Detection of Surface States in Quantum Materials ZrTe₂ and TmB₄ by Scanning Tunneling Microscopy

Abstract

Scanning Tunneling Microscopy and Spectroscopy (STM/S), with its exceptional surface sensitivity and exquisite energy resolution, is well suited for the investigation of surface states down to atomic length scales. As such, it became an essential tool to probe the surface states of materials, including those with non-trivial topology. One challenge, however, can be the preparation of clean surfaces which allow the study of preferably unchanged surface properties with respect to the bulk amount. Here, we report on the STM/S of two materials, ZrTe${}_2$ and TmB${}_4$. The former cleaves easily and defects can be examined in detail. However, our STS data can only qualitatively be compared to the results of band structure calculations. In the case of TmB${}_4$, the preparation of suitable surfaces is highly challenging, and atomically flat surfaces (likely of B-termination) were only encountered rarely. We found a large density of states (DOS) at the Fermi level $E_{\mathrm{F}}$ and a mostly featureless differential conductance near $E_{\mathrm{F}}$. Further efforts are required to relate our results to the electronic structure predicted by ab initio calculations.

1. Introduction

The interpretation of the quantum Hall effect, in terms of topology, has been well established for several decades [1]. More recently, the quantum spin Hall effect was predicted [2,3] and realized soon after [4]. These discoveries were followed by huge developments in the field of non-trivial topology, including materials such as topological insulators, semimetals and superconductors [5,6,7,8]. In particular, enormous efforts were undertaken to predict non-trivial topology in materials, see [9] and references therein. In this respect, both spin-orbit coupling and crystalline symmetry, as well as their interplay, are of particular importance.

Likewise, there have also been tremendous efforts to experimentally investigate and/or verify non-trivial topology in these materials. One of the primary tools here is angle-resolved photoemission spectroscopy (ARPES) as it can provide information on the materials’ electronic structure [10,11,12,13,14], in some cases even in a spin-resolved fashion [15,16,17]. As an example, ARPES can reveal the linear dispersion relation expected for electrons on a Dirac cone. One other method of choice is Scanning Tunneling Microscopy and Spectroscopy (STM/S) with its ability to get local insight into the single-particle spectrum [18]. It is extremely surface sensitive and can be conducted at ultra-low temperatures, in magnetic fields and with energy resolution in the meV-range or even below. As such, STM/S is well suited to investigate surfaces of topological quantum matter [19,20,21], specifically in cases where the involved energy scales are as small as in the correlated topological insulators SmB${}_6$ [22].

As a result of the extreme surface sensitivity of STM, a clean and atomically flat surface is often required for the successful spectroscopic analysis of the material’s electronic structure: if the investigated surface is rough on an atomic level, then the local environment of the surface atoms may differ from the one of the same atom in the bulk. Of course, this issue adds to the already incurred modified material properties at the surface of any solid (see e.g., the discussion in [23]) or possible surface reconstructions. As a consequence, special attention may have to be paid to the preparation of clean surfaces for STM investigations. Established methods here are in situ deposition of thin films or in situ cleaving of bulk samples. The latter can easily be conducted on van-der-Waals-bound layered materials (like Bi${}_2$Te${}_3$ [24]). However, for materials with a more three-dimensional (3D) crystallographic structure (like SmB${}_6$ [25]) cleaving can be a challenge. It should be noted that surface preparation for ARPES measurements is not quite as involved as for STM but it may need to receive some attention nonetheless [26].

We here report on STM investigations on two materials: ZrTe${}_2$ and TmB${}_4$. The former is a member of the extensively studied group of transition-metal dichalcogenides [27] and is discussed as a topological Dirac semimetal [28,29,30,31]. Moreover, signatures of a weak Kondo effect have been reported [32]. On the other hand, the material TmB${}_4$ crystalizes in a Shastry–Sutherland lattice which gives rise to frustrated magnetic behavior and, in particular, to fractional plateaus in its magnetization curves [33]. Interestingly, topology is mentioned as one possible reason for the fractional plateau phase [34,35], and the related compound PuB${}_4$ is discussed to be a strong topological insulator [36]. For both materials, our spectroscopic results by STS reveal substantial discrepancies compared to the results of bulk band structure calculations. These discrepancies are likely (at least in part) related to the extreme surface sensitivity of STS and highlight the need for further experimental and theoretical efforts to gain a comprehensive understanding of such materials, specifically with respect to applications.

2. Samples and Experiments

In the first synthesis step, microcrystalline ZrTe${}_2$ was obtained starting from a molar powder mixture of the elements zirconium (99.2% Alfa Aesar) and tellurium (99.999% Alfa Aesar) annealed at 600 ${}^{°}$C in the presence of iodine (99.998% Alfa Aesar) in an evacuated fused silica ampoule for one week. In the second step, single crystals of ZrTe${}_2$ were grown from this microcrystalline powder by chemical vapor transportation with iodine (4 mg/mL) as a transport additive. Here, a temperature gradient from 700 ${}^{°}$C (source with starting material) to 800 ${}^{°}$C (sink with deposited crystals) was applied. Single crystals grew in the shape of well-formed, several mm wide platelets along the crystallographic a–b directions with heights (along c) of order 0.2 mm. The characterization of the single crystals was conducted by electron probe microanalysis (EDXS) and X-ray powder diffraction; the latter confirmed the hexagonal structure (space group $P\overline{3}m1$ with lattice constants $a=$ 3.952 Å and $c=$ 6.66 Å), see Figure S1. For STM, ZrTe${}_2$ was cleaved along the crystallographic c direction, i.e., by breaking the van-der-Waals bonds.

TmB${}_4$ samples were cut from a single crystalline rod grown by an inductive, crucible-free-zone melting method described in detail in [37] (see also Supplementary Materials Section II and Figures S2 and S3). The lattice constants of the tetragonal lattice (space group $P4/mbm$, see Figure 1) are $a=$ 7.05 Å and $c=$ 3.98 Å. For STM measurements, samples were attempted to cleave along the $ab$ plane.

STM investigations were conducted using an ultra-high vacuum (UHV) system [38]. If not stated otherwise, the presented STM/STS data were obtained at its base temperature of $T=$ 4.6 K using electrochemically etched tungsten tips. STS was performed by utilizing a lock-in technique; to this end, a small ac modulation voltage $V_{\mathrm{mod}}$ of 1.0 mV with a frequency of 117 Hz was added to the bias voltage $V_{\mathrm{b}}$. In some cases, the reported STM data were obtained in a dual-bias mode, i.e., two different bias voltages (typically of opposite sign) were applied for the forward and backward scan of the fast scan direction. Bias voltage $V_{\mathrm{b}}$ and set-point current $I_{\mathrm{sp}}$ are given in the respective caption of each topography.

To avoid possible degradation, the ZrTe${}_2$ sample investigated here was stored and prepared for cleavage inside an Ar-filled glove box. All samples were cleaved in situ at a temperature of ∼20 K. After cleaving, the samples needed to be transferred from the cleaving stage into the STM head, during which time (few tens of seconds) the sample temperature is not controlled. Because of its layered structure, ZrTe${}_2$ cleaves easily and is exposed to large atomically flat surface areas. We, therefore, investigated one cleaved surface at numerous different positions. In contrast, TmB${}_4$ is very difficult to cleave and atomically flat areas could be found only rarely (see also Section 3.2.1 below). In order to, nonetheless, ensure the reproducibility of our results, cleaves of three TmB${}_4$ samples were studied.

3. Results

3.1. ZrTe₂

3.1.1. Topography

Figure 2 exhibits a topography overview of a cleaved ZrTe${}_2$ surface. The hexagonal structure can clearly be recognizedm along with two types of defects: the triangularly shaped elevations with an extension of five protrusions and single missing atoms. Given the crystalline structure of ZrTe${}_2$, the top-most layer of this material is expected to consist of Te atoms exclusively. A zoom into an almost defect-free area of $5\times 5$ nm${}^2$, Figure 3a, reveals a distance between the protrusions of approximately 0.38 nm, see the blue line in Figure 3a and corresponding height profile in Figure 3b. Note that this topography resembles those reported in [39], except for the STM-measured distance between the protrusions which is, in our case, in very good agreement with the lattice constant a. The presented topographies testify to an excellent overall sample quality and confirm that, primarily, only the top-most Te layer is visualized.

The very few single-site dents observed for positive and negative bias voltage in Figure 2 can certainly be related to missing Te atoms in the Te top-most layer (see also discussion in [40]). In contrast, the more numerous triangularly shaped defects extend over several lattice sites and appear to exhibit different contrast for opposite bias voltages in Figure 2. Very similar defects have been observed on ZrTe${}_2$ [41], but also on TiSe${}_2$ [40,42,43]. Specifically, the comparison to the latter suggests that these triangular defects may be caused by intercalated Zr atoms, i.e., by Zr at positions between two van der Waals-bound Te layers. The distinctive shape of this type of defect—three neighboring Te atoms in the top-most Te layer appearing bright—for negative $V_{\mathrm{b}}$ (Figure 2 right) compared to the less bright appearance for positive $V_{\mathrm{b}}$ (left) points to an electron-donating defect, in line with its assignment to an intercalated Zr [44]. However, in contrast to the observations of TiSe${}_2$ where the intercalated Ti atoms were discussed in relation to a charge density wave (CDW) [42,43], we could not detect any indication of such a CDW in our ZrTe${}_2$ (see also STS results below). To the best of our knowledge, a CDW has only been reported for single-layer ZrTe${}_2$ [45].

3.1.2. Spectroscopy

As mentioned above, much of the recent interest in ZrTe${}_2$ stems from its classification as a topological semimetal [28,29,30,31]. Hence, STS was conducted on ZrTe${}_2$ surfaces. The spectroscopy results presented in Figure 4a were obtained on the surface shown in Figure 4b. The spectrum averaged over the total area does not much differ from the one obtained within the predominantly defect-free area (red rectangle), i.e., we did not observe any significant differences in the local spectra despite the three obvious defects within the total area of Figure 4b. As is clearly revealed in the inset, the density of states (DOS) in close vicinity of the Fermi energy $E_{\mathrm{F}}$ is small but finite (at least at the surface). This behavior is in line with expectations for a semimetal [30] and the dI/dV follows the parabolic shape, as observed for similar semimetals, e.g., MoTe${}_2$ [46]. We also note that the formation of a CDW in a single layer of ZrTe${}_2$ resulted in a gap of ∼25 meV near $E_{\mathrm{F}}$ [45]. The absence of such a gap in our spectra is then a strong indication for the absence of a CDW in our bulk material, at least down to $T=$ 4.6 K.

It is instructive to compare the measured dI/dV, Figure 4, to the calculated band structure and DOS of ZrTe${}_2$. In Figure 5, the results from [47,48,49] are reproduced within an energy range −2 eV $\le (E-E_{\mathrm{F}})\le$ +2 eV. The overall behavior of the total DOS with a very small magnitude at $E_{\mathrm{F}}$ compares favorably to the dI/dV-data of Figure 4. The peak at positive $V_{\mathrm{b}}$ can be recognized in the calculated DOS, albeit at a somewhat larger energy (0.74 eV in the calculations). Here, we note that in our measurements, the position of this maximum varied slightly between 0.47 V (as in Figure 4) and 0.54 V for different areas on the sample surface. Moreover, a different calculation found a (double-) peak situated at ∼0.30 V and ∼0.47 V, while the overall parabola-shaped dI/dV-curve with a minimum close to $E_{\mathrm{F}}$ is not reproduced [50,51,52,53,54]. These comparisons emphasize that details of the local electronic structure of the sample surfaces may vary slightly and may even be different from band structure of the bulk.

The appearance of a weak Kondo effect in ZrTe${}_2$ was reported based on transport measurements [32]. Typically, signatures of the Kondo effect can be seen in the dI/dV spectra [18,55,56,57]. Our tunneling spectroscopy, Figure 4, does not provide any indication for a Kondo effect being at play in ZrTe${}_2$. It should be noted, however, that the Kondo effect may be suppressed at a sample surface due to a reduced Kondo screening as, e.g., experimentally observed in SmB${}_6$ [58].

3.2. TmB₄

3.2.1. Topography

Rare-earth tetraborides typically crystallize in the tetragonal ThB${}_4$ structure where the B atoms form a continuous 3D network of octahedra and dimers, while the rare-earth atoms lie in planes perpendicular to the c axis forming a two-dimensional (2D) Shastry–Sutherland lattice [37] (cf. Figure 1). The resulting 3D conduction along with the 2D magnetism gives rise to the interest in TmB${}_4$ [59]. TmB${}_4$ is difficult to cleave, albeit with a slightly higher success rate compared to the hexaborides [25]. Only rarely did we observe the atomically flat surfaces as those shown in Figure 6, where only a few step edges are found (Figure 6b). The height of these step edges is estimated to be 0.41 nm (Figure 6c) and hence, confirms a cleave along the crystallographic c direction.

Zooming into such terraces reveals two different types of termination: Type A is presented in the atomically resolved surface of Figure 7 (left).

Here, the distance between the protrusions is estimated to be about 0.50 nm, corresponding to $a/\sqrt{2}\approx$ 0.498 nm. This, along with the linear arrangement of the protrusions, likely indicates a B-terminated surface instead of a Tm one in Figure 1b. Indeed, one may speculate that in the case of the red line, the tip scans over the apex B-atoms of the B octahedra in TmB${}_4$, while the blue line scan involves the dimer B atoms (in the latter case, the dimers are alternately aligned parallel and perpendicular to the scan direction). Such an assignment is supported by the distance between the red and blue lines of 0.25 nm $\approx \frac{1}{4}a\sqrt{2}$. A Tm terminated surface is unlikely since an equal number of squares and triangles of Tm would be expected to be observed in that case, along with a distance between Tm atoms of 3.62 Å.

A topography of termination type B is shown in Figure 8. Here, the individual protrusions can more easily be recognized, but there also is a larger number of defects present. The distance between protrusions of ∼0.7 nm fits well to the lattice constant $a=$ 0.705 nm. In this case, a Tm termination is unlikely given the overall square arrangement of the protrusions. We note that the topographies of Figure 7 and Figure 8 were obtained within different surface areas of the same sample, i.e., the underlying crystallographic alignment is identical. With the line scans shown in Figure 7 likely taken along the [110] crystallographic direction, the line scans of Figure 8 should correspond to the [100] direction. However, from a merely crystallographic viewpoint, a distance between protrusions of a along the main crystallographic direction is not expected. Here, one possibility that cannot be ruled out is a surface reconstruction. Similarly, superstructures may form at the surface as, e.g., observed on Fe${}_2$O${}_3$ [60]. Another intriguing possibility is an interplay between the electronic and magnetic degrees of freedom. At our measurement temperature of 4.6 K, TmB${}_4$ orders antiferromagnetically with the Tm moments pointing along the [001] direction [33,61] and resulting in a magnetic square unit cell of length a (see, e.g., [33]). One may speculate that this magnetic order has some influence on the topography of Figure 8, either by locally modifying the density of states or, if by chance our W tip had picked up a Tm atom from the surface and turned into a magnetic tip, by directly visualizing the magnetic order (see e.g., [25,62]). These possibilities have to be scrutinized by future investigations.

3.2.2. Spectroscopy

Tunneling spectroscopy averaged over the areas marked in Figure 6b is presented in Figure 9. In line with TmB${}_4$ being a metal [33,59], there is a large DOS found at $E_{\mathrm{F}}$. We note that the two dI/dV-curves are qualitatively very similar and rather featureless. The latter is consistent with the small crystal field energy scales suggested in [59] which cannot be resolved by our STS. Moreover, a featureless DOS near $E_{\mathrm{F}}$ has also been predicted in [63] (albeit without magnetic ordering). In contrast, strong peaks in the (spin resolved) DOS close to $E_{\mathrm{F}}$ were reported in [64] based on band structure calculations including strong electronic correlation effects, but not confirmed by our STS data. Here, we should note that the aforementioned calculations are bulk calculations, i.e., they did not take into consideration any surface termination (as, e.g., in the case of slab calculations). As a consequence, the calculated (bulk) DOS and the surface DOS can differ considerably. Clearly, further efforts are required to provide insight into the electronic band structure of TmB${}_4$.

Figure 9. Spectroscopy on TmB${}_4$ within the two areas (denoted as S1 and S2) marked by the same color in Figure 6b. Set point: $V_{\mathrm{b}}=+$0.8 V, $I_{\mathrm{sp}}=$ 0.6 nA.

Figure 9. Spectroscopy on TmB${}_4$ within the two areas (denoted as S1 and S2) marked by the same color in Figure 6b. Set point: $V_{\mathrm{b}}=+$0.8 V, $I_{\mathrm{sp}}=$ 0.6 nA.

4. Discussion

Both materials, ZrTe${}_2$ and TmB${}_4$, were successfully prepared for STM/S investigations by in situ cleaving. In the case of ZrTe${}_2$, excellent atomically resolved surfaces could be obtained effortlessly, as expected for this 2D compound. The observed defects point to a small number of intercalated Zr (from Figure 2 approximately one intercalated Zr per 56 unit cells) and a tiny amount of Te vacancies (about one vacancy per 500 unit cells) testifying the excellent quality of the material. Nonetheless, these defects may give rise to some amount of doping in this material [65]; in particular, intercalated Zr may act as an electron donor. Such doping effects may contribute to the fact that the calculated electronic band structure of ZrTe${}_2$ can only qualitatively be compared to the measured dI/dV-spectra. In addition, we wish to emphasize again that STS is extremely surface sensitive while the calculations of Refs. [47,48] were conducted for the bulk of the material.

Atomically flat surfaces of TmB${}_4$ could only rarely be located, similar to the case of the hexaborides [25]. Two different types of surfaces could be found, both of which are unlikely to correspond to Tm terminations. Our dI/dV-data clearly reflect the metallic nature of TmB${}_4$. Beyond this, however, a comparison between the DOS inferred from our STS and the results of band structure calculations is difficult.

Clearly, for both materials further insight from theory as well as from future experiments (including also ARPES) is highly needed. Here, we emphasize that, specifically if non-trivial topology is to be utilized in future applications, the materials properties of the surface play an important role.