Strong bulk-surface interaction dominated in-plane anisotropy of electronic structure in GaTe

19:17 09 junio in Sin categoría by Consultora CIS

Geometric and electronic structure of GaTe

Bulk GaTe is a monoclinic p-type semiconductor with the C2/m space group and possesses two kinds of Ga-Ga bonds with different orientations, one of which lies almost within the layer plane and the other is oriented in the out-of-plane direction. The primitive cell of bulk GaTe is shown in Fig. 1a. The cleavage plane of bulk GaTe corresponds to the (1 1 1) plane, thus the surface Brillouin zone (BZ) is obtained by projecting the first BZ of bulk onto the (1 1 1) plane of the reciprocal space as demonstrated in Fig. 1b. After the formation of surface, the Γ and Z points in bulk BZ fold to the \(\bar{\Gamma }\) point and the in-plane high-symmetry H-Z-L path of the bulk projects onto the \(\bar{{{{{{\rm{Y}}}}}}}\)–\(\bar{\Gamma }\)–\(\bar{{{{{{\rm{X}}}}}}}\) path of the surface. The GaTe band structure revealed by ARPES using He I α line is shown in Fig. 1c. The VBM is located at \(\bar{\Gamma }\) point, and the dispersion of highest valence band along the \(\bar{\Gamma }\)–\(\bar{{{{{{\rm{Y}}}}}}}\) direction is stronger than that along the \(\bar{\Gamma }\)–\(\bar{{{{{{\rm{X}}}}}}}\). The hole effective mass along x direction is about 3.5 times larger than that along y direction (Supplementary Fig. 1a). Meanwhile, the anisotropic valence bands can also be visualized by the constant energy surfaces (Fig. 1d). They exhibit two-fold in-plane symmetry from VBM to a binding energy of −0.5 eV. The valence band spectral intensity along \(\bar{\Gamma }\)–\(\bar{{{{{{\rm{X}}}}}}}\) direction is elongated, which implies a stronger dispersion of the highest valence band along y direction than that along x direction. The constant energy surface reveals a four-fold in-plane symmetry at a binding energy of −1.4 eV.

The origin of in-plane anisotropy of band structure in GaTe

In order to assess whether the observed anisotropy of energy band structure of GaTe originates from the low crystallographic symmetry, the band structure of monolayer (1 ML) GaTe is calculated by using PBE functional with the inclusion of spin-orbit coupling (SOC) effect. As shown in Fig. 2a, the direct band gap is located at \(\bar{{{{{{\rm{X}}}}}}}\) point, and the highest valence band dispersion along x direction is stronger than that along y direction. These results are inconsistent with our experimental observation, indicating that the in-plane anisotropy of energy band structure of GaTe obtained by ARPES doesn’t originate from the low crystallographic symmetry. Moreover, a higher specific surface area is expected in 1 ML GaTe as compared to its bulk counterpart and the surface effect dominates the electronic structure of the system. These results imply that the bulk effect plays an important role in the observed in-plane anisotropy of band structure of GaTe.

**Fig. 2: Comparison between anisotropic band structures for experiment and theoretical models.**

Therefore, the band structure of infinitely extended bulk GaTe is calculated. The geometric structure of bulk primitive cell is fully optimized by the optB88-vdW functional. The lattice parameters of GaTe bulk unit cell predicted by optB88-vdW functional are approximately 1.2–2.0% larger than those obtained in the experiment¹⁴, and better than those calculated by PBE functional (Supplementary Table 1). Figure 2b shows that the band structure of bulk model possesses a direct band gap at Z point. This agrees with previous theoretical results^12,21. Like 1 ML system, the hole effective mass along x direction is smaller than that along y direction for the bulk model, which doesn’t agree with our experimental result (Fig. 2c and Supplementary Fig. 1b, c). This suggests neither bulk nor surface effect could solely determine the observed in-plane anisotropy of energy bands of GaTe. Both the bulk and surface effect thus should be included in the theoretical model in order to interpret experiment.

We next perform the band structure calculation of a slab configuration with thickness of 7 ML GaTe. This configuration is built on the basis of bulk unit cell relaxed by optB88-vdW functional (Supplementary Fig. 2), in which the middle five layers are fixed as bulk region while the top and bottom mono-layer are regarded as surface region, respectively. The positions of surface atoms are also optimized by the optB88-vdW functional. As shown in Fig. 2d, the PBE + SOC method predicts that the VBM of GaTe slab model is located at \(\bar{\Gamma }\) point, and the highest valence band dispersion along \(\bar{\Gamma }\)–\(\bar{{{{{{\rm{Y}}}}}}}\) direction is stronger than that along \(\bar{\Gamma }\)–\(\bar{{{{{{\rm{X}}}}}}}\) direction. The hole effective mass along x direction is about 2.3 times larger than that along y (Fig. 2c and Supplementary Fig. 1d). These represent the anisotropic band structure of 7 ML slab model agrees well with our experimental result. Despite the agreement of calculation with experiment, the 7 ML slab model is not thick enough to eliminate the quantum confinement effect on the anisotropic band structure of GaTe. We then calculate the band structures for GaTe with thickness of 8, 9, 13, 16, 20, 25 and 30 ML. The geometric structures of all multilayer systems are fully relaxed by optB88-vdW functional. The Supplementary Fig. 3a shows the values of in-plane lattice constant and the band gap of the multilayer GaTe gradually converge and are close to those of bulk model as the thickness increases to 30 ML GaTe. The anisotropy of hole effective mass of 8 ML GaTe is consistent with that of 30 ML GaTe (Supplementary Fig. 3b and Supplementary Fig. 4), which indicates the quantum confinement effect doesn’t play a primarily role in the in-plane anisotropy of band structure of GaTe.

Moreover, Supplementary Fig. 5 shows that the ARPES intensities around Fermi level (E_F) as a function of the momentum k_y as well as the probing photon energy are rather slender (i.e. along the k_z direction). From these spectra, photon energies 20 eV and 30 eV seem to be corresponding to high-symmetry points, while an inner potential V₀ of 16.4 eV has been obtained which qualitatively agrees with the earlier experiments²¹. In contrast to the bulk model calculations where the band structures at Γ and Z points have obvious differences, the VBM at the aforementioned two different high-symmetry points are quite close and their dispersions are similar as shown in Supplementary Fig. 6. These results suggest that the k_z dispersion is considerably weak and GaTe doesn’t possess obvious surface states, which also agrees with early reported results²¹.

Furthermore, our band structure calculation for 7 ML slab model shows that the highest valence band is dominated by the p_z orbitals from bulk region (Fig. 2e, f). Here, we also performed the polarization-dependent ARPES measurements. The scheme of our polarization-dependent measurements is shown in Fig. 2g. According to the selection rule, the s(LV) polarization is sensitive to probe the p_y orbitals, while for the p(LH) polarization, the transition matrix element is nonzero only for photoemission originating from p_x and p_z orbital. Here, as we can see in Fig. 2h, for the highest valence band, the result of p(LH) polarization yields stronger spectral weight than that of s(LV) polarization, moreover, the valence bands between −1.5 and −2.0 eV below E_F that also dominated by the p_z orbital is significantly more distinguishable when probing with p(LH)-polarization. As for valence bands surrounding the \(\bar{\Gamma }\) point while locate at −1.0 eV and higher binding energies are dominated by p_x and p_y orbitals, these band features are both pronounced under different polarizations. The distinguishing spectral weight distributions between the two measurements illustrate that the highest valence band hosts a predominantly different orbital makeup compared to band structures reside at binding energies higher than −1.0 eV.

In the discussion above, we find that the experimentally measured in-plane anisotropy of energy bands in GaTe doesn’t originate from the low crystallographic symmetry and the quantum confinement effect, and could not be reproduced by the system solely involving the surface or bulk effect. Only by considering both the bulk and surface effect does the calculated anisotropic band structure of GaTe agree with the experimental observations. Hence, there exists a strong bulk-surface interaction which dominates the in-plane electronic structure anisotropy in GaTe. The influence of bulk on the surface is attributed to the interlayer coupling. To verify this, we perform band structure calculation for the 7 ML GaTe slab model with weakened interlayer coupling, in which the interlayer distances of the bulk region are 0.5 Å larger than the equilibrated ones. As shown in Supplementary Fig. 7a, the band structure of the system exhibits an indirect band gap. The VBM of the system is located at the point closed to \(\bar{{{{{{\rm{X}}}}}}}\) and contributed by both the p_z and p_xy orbitals (Supplementary Fig. 7b), instead of p_z orbitals predominantly. This feature is approximate to that of 1 ML GaTe, in which the VBM is dominated by the p_xy orbitals (Supplementary Fig. 7c). These results indicate that the interlayer coupling will reduce the surface effect in the multilayer GaTe, which is naturally included in the bulk system. However, the significant influence of the surface effect on the in-plane band structure anisotropy of GaTe remains even though the number of layers reaches 30 ML. As shown in Supplementary Fig. 3b, with the number of layers increasing to 30 ML, the hole effective mass along y direction gradually converges to that of bulk model, and a large difference between 30 ML and bulk GaTe could be found for x direction. As a result, 30 ML GaTe has an opposite in-plane anisotropy compared with that of the bulk model. This means that once the periodicity perpendicular to the cleavage plane of bulk GaTe breaks down, the highest valence band dispersion along x direction becomes much weaker than that along y direction. Therefore, the bulk-surface interaction originates from the interlayer coupling and out-of-plane periodicity breaking in GaTe.

Band structure evolution from monolayer to few-layer GaTe

The difference between the positions of VBM in 1 ML and 7 ML GaTe suggests a band structure evolution from monolayer to few-layer GaTe. To verify this, we provide theoretical calculations for the electronic structures of GaTe in dependence on the number of layers from 1 to 9. The geometric structures of all the systems are fully optimized using optB88-vdW functional. Supplementary Table 2 summarizes the structural parameters of few-layer GaTe. The in-plane lattice parameter of the system is non-monotonically increasing with thickness. The values of interlayer distances are in the range from 2.01 to 2.16 Å, which are much smaller than those in BP²⁰. The charge density difference between 6 ML and 1 ML GaTe shows electron accumulation in the interlayer region of GaTe, indicating strong interlayer coupling in GaTe (Supplementary Fig. 8). As shown in Fig. 3a–i, the band structures calculated by PBE + SOC method for few-layer GaTe suggest the system experiences a direct-indirect-direct band gap transition with the thickness increasing from 1 to 5 ML.

**Fig. 3: Layer-dependent band structures in GaTe.**

We further analyze the orbital-projected band structures of GaTe for the number of layers from 1 to 6. As shown in Supplementary Fig. 9a, both the CBM and VBM of 1 ML GaTe situated at \(\bar{\Gamma }\) are derived from the delocalized out-of-plane p_z orbitals. When two monolayers are stacked to form 2 ML GaTe, the VBM of \(\bar{\Gamma }\) point is lifted in energy relative to that of \(\bar{{{{{{\rm{X}}}}}}}\), and the positions of CBM and VBM shift from \(\bar{{{{{{\rm{X}}}}}}}\) to the points close to \(\bar{\Gamma }\) and \(\bar{{{{{{\rm{X}}}}}}}\), respectively, as a result of strong interlayer coupling. This induces a direct-to-indirect band gap transition. The 2, 3 and 4 ML GaTe are indirect band gap semiconductors, in which the VBM and CBM are composed of p_xy and p_z orbitals (Supplementary Fig. 9b–d). When the number of layers reaches 5, the VBM and CBM shift to \(\bar{\Gamma }\) point and are dominated by the p_z orbitals (Supplementary Fig. 9e), leading to an indirect-to-direct band gap transition. As shown in Fig. 3j as well as in Supplementary Fig. 1b and Supplementary Figs. 10, 11, the in-plane anisotropy of hole effective masses is reversed with the number of layers, and the ratio between hole effective masses along x and y directions reaches minimum and maximum value in 3 ML and 5 ML GaTe, respectively. In contrast to the layer-dependent anisotropy of hole effective mass, the anisotropy of electron effective masses shows layer-independent feature. Moreover, we conduct angle-resolved polarized Raman measurement for GaTe thin films with thickness of 3.53, 4.87 and 6.47 nm encapsulated by hexagonal boron nitride (h-BN). The optical microscopy images, Raman maps and atomic force microscope (AFM) height profiles of GaTe thin films are shown in Supplementary Fig. 12. The polarized Raman spectra exhibit strong in-plane anisotropy of the Raman intensity which is consistent with that of bulk GaTe (Supplementary Figs. 13, 14). This indicates that the GaTe thin flake may be very sensitive to ambient conditions, though a monoclinic to hexagonal phase transition with the decreasing of the GaTe layer thickness has been reported before^14,22. Our results demonstrate that the GaTe monoclinic phase is robust for the flake thickness down to 3.5 nm, and the anisotropic band structure evolution with thickness for GaTe is potentially feasible.

Previous studies show the quantum confinement effect plays an important role in the band gap evolution of layered materials^23,24. We thus use the empirical equation E = A/N^α + E_bulk, where E is the band gap of multilayer GaTe, N is the number of layers and E_bulk is the band gap of bulk GaTe, to evaluate the influence of quantum confinement effect on evolution of band gap for GaTe. The fitted parameters A, α and E_bulk are 0.70 eV, 0.79 and 0.68 eV, respectively. As shown in Fig. 3k, the band gap of GaTe decreases as the thickness increases, following the 1/N^0.79 power law. The fitting exponent is smaller than the values of the infinite potential well model and BP²³, which suggests both quantum confinement and strong interlayer coupling control the band gap evolution of GaTe.

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