Open Access
Add to BibSonomy
Abstract
Transition metal dichalcogenide (TMDC) materials are considered extremely efficient materials with significant applications in photovoltaics and optoelectronics. Here, the electronic structure and optoelectronic features of new transition metal-containing dichalcogenides are studied using state-of-the-art density functional theoretical calculations. For the analysis of the electronic band structures, we employed a modified Becke-Johnson potential. According to the band structure analysis, Platinum-based dichalcogenides possess an indirect band profile, having the valence band maximum and the conduction band minimum situated at discrete symmetry regions. At the same time, the zirconium-based materials have a direct type band structure at the same Γ-point. We calculated cohesive energies and formation energies to assess the stability of these materials. The substantial optical parameters such as the two parts of the dielectric constant, absorption coefficients, energy loss functions, reflectivity spectra, refractive index, real optical conductivity spectra, spectra, and the extinction coefficients, are calculated. These findings provide insight into potential applications in optoelectronic devices. The calculated band gaps and refractive index revealed an inverse relationship. This research aims to make a significant contribution to the advancement of various and possibly gainful semiconducting technologies, as well as their practical applications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Dichalcogenide materials have garnered enormous interest due to their numerous prospective applications, particularly in solar energy harvesting and advanced optoelectronic devices [1–4]. These materials may adopt a two-dimensional structure depending on the transition metal and chalcogen constituent, which results in a wide range of properties such as Mott insulators, metals, charge density wave systems, superconductors, and semiconductors [5–13]. The 2D counterparts of these materials in the TMDC family exhibit intriguing and technologically significant features [14,15]. The stoichiometry of TM-based dichalcogenides, written as AM2, where “A” denotes transition metals and “M” denotes chalcogens, impacts whether they operate as metals or semiconductors and whether they exhibit direct or indirect band gaps. Semiconductive TM-based dichalcogenides are intriguing for a wide range of applications [16]. Researchers employed the Kramer-Kronig approach for generating the dielectric functions along with other related optical characteristics [17]. The reflectivity spectra of Zr-based dichalcogenides were investigated using the same electric vector Ec and photon energies ranging from 4.5 to 14.0 eV [18]. From 0.5 eV up to 5.0 eV energy range, polarization dependencies in ZrS2 reflectivity were predicted [19]. Several methodologies and approximations have been explored to precisely describe the electrical characteristics of these materials. For example, ZrSe2 was discovered to have an energy gap of about 1.2 eV [20], whereas the electrical properties of ZrS2 were studied theoretically, and a semiconductor energy gap of about 1.68 eV was estimated [21]. The structure, electronic, and optical nature of TcS2 and TcSe2 are further examined using the post-DFT methods and the van der Waals modifications, in addition to this the GW technique was employed for adjusting errors in the predicted DFT energy band gaps [22]. Materials having these band gaps have the potential to be used in third-generation solar cell manufacture as well as cathodes for rechargeable batteries [23]. The electronic structural characteristics of these TMDC families are studied using the linear tight-binding muffin-tin orbitals approach [24]. Similarly, theoretical studies on the optoelectronic characteristics of dichalcogenide monolayers containing transition metal tungsten under the biaxial strain [25] are reported using the conventional DFT exchange-correlation approximations. However, due to the layered nature of these structures, typical GGA functions found it challenging to foresee and define their structural properties [26]. Finally, the electrical excitations of TMDCs were investigated using the ab initio GW approach [27]. Long-range dispersive pressures are essential in correctly describing the structural characteristics of materials, which have a significant influence on their electrical properties. Standard techniques, such as PBE and LDA, are known to overstate semiconductor band gaps by 30-50%. An outstanding knowledge gap would be covered by studying these dichalcogenides and providing effective applications for creating third-generation photovoltaic converters. According to the DFT analysis, materials in this class frequently exhibit semiconductor behavior, with different energy gap values. We thoroughly examine the electronic structure and optoelectronic properties of these materials.
The study of these dichalcogenides materials’ electronic and optical characteristics plays an essential role in the fields of materials science and condensed matter physics. Understanding the behavior of dichalcogenides such as ZrS2, ZrSe2, PtS2, and PtSe2 is especially important because of their distinct and promising properties. The research might lead to eco-friendly alternatives to traditional materials in a variety of applications. Investigating their qualities may lead to the creation of more environmentally friendly technology. Dichalcogenides exhibit exciting electrical and optical features that are still being studied. Investigating these materials will help us gain a better understanding of their behavior, offering us new avenues for scientific inquiry and discovery. The study of these dichalcogenides’ electrical and optical characteristics using DFT is not only scientifically exciting but also offers considerable promise for technological development and innovation. We may pave the path for the development of cutting-edge technology, energy-efficient solutions, and ecologically responsible applications by getting a thorough understanding of these materials. For better knowledge of the electronic features, we computed the band structures by employing the TB-mBJ potential. Moreover, for computing the optical properties, the Bethe-Salpeter equations are employed [28]. We use the TB-mBJ approximation to improve the accuracy of our models, which is recognized to be the advanced approach used frequently for estimating the energy band gap values of most semiconductors and insulators. The TB-mBJ has an accuracy of around 10% and the predicted values are mostly comparable to the experimental results. Our paper is arranged as: In the next second section, our computational approach is presented. The third section contains the results and discussion, while the fourth section provides the attained outcomes. The purpose of carrying out the present work was to bridge a knowledge gap in the electrical and optical properties of these materials for potential applications in nonlinear optics and optoelectronics.
2. Computational method
To conduct our analysis, we employed the WIEN2k code [29] as used in the density functional theory. For describing the exchange correlations, we employed the PBE-GGA generalized gradient approximation method [30]. The ab initio modeling of the density functional theory is used for exploring the structural, electronic, and optical characteristics of these dichalcogenides [31]. The use of PBE-GGA is vital in DFT calculations since it accounts for electron exchange and correlation effects. Here we employed the TB-mBJ scheme because it has been demonstrated to increase the accuracy of several material systems. This capacity enables more exact reproduction of real-world data, including lattice constants and formation energies, as well as predictions of electronic structural factors like band alignments and band gaps. To improve the accuracy of our electronic band gap calculations, we additionally employed the TB-mBJ potential [32]. Because of the unique interactions among electrons, this potential properly tackles this issue, where the exchange term accounts for attraction and the correlation term reflects electron repulsion. To prolong the states of electrons within the atomic sphere, we used spherical harmonics by selecting the Lmax = 10. We calculated electrical properties using a denser 10 × 10 × 10 k-mesh. The RMT × Kmax = 7 interstitial plane wave expansion threshold was chosen. Self-consistency cycles were performed until the 0.0001 Ry threshold was met to ensure convergence. The imaginary component of the complex dielectric function is given as [33]:
Moreover, along with the imaginary component, we resolved the real component by employing the Kramer-Kronig equation which is given as:
In the above relation (2), P represents the complex shift and the main value. These relations are further employed to calculate the other vital optical parameters that are given:
3. Results and discussion
3.1 Structural properties
The Zr-based studied dichalcogenides crystallize in the orthorhombic structure with the space group Pmmn. The structure is two-dimensional in which the Zr2+ was bonded to the equivalent four M2− atoms forming edge-sharing ZrM6 octahedra. There are two shorter bond lengths (2.63 Å) and two large bond lengths (2.81 Å) between Zr–M. Similarly, the PtS2 crystallizes in the trigonal structure with a space group of $\overline{{\rm P}3}$m1. The PtM2 has also a two-dimensional structure that contains one PtM2 sheet that is oriented in the direction (0, 0, 1). The Pt++ atoms are bonded to equivalent six M2− atoms forming an edge-sharing PtM6 octahedra. All the bond lengths of Pt–M are 2.43 Å. The M2− atoms were bonded in a three-coordinate geometry to equivalent three Pt++ atoms. To induce structural relaxation, we employed both the used potentials. We investigated a variety of them to discover the optimum function for predicting material attributes. The technique for relaxing was broken into two phases. Initially, we allowed fluctuations in atomic location and volume to determine the relaxed volume. Next, we generated a total of thirteen volume alternatives within the projected equilibrium state volume, we further relaxed the structures this is done by changing atomic positions. The predicted lattice constant along with the available data from the literature presented in Table 1 confirms that our predicted structural parameters were in fine agreement with those reported previously. The cohesive energy was calculated by combining the results of several structural relaxations and atomic volumes. The volume that has the lowermost cohesive energy was chosen and structural properties were determined using this volume. The relaxed unit cell as well as the equilibrium structural features are depicted in Fig. 1 with the larger atoms indicating metals. The formation and cohesive energy per atom decreased as the atomic number of the chalcogen atom grew, suggesting that the compounds were less stable. Throughout this study, the lattice constants, bulk moduli, and unit cell volume were all crucial properties to seek for. As the optimization process advanced, total energy values for various unit cell volumes were calculated, increasing both the ground state energy and volume while reducing the bulk moduli. These results confirm the computed cohesive energy trends and are compatible with the calculations done using the provided formulation [34]:
Here ${N_A},$ and ${N_M}$ represent the “A”, and “M” atoms, respectively. The $E_{atom}^A$ $E_{atom}^M$ isolates with energy for the “A”, and “M” atoms respectively. Moreover, the $E_{tot}^{A{M_2}}$ indicates the energy in bulk for AM2 materials [34]. In this study, the DFT calculations are performed to compute the cohesive energy values of these dichalcogenides. The total energy of these compounds and their separated free atoms was computed with values of 2.23 eV/atom was attained for ZrS2, 2.42 eV/atom for ZrSe2, 2.51 eV/atom for PtS2, and 3.23 eV/atom for PtSe2. According to these results, PtSe2 possesses weak bonds among the studied dichalcogenides, while the ZrS2 possess the strongest bonds. The observation is reliable when compared to bulk moduli measurements, supporting the idea that the ZrS2 could be more resistant to exterior pressure [34]:
The formation energies for PtS2, PtSe2 ZrS2, and ZrSe2 are −1.46, −1.69 eV −1.39, and −1.41 per formula unit (eV/f. u), respectively. The energy values, that take values ranging −1.28 up to -3.2 (eV/f. u) were found substantially lesser as compared to equivalent elemental states, indicating that these materials have a high degree of stability. The high correlation found between A-M (metal) bond formation energy and ionicity level demonstrates that less formation energies correspond to more ionic bonding. The convex hull, together with the formation energy values obtained [34], as well as its proximity to the compositions of interest, increases its reliability as a representation of material stability.
Table 1. The atomic sites, Lattice parameters, and Bandgap for the AM2 (A = Zr, Pt and M = S, Se) materials.
3.2 Electronic properties
The density of states indicated in what manner various energy states contributed in the valence and conduction bands, demonstrating a consistent pattern of behavior for these compounds. These compounds have semiconducting properties due to the presence of a Fermi level that separates the VB from the CB. As seen in Fig. 2(a), the Zr and the S atoms contributed relatively slighter between 0 up to −5.0 eV energy region within the VB range. Instead, the d states of Zr and the p state of S are the key contributors. The total-Zr, together with the d state of Zr and p states of in partial density of states, considerably contribute to the conduction band, particularly from 2 eV up to 5.0 eV. According to Fig. 2(b), in the case of ZrSe2, the total-Zr and total-Se states meaningly contribute from 0 eV to −5.0 eV within the VB. In this case, the d states of Zr and the p states of Se are vital. In the conduction band, between 2 to 5 eV, the total-Zr states are the largest contributor, but the d states of Zr and the p states of Se in the partial density of states also contribute considerably. As seen in Fig. 3(a), the total-Pt and total-S atoms contributed to the VB in 0.0 up to −5.0 eV. Here d state of Pt and p state of S also possess a substantial part. Likewise, in the CB region, total-Pt states contributes ranging from 2 eV to 5.0 eV, where, the d states of Pt and p states of S contribute the most. As seen in Fig. 3(b), the total-Pt along with the total-Se atoms played a substantial role in the VB in 0 to −5 eV. Here again, the Pt-d and Se-p states have a substantial part in this energy range in the VB. Within the given energy range, the Pt-d and Se-p orbitals of Se make substantial contributions. Similarly, the d and p states of Pt and Se, respectively are the major donors in this energy range.
The knowledge about the band structures is vital since it governs the majority of solid-state physical properties. The size of the energy band gap influences semiconductor photonic and charge-transfer capacities significantly. While Kohn and Sham-DFT were beneficial in anticipating the ground state characteristics of materials. A comprehensive examination of the band profile is carried out within the first Brillouin zone. In this context, very symmetrical points were considered as the key sites associated with a single reciprocal lattice primitive cell and are determined by the crystalline structure's symmetry group. Table 1 illustrates our predicted band gap values along with the calculated band gap values from the literature. The PtM2 compounds possess an indirect band gap semiconductor character, as shown in Fig. 4(c-d), with the VBM and CBM located at unlike high-symmetry positions. The ZrS2 is expected to be a semiconducting material with a 1.59 eV straight band gap. In the conduction band, Zr-d and S-p orbitals dominate band formations with energies ranging from 1.21 eV to 5 eV and 0 eV to −5 eV. Figure 4(b) depicts the band structure of ZrSe2 with a direct type of band gap with value of about 1.09 eV. The d states of Zr and p states of Se are mainly significant in the band’s development in the valence band region of (0 to −5 eV) and conduction band regions of (1.10 to 5 eV), respectively. Furthermore, PtS2 exhibits a 1.37 eV indirect band gap, with the d states of Pt and p states of Se mainly accountable for bands creation in the conduction (1.39 eV to 5 eV) and valence bands (0 to −5.0 eV). Similarly, PtSe2 has a 0.80 eV indirect band gap, with the d states of Zr and p states of Se playing major roles in band formation from (0 to −5 eV). In ascending order, the energy gaps are as follows: ZrS2 > ZrSe2 and PtS2 > PtSe2.
3.3 Optical properties
The optical character in materials is significant specifically for optoelectronic applications. Both real and imaginary components of complex dielectric constants play an important role in estimating substantial optical characteristics [44,45]. In Fig. 5(a), the calculated ε1(ω) of the dielectric function for these dichalcogenides is displayed as a function of energy. The zero-frequency limit ε1(0) also known as the static dielectric constant, is determined to be 7.81 for ZrS2, 6.88 for ZrSe2, 7.21 for PtS2, and 10.31 for PtSe2 (see Table 2). It is worth noting that these two measurements have a well-known inverse relationship. As Penn [46] anticipated, by substituting “M” atoms when moving from S towards Se, the ε1(ω) moves in the inverse direction as to band gap values. It is to be noted that in all scenarios larger and sudden peaks are caused due to the interband transitions. Sharp peaks were seen between 2.0 and 6.0 eV. High intense peaks in the ε1(ω) designate greater absorption along explicit energies. The sharp peaks are caused by the electronic states of materials where resonant photons are absorbed. When the sharp peaks reach their maximum values, the ε1(ω) starts to shrink and then transfer to a negative value. This phenomenon is caused by a combination of interband transition along with the electronic band structures of these materials. If the ε1(ω) drops, the material's capability of absorbing light at the specific energy levels falls. It's worth noting that ε1(ω) returns negative results for ZrS2, ZrSe2, PtS2, and PtSe2 from 5.91 to 13.5 eV. In these dichalcogenides, the electronic band structures and interband transition dictate how the ε2(ω) acts at high energy values. Figure 5(b) depicts the ε2(ω) with remarkably comparable patterns as the energy varies. These chalcogenides have distinct strong peaks at 6.12, 5.62, 3.02, and 2.73 eV for ZrS2, ZrSe2, PtS2, and PtSe2, respectively. The cause of these intense peaks is due to the electronic transitions from the d states of transition metal and p states of chalcogens in these materials. The greatest values for ε2(ω) for the related materials are 6.76, 7.20, 7.81, and 9.47. Following these energy peaks, ε2(ω) has a consistent trend of decreasing values, just marginally increasing at 8.39 eV. As the “M” atoms shifted from Se towards S, the energy gap expanded, raising the entire spectrum to higher energies. For higher density of states as observed in some materials, phase space-filling effects usually limit the absorption coefficient. This means that states were mostly filled, and very few electronic states were available for transitions. At higher energies, the transitions that are ready might increase, resulting in a drop in the I(ω). When electronic interactions and screening outcomes develop at high energy values, the optical properties and dielectric response of the material might alter.
Fig. 5. The plots for (a) real components, (b) imaginary components, of dielectric constant (c) Absorption coefficients, and (d) Real optical conductivities of the studied systems.
Table 2. The static dielectric constant, reflectivity, and refractive index of the AM2 (A = Zr, Pt and M = S, Se) materials.
These screening effects can reduce the I(ω) at high energy. Figure 5(c) depicts the projected absorption coefficient as a function of energy. The highest I(ω) of ZrS2, ZrSe2, were 127.8, and 119.86 and of PtS2, PtSe2 were 152.12, and 145.35, respectively. The maximum values are surely placed in the ultraviolet (UV) spectrum at energy values of 6.43, 5.37, 7.89, and 6.88 eV. The optical absorption peak in ZrM2 indicates a direct band gap transition, in which electrons travel from the valence to conduction bands without changing momentum. The cause of these intense peaks is due to the Zr-d and M-p states of these materials as confirmed by the electronic band structure and density of states calculations. Similarly, the reason for the intense peaks in absorption peaks of PtM2 dichalcogenides is due to the Pt-d and M-p states. The absorption coefficients have the most peaks ranging from 4.71 eV up to 8.2 eV. Because the incidence of photon energy was near or somewhat larger than the band gap values, the absorption coefficient displays a dramatic peak in this area. When the energy exceeds 8.2 eV and approaches 9.5 eV, the absorption coefficient begins to decrease. The reason for this decrease is that electrons have a lower likelihood of migrating to the conduction band since photon energies are meaningly large as compared band gap. As the absorption coefficient decreases, a very small number of photons are absorbed. At 10.0 eV, the absorption coefficient begins to rise again. The cause for the rise was that incoming photons’ energy was larger as compared to the energy levels of these materials. When new energy levels are made available, the absorption coefficient begins to grow once more. The intense peaks in L(ω) as in Fig. 6(a) are caused by the plasma oscillations that create these frequencies and are termed to be plasma frequencies. The main reason can be the valance electron oscillation’s collective longitudinal reaction to the plasma-frequency background of the atomic cores. Valence electron excitation was connected with a decline in the L(ω) that ranges from 4.5 up to 8 eV. One of these excitations is the valence band transition, in which electrons move from filled to empty electron states. For high energy values, particularly in between 8 to 13 eV, the L(ω) becomes more visible. Depending on the band structure, band size, and material composition, the specific energy ranges in which these behaviors exhibit themselves can vary.
Fig. 6. The plots for (a) Energy loss functions, (b) Reflectivity spectra, (c) Refractive indices spectra, and (d) Extinction coefficients for the studied systems.
The capacity of a substance to reflect electromagnetic radiation is linked to its reflectivity dispersion R(ω). Figure 6(b) illustrates the reflectivity R(ω) of these compounds under investigation. The reflectivity spectra R(ω) average for other than zero component displays unnotably variations in reflectance spectra for concentration in the AM2 compounds fluctuate. There are minor, irregular peaks during the inter-band transition, followed by a notable spike observed in the reflectance. The reflectance increases rapidly up to 8.0 eV before progressively decreasing when it approaches to 8.25 eV. In between 5.7 to 12.0 eV, the reflectance of the investigated materials is noted to be fairly constant. This trend might be explained by the nonappearance or reduced strength of the interband transitions, as well as the presence of extra absorption processes. When incoming light is highly and frequently reflected then absorption, resulting in increased reflectivity. The actual measure of optical conductivity is a substance's ability to carry light or other electromagnetic waves. Because of a multitude of variables, the peaks from 4 eV to 6 eV and then drops the concentrations of charges climb to around 10 eV. The larger peaks in the σ(ω), which span between 4.5 eV to 7.0 eV, indicate a substantial degree of absorptive behavior or has much potential in transferring light at such energy. The electronic band profiles of AM2 dichalcogenide dictate the precise energy sites of the peaks. The decrease in the real optical conductivity from 8 to 10 eV can be attributed to reduced interband transition or changes in electronic structures. This drop in the real optical conductivity specifies that certain compounds have a lower ability to transmit or absorb light. The refractive index average of the non-zero components demonstrates no discernible shift in the refractive spectrum when the concentration in the AM2 materials change as observed in Fig. 6(c). The refractive index value rises significantly when small, irregular peaks associated with inter-band transitions appear. At 2.5 eV, the refractive index of ZrS2 and ZrSe2 rapidly rises and then begins to decline as it approaches 5.5 eV. In the case of PtS2, and PtSe2, n(ω) rises at around 4.2 eV and extends to 6.29 eV. The dichalcogenides under investigation have favorable refractive index values from 6.0 to 10 eV. Each of the studied dichalcogenides possesses a high refractive index in both the UV and visible spectra. The band gap of the material is bridged during higher-energy electronic transitions, causing some dichalcogenides to lose a portion of their refractive index. Figure 6(d) depicts the connection between the extinction coefficient k(ω) and energy. The threshold energies for each chemical are 1.5 eV, 1.4 eV, 0.8 eV, and 0.7 eV, respectively. Above these limitations, the energy causes the extinction coefficient to steadily grow. Sharp peaks are visible in the k(ω) spectra between 1.5 to 3.3 eV and 5 to 8 eV, respectively. The peaks for ZrS2, ZrSe2, PtS2, and PtSe2 were 2.4, 2.01, 3.21, and 2.64, respectively. These peak values in the k(ω) spectra indicate the greatest absorption behavior of the materials. With increasing photon energy, the amplitude of the k(ω) spectra diminishes dramatically beyond these peaks.
4. Conclusion
In conclusion, by means of density functional theory computations, we explored the structure, electronic, and optical nature of AM2 (A = Zr, Pt and M = S, Se) dichalcogenides. These materials are predicted as semiconducting with a direct type of band gap of ZrM2 and an in-direct band gap of PtM2 being noticed. The band formations are mostly attributed to the transition metal d states and chalcogen p states. The band gaps are set up are ZrS2 > ZrSe2 and PtS2 > PtSe2 illustrating that the electronic bandgap narrows by increasing the atomic number of the chalcogenides. This work also investigated the ε1(ω), which exhibited substantial optical absorption at specific energies. However, subsequently attainment of the extreme peaks, the ε1(ω) started to decrease and then move towards a negative value. This phenomenon was attributed to inter-band transition and the material's band profile. Because the band gap expands in that direction, the e spectrum shifted to the maximum value of energy when the “M” atom was exchanged i.e., from Se to S. Screening effects at higher energies have been demonstrated to reduce the I(ω). The value then decreased when the photon energy climbed significantly over the bandgap energy from 8.20 to 9.50 eV. As a result, fewer photons in this energy range were absorbed. Furthermore, valence electron excitations lowered the L(ω) from the 0.0-10.0 eV energy range. There was also a considerable increase in reflectivity and a few minor fluctuating peaks associated with inter-band transitions. Higher peak values in the σ(ω) ranges from 4.5 up to 9.5 eV showed stronger absorption and the material's efficiency in absorbing light.
Funding
King Saud University (RSPD2023R1047).
Acknowledgment
This work was funded by the Researchers Supporting Project Number (RSPD2023R1047), King Saud University, Riyadh, Saudi Arabia.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. S. Bikorimana, P. Lama, A. Walser, R. Dorsinville, S. Anghel, A. Mitioglu, A. Micu, and L. Kulyuk, “Nonlinear optical responses in two-dimensional transition metal dichalcogenide multilayer: WS2, WSe2, MoS2 and Mo0.5W0.5S2,” Opt. Express 24(18), 20685 (2016). [CrossRef]
2. K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nat. Photonics 10(4), 216–226 (2016). [CrossRef]
3. C. Chakraborty, A. Mukherjee, L. Qiu, and A. N. Vamivakas, “Electrically Tunable Valley polarization and Valley Coherence in monolayer WSe&NbSP2 embedded in a van der waals heterostructure,” Opt. Mater. Express 9(3), 1479 (2019). [CrossRef]
4. Y. Feldman, E. Wasserman, D. J. Srolovitz, and R. Tenne, “High-Rate, Gas-Phase Growth of MoS2Nested Inorganic Fullerenes and Nanotubes,” Science 267(5195), 222–225 (1995). [CrossRef]
5. S. Guddala, R. Bushati, M. Li, A. B. Khanikaev, and V. M. Menon, “Valley selective optical control of excitons in 2D semiconductors using a chiral metasurface,” Opt. Mater. Express 9(2), 536 (2019). [CrossRef]
6. M. Remskar, A. Mrzel, Z. Skraba, A. Jesih, M. Ceh, J. Demšar, P. Stadelmann, F. Lévy, and D. Mihailovic, “Self-assembly of subnanometer-diameter single-wall mos2 nanotubes,” Science 292(5516), 479–481 (2001). [CrossRef]
7. H. Taghinejad, A. A. Eftekhar, and A. Adibi, “Lateral and vertical heterostructures in two-dimensional transition-metal dichalcogenides,” Opt. Mater. Express 9(4), 1590 (2019). [CrossRef]
8. Q. Wang, J. Lai, and D. Sun, “Review of photo response in semiconductor transition metal dichalcogenides based photosensitive devices,” Opt. Mater. Express 6(7), 2313 (2016). [CrossRef]
9. H. Li, B. Wang, J. Chen, H. Jiang, X. Li, J. Liu, Q. Gong, Z.-C. Yan, and P. Fu, “Effects of a static electric field on nonsequential double ionization,” Phys. Rev. A 76(3), 033405 (2007). [CrossRef]
10. S. Roy and P. Bermel, “Investigation of pure and hybrid tungsten-based transition metal di-chalcogenides for radiation resistant space photovoltaic applications,” Opt. Mater. Express 13(8), 2214 (2023). [CrossRef]
11. S. W. Han, H. Kwon, S. K. Kim, S. Ryu, W. S. Yun, D. H. Kim, J. H. Hwang, J.-S. Kang, J. Baik, H. J. Shin, and S. C. Hong, “Band-gap transition induced by Interlayer van der Waals interaction in MOS,” Phys. Rev. B 84(4), 045409 (2011). [CrossRef]
12. N. Dong, Y. Li, Y. Feng, S. Zhang, X. Zhang, C. Chang, J. Fan, L. Zhang, and J. Wang, “Optical limiting and theoretical modelling of layered transition metal dichalcogenide nanosheets,” Sci. Rep. 5(1), 14646 (2015). [CrossRef]
13. E. Morosan, H. W. Zandbergen, B. S. Dennis, J. W. Bos, Y. Onose, T. Klimczuk, A. P. Ramirez, N. P. Ong, and R. J. Cava, “Superconductivity in Cuxtise2,” Nat. Phys. 2(8), 544–550 (2006). [CrossRef]
14. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012). [CrossRef]
15. W. Li, J. Peng, Y. Zhong, D. Wu, H. Lin, Y. Cheng, Z. Luo, J. Weng, H. Xu, and Z. Cai, “Orange-light passively Q-switched Pr3+-doped all-fiber lasers with transition-metal dichalcogenide saturable absorbers,” Opt. Mater. Express 6(6), 2031 (2016). [CrossRef]
16. M. Drüppel, T. Deilmann, P. Krüger, and M. Rohlfing, “Diversity of trion states and substrate effects in the optical properties of an MOS2 monolayer,” Nat. Commun. 8(1), 2117 (2017). [CrossRef]
17. H. Knopf, N. Lundt, T. Bucher, S. Höfling, S. Tongay, T. Taniguchi, K. Watanabe, I. Staude, U. Schulz, C. Schneider, and F. Eilenberger, “Integration of atomically thin layers of transition metal dichalcogenides into high-Q, Monolithic Bragg-Cavities: An experimental platform for the enhancement of the optical interaction in 2D-materials,” Opt. Mater. Express 9(2), 598 (2019). [CrossRef]
18. H. P. Hughes and W. Y. Liang, “Vacuum ultraviolet reflectivity spectra of the disulphides and diselenides of titanium, zirconium and hafnium,” J. Phys. C: Solid State Phys. 10(7), 1079–1087 (1977). [CrossRef]
19. S. C. Bayliss and W. Y. Liang, “Symmetry dependence of optical transitions in Group 4B Transition metal Dichalcogenides,” J. Phys. C: Solid State Phys. 15(6), 1283–1296 (1982). [CrossRef]
20. P. A. Lee, G. Said, R. Davis, and T. H. Lim, “On the optical properties of some layer compounds,” J. Phys. Chem. Solids 30(12), 2719–2729 (1969). [CrossRef]
21. D. L. Greenaway and R. Nitsche, “Preparation and optical properties of Group IV–VI2 Chalcogenides having the CDI2 structure,” J. Phys. Chem. Solids 26(9), 1445–1458 (1965). [CrossRef]
22. P. Novák, R. Imhof, and O. Haas, “Magnesium insertion electrodes for rechargeable non aqueous batteries — a competitive alternative to lithium?” Electrochim. Acta 45(1-2), 351–367 (1999). [CrossRef]
23.
24. G. Kalpana, G. Pari, A. Mookerjee, and A. K. Bhattacharyya, “ab initio electronic band structure calculations for Beryllium Chalcogenides,” Int. J. Mod. Phys. B 12(19), 1975–1984 (1998). [CrossRef]
25. J. Liu, H. Liu, J. Wang, H. Sheng, G. Tang, J. Zhang, and D. Bai, “Optical and electronic properties of dichalcogenides WX2 (X = S, SE, and te) monolayers under biaxial strain,” Phys. B 568, 18–24 (2019). [CrossRef]
26. P. Rivera, H. Yu, K. L. Seyler, N. P. Wilson, W. Yao, and X. Xu, “Interlayer valley excitons in heterobilayers of transition metal dichalcogenides,” Nat. Nanotechnol. 13(11), 1004–1015 (2018). [CrossRef]
27. A. Fleszar and W. Hanke, “Electronic excitations in beryllium chalcogenides from theab initio,” Phys. Rev. B 62(4), 2466–2474 (2000). [CrossRef]
28. G. Onida, L. Reining, and A. Rubio, “Electronic excitations: Density-functional versus many-body green’s-function approaches,” Rev. Mod. Phys. 74(2), 601–659 (2002). [CrossRef]
29. P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. Madsen, and L. D. Marks, “Wien2k: An APW + Lo program for calculating the properties of Solids,” J. Chem. Phys. 152(7), 074101 (2020). [CrossRef]
30. Z. Wu and R. E. Cohen, “More accurate generalized gradient approximation for solids,” Phys. Rev. B 73(23), 235116 (2006). [CrossRef]
31. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. E 77(18), 3865–3868 (1996). [CrossRef]
32. M. Moakafi, R. Khenata, A. Bouhemadou, F. Semari, A. H. Reshak, and M. Rabah, “Elastic, electronic and optical properties of cubic antiperovskites SBNCA3 and BINCA3,” Comput. Mater. Sci. 46(4), 1051–1057 (2009). [CrossRef]
33. R. Khenata, M. Sahnoun, H. Baltache, M. Rérat, A. H. Reshak, Y. Al-Douri, and B. Bouhafs, “Full-potential calculations of structural, elastic and electronic properties of MgAl2O4 and ZNAL2O4 compounds,” Phys. Lett. A 344(2-4), 271–279 (2005). [CrossRef]
34. B. K. Moghal and M. R. Islam, “Tuning the electronic, Phonon, and optical properties by strain-induced on the monolayer transition metal dichalcogenides ASe2 (A = Mo and W),” Mater. Today Commun. 31, 103240 (2022). [CrossRef]
35. Q. Song, X. Liu, H. Wang, X. Wang, Y. Ni, and H. Wang, “Strain-tuned mechanical, electronic, and optoelectronic properties of two-dimensional transition metal sulfides ZrS2: A first-principles study,” J. Mol. Model. 28(3), 63 (2022). [CrossRef]
36. Z. Huang, W. Zhang, and W. Zhang, “Computational search for two-dimensional MX2 semiconductors with possible high electron mobility at room temperature,” Materials 9(9), 716 (2016). [CrossRef]
37. H. L. Zhuang and R. G. Hennig, “Computational search for single-layer transition-metal dichalcogenide photocatalysts,” J. Phys. Chem. C 117(40), 20440–20445 (2013). [CrossRef]
38. J. Zhang, Y. Xie, Y. Hu, and H. Shao, “Remarkable intrinsic ZT in the 2d ptx2(x = O, S, Se, te) monolayers at room temperature,” Appl. Surf. Sci. 532, 147387 (2020). [CrossRef]
39. D. S. Koda, F. Bechstedt, M. Marques, and L. K. Teles, “Coincidence lattices of 2D crystals: Heterostructure predictions and applications,” J. Phys. Chem. C 120(20), 10895–10908 (2016). [CrossRef]
40. A. Carvalho, R. M. Ribeiro, and A. H. Castro Neto, “Band nesting and the optical response of two-dimensional semiconducting Transition Metal Dichalcogenides,” Phys. Rev. B 88(11), 115205 (2013). [CrossRef]
41. Y. Zhao, J. Qiao, P. Yu, Z. Hu, Z. Lin, S. P. Lau, Z. Liu, W. Ji, and Y. Chai, “Extraordinarily strong interlayer interaction in 2D layered PTS2,” Adv. Mater. 28(12), 2399–2407 (2016). [CrossRef]
42. M. Sajjad, N. Singh, and U. Schwingenschlögl, “Strongly bound excitons in monolayer PTS2 and ptse2,” Appl. Phys. Lett. 112(4), 043101 (2018). [CrossRef]
43. Y. Wang, L. Li, W. Yao, et al., “Monolayer PtSe2, a new semiconducting transition-metal-dichalcogenide, epitaxially grown by direct selenization of Pt,” Nano Lett. 15(6), 4013–4018 (2015). [CrossRef]
44. T. Cheng, P. Cheng, H. Zhao, T. Fei, L. Zhang, Z. Zuo, L. Liu, and J.-Y. Yang, “Effect of structural morphology and material factors on radiative properties of hybrid perovskite/nanoporous gan hierarchical composite structure,” ACS Appl. Opt. Mater. 1(1), 261–273 (2023). [CrossRef]
45. G. Xiang, Y. Wu, Y. Li, C. Cheng, J. Leng, and H. Ma, “Structural and optoelectronic properties of two-dimensional ruddlesden–popper hybrid perovskite CsSnBr3,” Nanomater. 11(8), 2119 (2021). [CrossRef]
46. 1DR Penn, “Wave-number-dependent dielectric function of semiconductors,” Phys. Rev. E 128(5), 2093–2097 (1962). [CrossRef]
