Epitaxial HfTe₂ Dirac semimetal in the 2D limit

Topological materials have recently emerged and gained attention due to their unique electronic properties for realizing both fundamental physics and technological applications.^1–10 A particular class of topologically non-trivial matter, known as “three dimensional (3D) graphene,” is the Dirac semimetals, which possess crossing linearly dispersive valence and conduction bands.^11,12 To date, the majority of 3D Dirac semimetals has been grown by bulk methods and appears in the bulk form, while their epitaxial growth results in defective and discontinuous films.^13–15 Only recently, it has been shown that high quality crystalline ZrTe₂, HfTe₂, and Hf_xZr_1−xTe₂ thin films, whose electronic band structure exhibits similar behavior^16–18 with the already proven 3D Dirac semimetals, can be grown epitaxially on InAs(111) and AlN(0001) substrates.

Recent theoretical calculations^19,20 predict that both ZrTe₂ and HfTe₂ materials possess topological properties. However, experimental results are not yet conclusive. Magnetotransport measurements of ZrTe₂ thin films²¹ reveal a negative magnetoresistance in a parallel magnetic and electric field configuration, which is probably ignited by the chiral anomaly effect, which is related to topological semimetals. In addition, nuclear magnetic resonance in bulk ZrTe₂ single crystals²² reveals that ZrTe₂ is a quasi-two dimensional (2D) Dirac semimetal with a nodal line between Γ and A. Regarding HfTe₂, magnetoresistance measurements in bulk crystals²³ revealed a large and unsaturated magnetoresistance effect, which, however, the authors attributed to the semimetallic nature of HfTe₂ with coexisting electrons and holes on the Fermi surface and the additional strong orbital mixing of Te p and Hf d states, excluding the presence of topological features in the material. Despite their topological properties, both ZrTe₂ and HfTe₂ materials offer the prospect of new functionalities since they may exhibit superconductivity and charge density waves,²⁴ strain induced enhancement of thermoelectric figure-of-merit,²⁵ positive value of the nonlinear refractive index coefficient,²⁶ and selective NO gas sensing.²⁷ 

Band structure calculations^23,28,29 along with Angle Resolved Photoelectron Spectroscopy (ARPES) measurements^30,31 of both ZrTe₂ and HfTe₂ films reveal a Dirac-like cone band at the center of the Brillouin zone and a Dirac point with band crossing along the high-symmetry Γ-A path in the Brillouin zone, which is located above the Fermi level. However, the location of the Dirac point is too far from the Fermi level, restricting the effect of Dirac fermion on transport properties. Doping with alkali metals, a commonly used strategy in ARPES experiments, may change this situation and engineer the properties of HfTe₂. However, the electronic structure of HfTe₂ and ZrTe₂ films can undergo significant changes upon potassium and chromium intercalation.^31–33 Appropriate electron doping from the substrate can be an alternative non-destructive way to alter the Fermi level at will.

In this work, we investigate the growth of 1ML HfTe₂ on various substrates to examine their influence on the HfTe₂ electronic structure. We employ three substrates, namely, InAs(111), MoS₂, and SiC/graphene, in order to cover a range of substrate electronic (metallic to semiconducting) and structural properties (2D to 3D). Combined Reflection High-Energy Electron Diffraction (RHEED), Scanning Tunneling Microscopy (STM), and Angle Resolved Photoelectron Spectroscopy (ARPES) indicate that 1ML HfTe₂ is grown epitaxially on all three substrates and the valence bands exhibit a Dirac-like cone independent of the substrate, showing that these bands originate from the material itself and are not hybridized bands coming from the interaction between the epilayer and the substrate. A difference in the energy position of the aforementioned HfTe₂ valence bands from one substrate to another is observed, which is attributed to the influence of the substrate due to possible electron doping.

The surface of the 1ML HfTe₂ epitaxial film grown on the Si(111)/InAs(111) substrate at the temperature of 450 °C (all growths on different substrates have been performed at the same temperature) is investigated by in situ room temperature ultra-high vacuum (UHV)-STM (Fig. 1). Figure 1(a) shows a large area scan of 200 × 200 nm² where only HfTe₂ areas are visible, indicating that there is a full coverage of the substrate. Moiré patterns, which also cover the entire surface, are also visible, which are attributed to the interaction of the HfTe₂ layer with the Si(111)/InAs(111) substrate. These patterns are typical of the growth of only one monolayer HfTe₂ epilayer, while thicker films do not show Moiré patterns. The surface morphology shows that the film is grown in a 2D island form, and the observed steps [Fig. 1(a), linescan across a step] with a height of ∼3.50 Å are assigned to InAs(111) substrate steps,¹⁶ which are “imprinted” in the epitaxial layer. One monolayer HfTe₂ is also grown on the SiC/graphene substrate, keeping the same temperature (450 °C) and rate growth (1ML/30 s) as in the case of Si(111)/InAs(111). A large area of 200 × 200 nm² is shown in Fig. 1(b). From this figure, we can deduce that HfTe₂ on graphene is grown in a nearly 2D form since only a portion of the second HfTe₂ monolayer is grown on top of the first monolayer before the substrate is fully covered. From the linescan in this figure, it can be inferred that the height of 1ML HfTe₂ is ∼6.60 Å. A high resolution image (10 × 10 nm²) of the HfTe₂ epilayer along with the corresponding Fast Fourier transform (FFT) is presented in Fig. 1(c). The hexagonal crystal structure of the HfTe₂ epilayer is clearly observed from both the real and reciprocal (FFT) space images, and its lattice constant is calculated at ∼4.0 Å.

The substrate and epilayer surface ordering and reconstruction are controlled by in situ RHEED (Fig. 2). The RHEED patterns along the [1-10] azimuth of InAs(111) prior and after 1ML HfTe₂ growth are shown in Fig. 2(a). After the cleaning process, a 2 × 2 reconstruction of the InAs(111) surface is observed, as expected for a clean (oxygen-free) In-terminated InAs(111).³⁴ After the HfTe₂ growth, extra sharp streaks attributed to HfTe₂ are observed in the RHEED patterns, confirming that flat HfTe₂ grows epitaxially on the InAs(111) substrate. Despite the appreciable lattice mismatch (−6.6%) between the epilayer and the substrate, HfTe₂ films are grown with a good crystalline quality, which is characteristic of quasi-van der Waals (vdW) epitaxial growth, where a 2D epilayer is grown on a 3D substrate. In those cases,³⁵ the effect of the lattice mismatch is considered as negligible due to the weak interactions at the interface of the two materials and strain is generally reported to be relaxed. It should be mentioned that 30° rotational domains are rarely observed in the quasi-vdW heteroepitaxy, as in our case, while the formation of stacking faults such as 60° twins cannot be excluded.³⁵ However, the latter cannot be identified by the RHEED method. Figure 2(b) shows the RHEED patterns of MoS₂ prior and after 1ML HfTe₂ growth along the aforementioned direction. The streaky pattern of 1 monolayer HfTe₂ films indicates smooth, well-ordered surfaces without any 30° rotational domains. Just like in the two previous cases, 1ML HfTe₂ is grown in a rotationally aligned mode relative to the graphene substrate [Fig. 2(c)]. However, a significant amount of 30° rotational domains is observed since [11-2] HfTe₂ domains are intermixed with [1-10] HfTe₂ domains as is evident from the RHEED picture of Fig. 2(c), which is grabbed along the [1-10] azimuth of the HfTe₂ epilayer. Rotated in-plane orientations, 30° as well as 60°, are often observed in the case of vdW heteroepitaxy, where a 2D epilayer (HfTe₂) is grown on top of a 2D substrate (graphene),^35,36 which are related to the very weak interactions, weaker than those in the quasi-vdW heteroepitaxy case, at the interface of the two materials. The weaker interactions in the case of the vdW compared to quasi-vdW heteroepitaxy are also obvious from the STM measurements of Fig. 1, where in the case of HfTe₂ growth on InAs, Moiré patterns cover the whole surface, indicating a stronger interaction between the epilayer and the substrate. Using the InAs(111), MoS₂, and graphene RHEED patterns as reference and knowing that the lattice constant of bulk InAs(111), MoS₂, and graphene is 4.28, 3.16, and 2.46 Å, respectively, the lattice constant of the hexagonal HfTe₂ lattice is estimated to be in the range of 3.96–3.98 Å.

The 1ML HfTe₂ electronic valence band structure is imaged along the ΓM direction of the Brillouin zone using HeI (21.22 eV) excitation energy for all substrates (Fig. 3). For the case of 1ML HfTe₂ on InAs(111) [Fig. 3(a)], a clear Dirac-like cone feature is observed at the center of the Brillouin zone, with its apex located about 0.05 eV below the Fermi level similar to that observed in the case of 1ML ZrTe₂ on InAs(111)¹⁶ but in contrast to undoped bulk HfTe₂ single crystals^32,33 and theoretical^23,28,29 results where the apex is located above the Fermi level. This cone-like band overlaps with a downward parabolic one at the M point of the Brillouin zone indicative of the semimetallic behavior of the thin HfTe₂ layer. In addition to the cone-like band at the Γ point, two more bands are observed, one parabolic and one with a M-like shape at about −0.75 and −2.1 eV, respectively. Both bands are also observed in thick HfTe₂ samples,^18,32 although the first one, in the case of the thick samples, is closer to the cone-like band than that of the 1ML case. Figures 3(b) and 3(c) show the valence band structure of 1ML HfTe₂ on SiC/graphene and MoS₂ substrates, respectively. In those cases, the valence band structures are similar to the case of 1ML HfTe₂ on InAs(111) with the only difference that the band structures in the latter cases have shifted upward by about 0.2 and 0.35 eV. As is evident, the Fermi energy cut the cone-like bands below their apexes, while the parabolic bands in the M point are either barely visible or totally invisible. ARPES measurements in the three aforementioned cases highlight two important points. First, the band structure that is mapped with ARPES is that of the HfTe₂ epilayer itself and is not a hybridized band structure originating from the interaction between the epilayer and the substrate. It should be noted that although, at least in the case of the InAs substrate, there is an interaction evident from the existence of the Moiré patterns [Fig. 1(a)], this interaction is probably weak since it does not cause any change in the ARPES pictures (Fig. 3) among the three aforementioned cases. Second, there is possibility of altering the Fermi energy as desired by choosing the appropriate substrate as the template for the growth of the HfTe₂ epilayer. In the case of a 2D semiconducting van der Waals substrate such as MoS₂, which exhibits a large energy gap in the range of ∼1.29 to 1.90 eV depending on its thickness,³⁷ the Fermi energy cut the cone-like band at about 0.3 eV below its apex since there is no possible electron doping from the substrate. In this case, the Dirac point along the high-symmetry Γ-A path in the Brillouin zone is located far above the Fermi level, restricting the effect of Dirac fermions on transport properties. On the other hand, a conducting substrate, such as InAs(111), or a semimetallic one, such as graphene, can dope HfTe₂ with electrons lowering their energy bands and bringing the Dirac point closer to Fermi energy.

Figure 4 shows the k_x − k_y constant energy contour plots (CECPs) where portions of the k-space at different binding energies below the Fermi level are imaged for the three aforementioned cases. The conical shaped bands for the three cases around the Γ-point are visible and indicated with blue dashed lines. The linear variation of the conical bands indicates Dirac-like dispersion, which is characteristic of massless particles. The Fermi velocity can be calculated from both Figs. 3 and 4 using the E = ℏv_Fk relation to be ∼0.7 × 10⁶ m/s. For the case of 1ML HfTe₂ grown on the InAs(111) substrate [Fig. 4(a)], a point-like feature at the Γ-point at the Fermi level is visible corresponding to the apex of the Dirac-like cone in agreement with Fig. 3(a). Also visible, at the Fermi level, is the edge of the energy band at the high symmetry point M at k_x ∼ 0.5 Å⁻¹. As mentioned above, the energy band at the M point is not visible for the cases of 1ML HfTe₂ on graphene and MoS₂ [Figs. 4(b) and 4(c)], since the energy bands are shifted upward by 0.2 and 0.35 eV, respectively, relative to the 1ML HfTe₂/InAs case due to different amounts of doping among the various substrates and HfTe₂ epilayer. This band shift caused by possible substrate doping is also responsible for the cone apex shift above the Fermi level for the 1ML HfTe₂ on graphene and MoS₂ cases. In these cases, we observe a circular feature at the Fermi level instead of a point-like feature, as in Fig. 4(a). As we move away from the Fermi level and for binding energies smaller than −0.6 eV, the CECPs show a structure consisting of two conelike bands with hexagonal distortions, one within another in agreement with Fig. 3.

In order to estimate the surface density of the doping electrons, we performed quantum mechanical calculations based on density-functional theory (DFT) using the plane-wave code VASP.³⁸ We assumed a free standing monolayer of HfTe₂ with the in-plane lattice constants fixed to the experimental values (3.967 Å). Furthermore, the vacuum distance between two monolayers was set to 30 Å. We used the Perdew–Burke–Ernzerhof (PBE) functional for approximating the exchange–correlation interactions³⁹ and the projector-augmented wave method for describing the electron–ion interactions.⁴⁰ The kinetic energy cutoff for the plane waves was set to 400 eV. Sampling of reciprocal space in total energy calculations was performed with the Monkhorst–Pack⁴¹ method. We used a 30 × 30 × 1 k-point dense grid for the integration in reciprocal space. By tuning the number of electrons per unit area and calculating the Fermi energy shift in each case, we were able to have an estimate of the electron surface density that could induce the experimentally observed Fermi energy shifts. In Fig. 5, the correlation between the Fermi energy shift and the doping electron surface density is depicted. Thus, for the case of the InAs substrate, the calculated electron surface density is 5.5 × 10¹³ electrons/cm², whereas for graphene, it is 3.2 × 10¹³ electrons/cm².

In summary, 1ML HfTe₂ semimetallic films are grown on three different substrates, namely, Si(111)/InAs(111), SiC/graphene, and sapphire/MoS₂ in order to study the substrate effect on the electronic properties of the HfTe₂ epilayer. The electronic band structures for the three cases are very similar, which leads to the conclusion that the HfTe₂ epilayer does not interact, at least to a great extent, with any of the substrates to form hybridized bands and the energy bands are exclusively of the HfTe₂ material itself. Although the band features are identical, an energy band shift among the three aforementioned cases is observed. On the other hand, when 1ML HfTe₂ is grown on the semimetallic graphene, the energy bands move downward due to possible electron doping from the substrate. The doping effect is more pronounced in the case of HfTe₂ growth on the highly doped metallic InAs, enabling us to shift the Fermi level at will in a non-destructive way. With the appropriate substrate, we could move the position of the Dirac point closer to the Fermi energy in order to benefit from the Dirac fermion behavior on transport properties of HfTe₂.

This work was supported by the Horizon 2020 projects SKYTOP—“Skyrmion-Topological Insulator and Weyl Semimetal Technology” (Grant No. 824123) and MSCA ITN SMART-X (Grant No. 860553), the Hellenic Foundation for Research and Innovation and the General Secretariat for Research and Technology [Grant No. 435 (2D-TOP)], and the FLAG-ERA project MELoDICA. This work was also supported by computational time granted from the Greek Research and Technology Network (GRNET) in the National HPC facility—ARIS—under Project No. pr011001-“2D-MAGTOP.”

The data that support the findings of this study are available from the corresponding author upon reasonable request.