in Single Bi(111) BilayerSubnanometre-wide electron channels protected by topologyObservation of topological states residing at step edges of WTe2Quantum spin Hall state in monolayer 1T'-WTe2Robust spin-polarized midgap states at step edges of topological crystalline insulatorsEvidence for Topological Edge States in a Large Energy Gap near the Step Edges on the Surface of ZrTe 5 Experimental Observation of Topological Edge States at the Surface Step Edge of the Topological Insulator ZrTe 5 Experimental observation of conductive edge states in weak topological insulator candidate HfTe 5Transition-Metal Pentatelluride ZrTe 5 and HfTe 5 : A Paradigm for Large-Gap Quantum Spin Hall Insulators
[1] Liu C, Hughes T L, Qi X L, Wang K and Zhang S C 2008 Phys. Rev. Lett. 100 236601
[2] Weng H, Ranjbar A, Liang Y, Song Z, Khazaei M, Yunoki S, Arai M, Kawazoe Y, Fang Z and Dai X 2015 Phys. Rev. B 92 075436
[3] Liu C C, Feng W and Yao Y 2011 Phys. Rev. Lett. 107 076802
[4] Xu Y, Yan B, Zhang H J, Wang J, Xu G, Tang P, Duan W and Zhang S C 2013 Phys. Rev. Lett. 111 136804
[5] Si C, Liu J, Xu Y, Wu J, Gu B L and Duan W 2014 Phys. Rev. B 89 115429
[6] Zhou J J, Feng W, Liu C C, Guan S and Yao Y 2014 Nano Lett. 14 4767
[7] Qian X, Liu J, Fu L and Li J 2014 Science 346 1344
[8] Nie S M, Song Z, Weng H and Fang Z 2015 Phys. Rev. B 91 235434
[9] Sun Y, Felser C and Yan B 2015 Phys. Rev. B 92 165421
[10] Xu Q, Song Z, Nie S, Weng H, Fang Z and Dai X 2015 Phys. Rev. B 92 205310
[11] Ma Y, Kou L, Li X, Dai Y, Smith S C and Heine T 2015 Phys. Rev. B 92 085427
[12] Yang F, Miao L, Wang Z F, Yao M Y, Zhu F, Song Y R, Wang M X, Xu J P, Fedorov A V, Sun Z, Zhang G B, Liu C, Liu F, Qian D, Gao C L and Jia J F 2012 Phys. Rev. Lett. 109 016801
[13] Pauly C, Rasche B, Koepernik K, Liebmann M, Pratzer M, Richter M, Kellner J, Eschbach M, Kaufmann B, Plucinski L, Schneider Claus M, Ruck M, van den Brink J and Morgenstern M 2015 Nat. Phys. 11 338
[14] Peng L, Yuan Y, Li G, Yang X, Xian J J, Yi C J, Shi Y G and Fu Y S 2017 Nat. Commun. 8 659
[15] Tang S, Zhang C, Wong D, Pedramrazi Z, Tsai H Z, Jia C, Moritz B, Claassen M, Ryu H, Kahn S, Jiang J, Yan H, Hashimoto M, Lu D, Moore R G, Hwang C C, Hwang C, Hussain Z, Chen Y, Ugeda M M, Liu Z, Xie X, Devereaux T P, Crommie M F, Mo S K and Shen Z X 2017 Nat. Phys. 13 683
[16] Sessi P, Di Sante D, Szczerbakow A, Glott F, Wilfert S, Schmidt H, Bathon T, Dziawa P, Greiter M, Neupert T, Sangiovanni G, Story T, Thomale R and Bode M 2016 Science 354 1269
[17] Wu R, Ma J Z, Nie S M, Zhao L X, Huang X, Yin J X, Fu B B, Richard P, Chen G F, Fang Z, Dai X, Weng H M, Qian T, Ding H and Pan S H 2016 Phys. Rev. X 6 021017
[18] Li X B, Huang W K, Lv Y Y, Zhang K W, Yang C L, Zhang B B, Chen Y B, Yao S H, Zhou J, Lu M H, Sheng L, Li S C, Jia J F, Xue Q K, Chen Y F and Xing D Y 2016 Phys. Rev. Lett. 116 176803
[19] Liu S, Wang M X, Chen C, Xu X, Jiang J, Yang L X, Yang H F, Lv Y Y, Zhou J, Chen Y B, Yao S H, Lu M H, Chen Y F, Felser C, Yan B H, Liu Z K and Chen Y L 2018 APL Mater. 6 121111
[20] Weng H, Dai X and Fang Z 2014 Phys. Rev. X 4 011002