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1Physics of Complex Systems, 2024, vol. 5, no. 1 _www.physcomsys.ru
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Physics of Semiconductors. Computational materials science
UDC 538.913 EDN SUQFNX
https://www.doi.org/10.33910/2687-153X-2024-5-1-30-38
Uniaxial pressure modulation of two-dimensional materials: Insights into the structure and electronic properties
of MoTe2 and Sb2Te3
R. S. Stepanov H 1
1 Herzen State Pedagogical University of Russia, 48 Moika Emb., Saint Petersburg 191186, Russia
Author
Roman S. Stepanov, ORCID: 0000-0003-2559-7598, e-mail: stepanovroman@herzen.spb.ru For citation: Stepanov, R. S. (2024) Uniaxial pressure modulation of two-dimensional materials: Insights into the structure and electronic properties of MoTe2 and Sb2Te3. Physics of Complex Systems, 5 (1), 30-38. https://www.doi.org/10.33910/2687-153X-2024-5-1-30-38 EDN SUQFNX
Received 16 January 2024; reviewed 6 February 2024; accepted 6 February 2024.
Funding: The research was supported by the Ministry of Education of the Russian Federation as part of the state-commissioned assignment project No. VRFY-2023-0005.
Copyright: © R. S. Stepanov (2024). Published by Herzen State Pedagogical University of Russia. Open access under CC BY-NC License 4.0.
Abstract. This research focuses on DFT modeling of the effects of uniaxial pressure on the electronic and structural properties of two-dimensional materials, such as MoTe2 and Sb2Te3. Special attention is given to the reconfiguration of the van der Waals (vdW) gap. Intuitively, the application of uniaxial pressure is expected to reduce the distance between layers, leading to a transition from 2D to 3D. Investigations under uniaxial pressure on Sb2Te3 revealed metallization at 3 GPa. Further pressure increase induces a phase transition at 7 GPa, resulting in the disappearance of the vdW gap in the new phase. However, a transition to a bulk phase does not always occur. In the case of MoTe2, pressure leads to an isostructural transition to a metallic state at 10 GPa. A further increase in pressure to 37 GPa causes a phase transition to a two-dimensional structure with a change in the orientation of the vdW gap. It is crucial to note that this MoTe2 case is analogous to the situation observed in GaSe after relaxation, which is also the subject of the study.
Keywords: 2D semiconductors, van der Waals interaction, DFT, uniaxial pressure, MoTe2, Sb2Te3, structural transitions
Introduction
Among various techniques of manipulating quantum mechanical effects in materials, strain engineering has emerged as a powerful and versatile tool. In this field, layered materials, characterized by covalently bonded layers held together by weak van der Waals (vdW) forces, have become particularly promising. Applications vary from microchip production (Benck et al. 2014; Gao et al. 2013; Li et al. 2019; Pan et al. 2019; Wang et al. 2014) to supercapacitors and phase-change memory devices (Lee et al. 2020; Mu et al. 2021; Peng et al. 2014; Pumera et al. 2014; Raty, Noé 2020; Wang et al. 2014). The discovery of topological materials (Bernevig et al. 2006; Chen et al. 2009; Kane, Mele 2005a; Konig et al. 2007) with their unique properties has further expanded the horizons of materials science, particularly in the field of straintronics. Topological materials have attracted considerable attention due to their distinctive features. For instance, the inversion of the band gap at an odd number of time-reversed points in the Brillouin zone (Bernevig 2013; Kane, Mele 2005b; Qi, Zhang 2011) leads to interesting properties such as locking the spin momentum of surface states (Singh, Prasad 2016) and the magne-toelectric effect (Tominaga et al. 2015).
In dichalcogenides, monochalcogenides, and certain topological insulators (such as Sb2Te3), fine-tuning the properties by altering the interlayer distance appears feasible, due to the strong dependence of the electronic and optical properties on the width of the vdW gap (Fan et al. 2015; Stepanov et al. 2023b; Zhao et al. 2015). As the vdW gap width decreases, a transition from a layered material to a bulk one is expected, leading to radical changes in properties related to structure and non-covalent interactions. However, the anticipated transition from quasi-2D to 3D may not occur (Stepanov et al. 2023a). Therefore, it is crucial to elucidate how noncovalent interactions are distributed during the disruption of the vdW gap and how it affects the geometry and properties of the new phase.
Due to the small band gap in Sb2Te3 and MoTe2, metallization is expected to occur before the structural phase transition. Indeed, for both Sb2Te3 and MoTe2, external hydrostatic pressure can lead to isostructural phase transitions (IPT), often resulting in anomalies in mechanical, electrical, thermodynamic, and vibrational properties (Bera et al. 2020; Zhao et al. 2015). In this context, interlayer interaction plays a pivotal role; it has been reported that neglecting vdW may lead to the erroneous conclusion that no IPT occurs in the material (Gomis et al. 2011; Zhao et al. 2015). Studying the influence of uniaxial pressure can contribute to a better understanding of the role of vdW interaction in this process.
In this study, in order to generalize and identify patterns in the transformation of non-covalent interactions in layered materials under uniaxial compression, we examine the structure and properties of the representatives of the most promising layered materials (MoTe2 dichalcogenides and Sb2Te3 topo-logical insulators). Another important aspect of the study is to consider the influence of non-covalent interactions on the structure after the phase transition and how it affects the IPT.
Computational details
Calculations were performed using the CASTEP quantum chemistry package (Clark et al. 2005). The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) parameterization (Ernzerhof, Scuseria 1999) with vdW corrections, important for describing interaction between the layers, was used. The vdW interactions were taken into account using the Grimme method (Grimme 2006; Grimme et al. 2010; 2011). The k space integrals and plane wave basis sets were chosen to ensure total energy convergence at 1 meV/atom. It was found that a kinetic energy cut-off of 500 eV is sufficient for all calculations. Two-Point Steepest Descent (TPSD) algorithm was chosen for the optimization in CASTEP. Such algorithm had previously (Barzilai, Borwein 1988) showed computational structures in best agreement with experimental ones, especially with the application of pressure. Pressure modeling was carried out using uniaxial pressure along the c axis of conventional cells. To carry out relaxation, the structures were optimized at a pressure of 0 GPa.
To study the bonds in phases under pressure, the electron density difference analysis (CDD) was used. For a more detailed study of the vdW interaction, the CRITIC2 code was used (Otero-de-la-Roza et al. 2009; 2014), in which the analysis of the electron density gradient (RDG) between molecular fragments (Johnson et al. 2010) was used to assess their strength.
Results
For the first investigated material, MoTe2 (Fig. 1 (a, b)), as the applied uniaxial pressure increases up to 37 GPa, the valence angle decreases, but the overall structure remains unchanged. However, at a pressure of 37 GPa, a significant transformation occurs as the vdW gap collapses due to the formation of metal-chalcogen bonds through the gap. Simultaneously, based on the CDD analysis, it is observed that covalent bonds perpendicular to the Z axis are disrupted, leading to the rotation of the vdW gap and its reorientation along the Z axis (refer to Fig. 1 (c, d)). It is noteworthy that during this rearrangement, both molybdenum and tellurium maintain coordination consistent with the original structure, albeit violating the octet rule. With an even greater increase in pressure, a lateral displacement of the layers relative to each other occurs. A similar result was also observed for PbS2 in (Lei et al. 2020).
Fig. 2 illustrates the band structures of MoTe2 under varying pressures. Initially, under uniaxial pressure, the band gap is an indirect gap between the maximum of the valence band (VB) at point r and the minimum of the conduction band (CB), located between G- and K-points (Fig. 2 (c)). Upon closer examination, it becomes apparent that the band gap gradually decreases and approaches zero with increasing pressure, attributed to a reduction in the interlayer distance. Band overlap starts at 10 GPa between the top of the valence band and the bottom of the CB (Fig. 2 (e)). Our calculations align with experimental
Fig. 1. Transformation of the MoTe2 structure under the influence of axial pressure: (a)-(b) Initial structure (side and top view respectively), (c)-(d) New phase at 37 GPa (side and top view respectively)
measurements, where the onset of metallization occurs at a hydrostatic pressure of 9.6 GPa (Zhao et al. 2019).
With pressure increase, both the CB and VB experience energy shifts due to enhanced interlayer electronic coupling. At a pressure of 20 GPa (Fig. 2 (f)), the CB minimum and VB maximum intersect the Fermi level, signifying metallization. Importantly, the cell symmetry remains unchanged, indicating an IPT. Similar to other TMDs, pressure-induced shifts of extremes generate a series of electron and hole pockets. Given the larger atomic radius of Te and wider electron orbitals compared to Se and S, this may contribute to MoTe2 achieving metallization at a lower pressure than most other TMDs such as MoS2, MoSe2, and WS2.
As already mentioned, under pressure, the MoTe2 structure does not change coordination when transitioning to a new phase and it may resemble the relaxed GaSe structure. In our previous work (Stepanov et al. 2023a), it was established that in monochalcogenides the vdW gap closes under the action of applied uniaxial pressure. Analysis of the CDD distribution revealed the formation of quasi-one-dimensional chains with non-covalent interactions between them. In this work, during the relaxation of the structure in Fig. 3 (b), it is found that the original 0 GPa phase in Fig. 3 (a) is not restored. Instead, a distortion of the 14 GPa phase occurs, which leads to a transition from chains with non-covalent interactions between them to a two-dimensional structure, albeit with an orthogonally reoriented vdW gap (Fig. 3 (c)). It is important to note that the atomic coordination returns to its original state, breaking the octet rule. Thus, both MoTe2 and GaSe have in common the fact that in these materials it is possible to achieve reorientation of the vdW gap while maintaining coordination.
RDG analysis was used to confirm vdW gap reorientation in these materials. Figs. 4 (a, b) shows structures with a reoriented vdW gap for relaxed GaSe and MoTe2 under pressure. Isosurface between layers indicates the presence of non-covalent interactions between layers. In the case of GaSe, under uniaxial pressure, a redistribution of interactions occurs, which determines the chain structure. A more detailed study of the connections between chains is the subject of our further research. During the relaxation process, the material again becomes quasi-two-dimensional and the vdW surface is restored again.
Fig. 2. Band structure patterns for MoTe2 under different uniaxial pressures. (a)-(b) Brillouin zones for two phases (0 and 37 GPa). (c)-(h) Band structures for different pressure values
Fig. 3. Transformation of the GaSe structure under the influence of axial pressure and after releasing the pressure. (a) Initial structure, (b) New phase at 14 GPa, and (c) at a pressure of 0 GPa.
Yellow balls represent CDD clouds
Fig. 4. RDG analysis of relaxed GaSe and MoTe2 under pressure. Green isosurface shows the areas of vdW interaction
All of the above-mentioned classes of materials have one important common characteristic: the formation of a vdW gap, caused by additional CDD clouds associated with partial sp3 hybridization of chal-cogen atoms. Consequently, materials with similar CDD distributions are expected to exhibit similar vdW gap reconstruction patterns. For example, in graphite, which is known for the lack of additional density in the vdW gap, changes under pressure are significantly different. As for Sb2Te3, additional clouds of electron density in the gap are also observed in this material (Fig. 5 (a)). Despite that in the case of other materials (Figs. 1 and 3) these clouds undergo the transition to the new phase, but in the case of antimony telluride they retain their configuration and location in the new phase. Moreover, the question of the nature of interlayer interaction in Sb2Te3 remains unanswered, and there are reports that the connection between layers may be metavalent in nature (Zhang et al. 2023).
Under uniaxial pressure, antimony telluride undergoes a transition to a metallic state while preserving its layered structure. A further increase in pressure leads to a strong lateral displacement of the layers and a phase transition at 7 GPa (Fig. 5 (c)). In this case, the vdW gap disappears in the new phase. However, it is crucial to note that there are no bonds between the atoms through the gap; they possess lone pairs and engage in non-covalent interactions. Consequently, the closure of the gap is linked to the lateral sliding of the layers relative to each other along the vdW gap. This is distinct from the rearrangement of bonds seen in other layered materials.
When compared, the results at different pressures make it apparent that the impact of pressure on Sb2Te3 is mirrored in the band structure: bands at higher pressures exhibit slight broadening compared to those at lower pressures (Fig. 6 (c, d)). This aligns with heightened interactions between neighboring atoms, electrons, and orbitals resulting from a decreased interlayer distance.
Between pressures of 0 to 3 GPa (Fig. 6 (c, d)), the conduction band minimum (CBM) sharply decreases between points r and Z. The Valence Band Maximum (VBM) undergoes significant positional changes with pressure increase: at 0 GPa, it resides at point r, and with increasing pressure, it shifts from point r along the path to point M. By 3 GPa (Fig. 6 (d)), the CBM crosses the Fermi level, signifying metallization (Fig. 6 (e, f)) without undergoing a phase transition.
CDD analysis of the initial structures shows that the mechanism of interlayer interaction for all materials studied is determined to a large extent by the interaction between permanent dipoles, represented by the additional electron density in the vdW gap. When pressure is applied, all materials under study demonstrate different patterns of change in the vdW gap. In Sb2Te3, bonds inside the layer are not broken, and bonds through the gap arise due to the lateral displacement of the layers, without forming a vdW interaction plane, but creating regions with vdW interaction due to lone electron pairs.
At the same time, for GaSe and MoTe2, the bonds inside the layer between the metal and chalcogen atoms are broken and arise through the vdW gap. Two-dimensional layers appear in MoTe2, and quasi-one-dimensional chains appear in GaSe, and the symmetry of the cell in both these cases changes from hexagonal to orthorhombic. When GaSe relaxes, the symmetry does not increase and two-dimensional layers are formed with an orientation similar to the case of MoTe2 (under pressure).
This leads to an important point: the vdW interaction does not disappear when axial pressure is applied. From the presented results it is obvious that, depending on the magnitude of intralayer interaction, coordination and local symmetry, the vdW gap can either rearrange (MoTe2 and GaSe) or distribute, forming regions of non-covalent interaction, as seen in the example of Sb2Te3.
During relaxation of Sb2Te3, the regions of non-covalent interaction, due to an increase in symmetry, are united again into a single vdW surface. This result is consistent with the work of (Zheng et al. 2023),
Fig. 5. Transformation of the Sb2Te3 structure under the axial pressure. (a) Initial structure, (b) Structure at 6 GPa before the phase transition, (c) New phase at 7 GPa. Red balls represent CDD clouds
Fig. 6. Band structure patterns for Sb2Te3 under different uniaxial pressures. (a)-(b) Brillouin zones for two phases of Sb2Te3 (0 and 7 GPa). (c)-(e) Band structures for different pressure values
where it was shown that during the crystallization of Sb2Te3, the vdW gap is formed from vacancies (or, as we called it here, non-covalent interaction regions), which are pushed out in a correlated manner, forming a single defective surface — vdW surface.
Conclusions
It was shown that in MoTe2, as in Sb2Te3, an isostructural phase transition associated with metallization occurs. It is shown that at a pressure of 37 GPa, a restructuring occurs in MoTe2 with a change in the orientation of the vdW gap. Similar behavior is observed for the relaxed GaSe structure. For antimony telluride, the mechanism turned out to be different — it is associated with the redistribution of non-covalent interaction under the influence of axial pressure. In Sb2Te3, a phase transition occurs with
a change in symmetry due to the lateral sliding of the layers relative to each other, as a result of which a bulk structure with regions of non-covalent interaction is formed. It turned out that the symmetry and bond strength inside the layer play a significant role. Thus, it becomes possible to distinguish two mechanisms of destruction and formation of the vdW gap — with reconfiguration of the gap and redistribution of non-covalent interaction.
Conflict of Interest
The author declares that there is no conflict of interest, either existing or potential.
Acknowledgements
Author would like to express his sincere gratitude to Vasilisa Gerega, Anton Suslov, and Alexander Kolobov. Author is deeply appreciative of their insights, guidance, and comments, which have played a pivotal role in the successful completion of this work.
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