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A van der Waals (VDW) heterostructure offers an effective strategy to create designer physical properties in vertically stacked two-dimensional (2D) materials, and offers a new paradigm in designing novel 2D heterostructure devices. In this work, we investigate the structural and electronic features of the BP/MoGe2N4 heterostructure. We show that the BP/MoGe2N4 heterostructure exists in a multiple structurally stable stacking configuration, thus revealing the experimental feasibility of fabricating such heterostructures. Electronically, the BP/MoGe2N4 heterostructure is a direct band gap semiconductor exhibiting type-II band alignment, which is highly beneficial for the spatial separation of electrons and holes. Upon forming the BP/MoGe2N4 heterostructure, the band gap of the constituent BP and MoGe2N4 monolayers are substantially reduced, thus allowing the easier creation of an electron-hole pair at a lower excitation energy. Interestingly, both the band gap and band alignment of the BP/MoGe2N4 heterostructure can be modulated by an external electric field and a vertical strain. The optical absorption of the BP/MoGe2N4 heterostructure is enhanced in both the visible-light and ultraviolet regions, thus suggesting a strong potential for solar cell application. Our findings reveal the promising potential of the BP/MoGe2N4 vdW heterostructure in high-performance optoelectronic device applications.

Using first-principles calculations, the geometry, electronic structure, optical and photocatalytic performance of blueP and XYO (X = Ti, Zr, Hf; Y = S, Se) monolayers and their corresponding van der Waal heterostructures in three possible stacking patterns, are investigated. BlueP and XYO (X = Ti, Zr, Hf; Y = S, Se) monolayers are indirect bandgap semiconductors. A tensile strain of 8(10)% leads to TiSeO(ZrSeO) monolayers transitioning to a direct bandgap of 1.30(1.61) eV. The calculated binding energy and AIMD simulation show that unstrained(strained) blueP and XYO (X = Ti, Zr, Hf; Y = S, Se) monolayers and their heterostructures are thermodynamically stable. Similar to the corresponding monolayers, blueP-XYO (X = Ti, Zr, Hf: Y = S, Se) vdW heterostructures in three possible stacking patterns are indirect bandgap semiconductors with staggered band alignment, except blueP-TiSeO vdW heterostructure, which signifies straddling band alignment. Absorption spectra show that optical transitions are dominated by excitons for blueP and XYO (X = Ti, Zr, Hf; Y = S, Se) monolayers and the corresponding vdW heterostructures. Both EVB and ECB in TiSO, ZrSO, ZrSeO and HfSO monolayers achieve energetically favorable positions, and therefore, are suitable for water splitting at pH = 0, while TiSeO and HfSeO monolayers showed good response for reduction and fail to oxidise water. All studied vdW heterostructures also show good response to any produced O2, while specific stacking reduces H+ to H2.

Surface functionalization is one of the useful techniques for modulating the mechanical and electronic properties of two-dimensional systems. In the present study, we investigate the structural, elastic, and electronic properties of hexagonal boron phosphide monolayer functionalized by Br and Cl atoms using first-principles predictions. Once surface-functionalized with Br/Cl atoms, the planar structure of BP monolayer is transformed to the low-buckled lattice with the bucking constant of about 0.6 A for all four configurations of functionalized boron phosphide, i.e., Cl–BP–Cl, Cl–BP–Br, Br–BP–Cl, and Br–BP–Br. The stability of functionalized BP monolayers is confirmed via their phonon spectra analysis and ab initio molecular dynamics simulations. Our calculations indicate that the functionalized BP monolayers possess a fully isotropic elastic characteristic with the perfect circular shape of the angle-dependent Young's modulus and Poisson's ratio due to the hexagonal symmetry. The Cl–BP–Cl is the most stiff with the Young's modulus C2D = 43.234 N m−1. All four configurations of the functionalized boron phosphide are direct semiconductors with a larger band gap than that of a pure BP monolayer. The outstanding stability, isotropic elastic properties, and moderate band gap make functionalized boron phosphide a very intriguing candidate for next-generation nanoelectromechanical devices.

Motivated by the successful preparation of MoSi2N4 monolayers in the last year [Y.-L. Hong et al., Science, 2020, 369, 670–674], we investigate the structural, electronic and optical properties of the MoS2/MoSi2N4 heterostructure (HTS). The phonon dispersion and the binding energy calculations refer to the stability of the HTS. The heterostructure has an indirect bandgap of 1.26 (1.84) eV using PBE (HSE06) which is smaller than the corresponding value of MoSi2N4 and MoS2 monolayers. We find that the work function of the MoS2/MoSi2N4 HTS is smaller than the corresponding value of its individual monolayers. The heterostructure structure can enhance the absorption of light spectra not only in the ultraviolet region but also in the visible region as compared to MoSi2N4 and MoS2 monolayers. The refractive index behaviour of the HTS can be described as the cumulative effect which is well described in terms of a combination of the individual effects (the refractive index of MoSi2N4 and MoS2 monolayers).

In this work, we study systematically low-energy bands, optical absorbance and spin/valley-Hall conductivity of silicene and germanene in the presence of a perpendicular electric field. Our analytical calculations indicate that both silicene and germanene are semiconductors with a tiny energy gap and we can control their energy gap by the perpendicular electric field. Our calculations also demonstrate that the low-frequency optical absorbance of silicene is much greater than that of germanene and the external electric field plays an important role in determining the optical absorption peaks. When the Fermi level is in the forbidden band, the Hall conductivity is quantized, while spin/valley-Hall conductivities of both silicene and germanene depend strongly on the Fermi energy when the Fermi level is in the conduction band. Analytical results for spin/valley-Hall conductivities of silicene and germanene are presented in detail in this work.

The formation of van der Waals heterostructures (vdWHs) have recently emerged as promising structures to make a variety of novel nanoelectronic and optoelectronic devices. Here, in this work, we investigate the structural, electronic and optical features of ZnO/ZrSSe vdWHs for different stacking patterns of ZnO/SeZrS and ZnO/SZrSe by employing first-principles calculations. Binding energy and ab initio molecular dynamics calculations are also employed to confirm the structural and thermal stability of the ZnO/ZrSSe vdWHs for both models. We find that in both stacking models, the ZnO and ZrSSe layers are bonded via weak vdW forces, leading to easy exfoliation of the layers. More interestingly, both the ZnO/SeZrS and ZnO/SZrSe vdWHs posses type-II band alignment, making them promising candidates for the use of photovoltaic devices because the photogenerated electrons–holes are separated at the interface. The ZnO/ZrSSe vdWHs for both models possess high performance absorption in the visible and near-infrared regions, revealing their use for acquiring efficient photocatalysts. Moreover, the band gap values and band alignments of the ZnO/ZrSSe for both models can be adjusted by an electric field as well as vertical strains. There is a transformation from semiconductor to metal under a negative electric field and tensile vertical strain. These findings demonstrate that ZnO/ZrSSe vdWHs are a promising option for optoelectronic and nanoelectronic applications.

Motivated by the recent successful synthesis of the layered platinum mineral jacutingaite (Pt2HgSe3), we have studied the optoelectronic, mechanical, and thermoelectric properties of graphene hetero-multilayer on Pt2HgSe3 monolayer (PHS) heterostructures (LG/PHS) by using first-principles calculations. PHS is a topological insulator with a band gap of about 160 meV with fully relativistic calculations; when graphene layers are stacked on PHS, a narrow band gap of ∼10–15 meV opens. In the presence of gate-voltage and out-of plane strain, i.e. pressure, the electronic properties are modified; the Dirac-cone of graphene can be shifted upwards (downward) to a lower (higher) binding energy. The absorption spectrum shows two peaks, which are located around 216 nm (5.74 eV) and protracted to 490 nm (2.53 eV), indicating that PHS could absorb more visible light. Increasing the number of graphene layers on PHS has a positive impact on the UV-vis light absorption and gives a clear red-shift with enhanced absorption intensity. To investigate the electronic performance of the heterostructure, the electrical conductance and thermopower of a device composed of graphene layers and PHS is examined by a combination of DFT and Green function formalism. The number of graphene layers can significantly tune the thermopower and electrical conductance. This analysis reveals that the heterostructures not only significantly affect the electronic properties, but they can also be used as an efficient way to modulate the optic and thermoelectric properties.

In the present study, the effects of the strain engineering and electric field on electronic properties of the GaS monolayer are investigated by ab initio investigations. Our calculated results demonstrate that the GaS monolayer is a semi-conductor with a large indirect bandgap of 2.568 eV at the equilibrium. In the presence of a biaxial strain, the band structure of the GaS monolayer, especially the conduction band, changes significantly. However, while the effect of compressive strain on the energy gap of the GaS monolayer is quite weak, its energy gap depends strongly on the tensile strain. On the other hand, external electric fields can cause the semiconductor–metal transition in the monolayer. Being able to control electronic properties, especially the occurrence of the semiconductor–metal phase transition, makes the GaS monolayer a prospective material for nanoelectromechanical and nanospintronic applications.

In this study, we investigate systematically the effect of strain engineering and electric field on electronic properties of single-layer SnSe 2 using density functional theory . Our calculated results indicate that the single-layer SnSe2 is a semiconductor with a small band gap of 0.715 eV at the equilibrium state. The electronic states near the Fermi level are mainly contributed by Sn- d and Se-p orbitals, especially the contribution of the Se-p orbital to the valence band is dominant. Under biaxial strain, the band gap of the single-layer SnSe2 changes abnormally. While compressive biaxial strain reduces band gap rapidly, the band gap of the single-layer SnSe2 only increases slightly when increasing the tensile biaxial strain. In contrast to the strain-dependence case, the influence of the external electric field on the electronic properties of the single-layer SnSe2 is quite small and the energy gap of the single-layer SnSe2 does not depend on the direction of the perpendicular electric field. Our calculated results can provide more information for application possibility of the single-layer SnSe2 in nanoelectronic devices.

The vertical stacking and influence of external electric field are good techniques to tune the electronic properties of two-dimensional materials for potential nanoelectronics and optoelectronic devices. The structural and electronic properties of P-ZnO and SiC-ZnO van der Waals (vdW) heterostructures are investigated by first principles calculations. P-ZnO (SiC-ZnO) heterostructure exhibits an indirect type-I (direct type-II) semiconducting band character. The effect of perpendicular applied external electric field on the electronic properties of the most stable vdW heterostructure has also been systematically discussed. Remarkable variations in the band gap nature are induced by increasing field strength from 0.1 to 1.0 V/A (for P-ZnO) and 0.1 to 0.8 V/A (for SiC-ZnO). The intrinsic indirect type-I is modulated to type-II semiconducting band gap in P-ZnO by applying electric field strength 0.1 V/A. More interestingly, reduction in the size with transition from an indirect-to-direct type-II semiconductor band gap nature is noted at 0.5 V/A. However, a direct type-II semiconductor to metallic character is found at 1.0 V/A (for P-ZnO) and 0.8 V/A (for SiC-ZnO). Our results suggests that these vdW heterostructures are promising candidates for electronic and optoelectronic device applications.

Constructing van der Waals heterostructures (vdWHs) based on different two-dimensional materials could afford many interesting properties, which may not hold for single-layered materials. In this study, we design a novel vdWH-GaSe/MoSe2 and investigate its electronic properties using first-principles calculations. It has a type-II band alignment with an indirect bandgap. Moreover, we found that the band alignment transformation of the GaSe/MoSe2 vdWH from type-II to type-I can be realized by decreasing the interlayer distance or by applying a positive electric field. Our findings could provide fundamental insights into the GaSe/MoSe2 vdWH for designing high-performance optoelectronic nanodevices.

Strain effects on the electronic and optical properties of monolayer SnSe is studied by APW + lo method in DFT framework. The applied strains cause direct-indirect transition of SnSe band gap which is mainly constructed by s / p hybridization. The armchair e ac and zigzag e zz reduce the unstrained band gap of 1.05 eV down to 0 eV at 12% compression, but at 12% tension, the band gap decreases to 0.726–0.804 eV. The band gap always increases under biaxial strain e b at 12% compression to 12% tension. We observe an enhancement of real e 1 ( ω ) and imaginary e 2 ( ω ) parts of dielectric function by 14%–30% of magnitude, wider peak distribution to infrared and ultra-violet regions, and appearance of new peaks in the e 1 ( ω ) and e 2 ( ω ) spectrums. As a consequence, the light absorption α ( ω ) is significantly enhanced in the ultra-violet region and the absorption even starts at lower energy at infrared region.

In the present work, we consider electronic properties of WX2 (X = S, Se) monolayers under a biaxial strain e b using the first principles study. Our calculations indicate that, at equilibrium, the WS2 and WSe2 monolayers are semiconductors with a direct band gap of respectively 1.800 eV and 1.566 eV while their bulk structures are indirect semiconductors. The electronic properties of the WX2 monolayers are very sensitive with the biaxial strain, especially compression strain. The biaxial strain e b is the cause of the band gap of the WX2 monolayers and especially the semiconductor-metal phase transition has occurred in the WS2 monolayer at e b = - 10 % . In addition, the direct-indirect band gap transition was observed in both WS2 and WSe2 monolayers at a certain elongation of biaxial strain e b . The phase transitions in these monolayers can be very useful for their applications in nanoelectromechanical devices.

In this work, we consider systematically the influence of uniaxial strain and external electric field E on electronic properties of a monolayer InSe using ab initio approach based on density functional theory. Our calculations indicate that the monolayer InSe has a medium indirect energy bandgap of 1.38 eV at equilibrium. The calculated results also demonstrate that we can adjust the bandgap of the monolayer InSe by strain engineering or electric field. The bandgap of the monolayer InSe changes dramatically when the uniaxial strain is applied. Especially, under the compressed uniaxial strain, an indirect–direct bandgap transition has been observed at certain elongations. Within the electric field magnitude E range from 0 to 5 V/nm, the calculated results show that the negative electric field changes the bandgap of the monolayer InSe up to 23% while the positive electric field effect on its bandgap is negligible.

van der Waals heterostructures (vdWHs), obtained by vertically stacking different two-dimensional (2D) layered materials are being considered intensively as potential materials for nanoelectronic and optoelectronic devices because they can show the most potential advantages of individual 2D materials. Here, we construct the SnSe2/MoS2 vdWH and investigate its electronic and optical properties using first-principles calculations. We find that the band structures of both MoS2 and SnSe2 monolayers are well kept in the SnSe2/MoS2 vdWH because of their weakly interacting features via vdW interaction. The SnSe2/MoS2 vdWH forms a type-I band alignment and exhibits an indirect semiconductor band gap of 0.45 eV. The type-I band alignment makes the SnSe2/MoS2 vdWH a promising material for optoelectronic nanodevices, such as light emitting diodes because of ultra-fast recombination of electrons and holes. Moreover, the band gap and band alignment of the SnSe2/MoS2 vdWH can be tailored by the electric field and the insertion of a graphene sheet. After applying an electric field, type-I to type-II and semiconductor to metal transitions can be achieved in the SnSe2/MoS2 vdWH. Besides, when a graphene sheet is inserted into the SnSe2/MoS2 vdWH to form three stacking types of G/SnSe2/MoS2, SnSe2/G/MoS2 and SnSe2/MoS2/G, the p-type semiconductor of the SnSe2/MoS2 vdWH is converted to an n-type Ohmic contact. These findings provide theoretical guidance for designing future nanoelectronic and optoelectronic devices based on the SnSe2/MoS2 vdWH.

van der Waals heterostructures can be effectively used to enhance the electronic and optical properties and extend the application range of two-dimensional materials. Here, we construct for the first time MoSeTe/X(OH)2 (X = Ca, Mg) heterostructures and investigate their electronic and optical properties as well as the relative orientation of these layers with respect to each other and the effects of an electric field. Our results show that in the MoSeTe/X(OH)2 heterostructures, the Janus MoSeTe monolayer is bonded to the X(OH)2 layer via weak van der Waals forces. Owing to different kinds of chalcogen Se and Te atoms in both sides of Janus MoSeTe, there exist two main stacking types of the MoSeTe/X(OH)2 heterostructures, that are MoSeTe-Se/X(OH)2 and MoSeTe-Te/X(OH)2 heterostructures. Interestingly, the Se- and Te-interface can induce straddling type-II and type-I band alignments. The MoSeTe-Se/X(OH)2 heterostructure exhibits a type-II band alignment, thus endowing it with a potential ability to separate photogenerated electrons and holes. Whereas, the MoSeTe-Te/Ca(OH)2 heterostructure displays a type-I band alignment, which may result in an ultrafast recombination between electrons and holes, making the MoSeTe-Te/Ca(OH)2 heterostructure a suitable material for optoelectronic applications. The MoSeTe/X(OH)2 heterostructures show an isotropic behavior in the low energy region while an anisotropic behaviour in the high photon energy region. The dielectric function of the MoSeTe-Te/Ca(OH)2 heterostructure is high at low photon energy relative to other heterostructures verifying it to have a good optical absorption. Furthermore, the band gap values and band alignment of the MoSeTe/X(OH)2 heterostructures can be modulated by applying an electric field, which induces semiconductor-to-metal and type-I(II) to type-II(I) band alignment. These results demonstrate that the MoSeTe/X(OH)2 heterostructures are promising candidates for optoelectronic and photovoltaic nanodevices.

Janus monolayers and their van der Waals heterostuctures are investigated by hybrid density functional theory calculations. MoSSe, WSSe, MoSeTe and WSeTe are found to be direct band gap semiconductors. External electric fields are used to transform indirect MoSTe and WSTe to direct band gap semiconductors. MoSSe-WSSe, MoSeTe-WSeTe and MoSTe-WSTe vdW heterostructures are also indirect band gap semiconductors with type-II band alignment. Similar to the corresponding monolayers, in some of the above mentioned vdW heterostructures an external electric field and tensile strain can transform indirect to direct band gaps, while sustaining type-II band alignment. Janus monolayers have lower values of the work function (φ) than their vdW heterostructure counterparts. Furthermore, absorption spectra, absorption efficiency, and valence(conduction) band edge potentials are calculated to understand the optical and photocatalytic behavior of these systems. Red and blue shifts are observed in the position of excitonic peaks due to the induced strain in Janus monolayers. Strong device absorption efficiencies (80-90%) are observed for the WSeTe, MoSTe and WSTe monolayers in the visible, infra-red and ultraviolet regions. Energetically favourable band edge positions in Janus monolayers make them suitable for water splitting at zero pH. We find that the MoSSe-WSSe heterostructure and the MoSTe monolayer are promising candidates for water splitting with conduction and valence band edges positioned just outside of the redox interval.

In this paper, we study the difference in electronic and optical properties of bulk and monolayer zirconium sulfide by applying the APW + lo method in the framework of density functional theory. All calculation is performed at the energy level of visual light and higher ranging from 0 eV to 15 eV. Our results demonstrates that except for the underestimated band gap like other GGA calculation, the remain properties like dielectric function, the reflectivity, absorption and loss energy are close to experiment. The valence band is constructed by mainly sulfur s/p-states and the lower portion of zirconium s/p/d-states. The conduction band is mostly donated by zirconium d-state. In contrast with bulk structure, the valence band maximum in monolayer has the triple peak at Γ point, making its monolayer be more sensitive to light absorption. The dielectric function has the highest peak at about 1.5–2.5 eV with remarkable anisotropy, beyond this level to the ultraviolet region the anisotropy decreases and almost disappears at energy larger than 10 eV. The absorption is at 106 x 10 4 cm -1 for energy range 5–10 eV, while the reflectivity is at its highest value of 30 %–50 % in the energy range from 0 to 8 eV. The energy loss of monolayer is higher than those of bulk. For optical and electronic properties, the monolayer show sharper peaks and their clear separation indicate the progressive application of monolayer zirconium sulfide.

Graphene-based van der Waals heterostructures by stacking graphene on other two-dimensional materials have recently attracted much attention due to their extraordinary properties and greatly extend the applications of the parent materials. By means of the density functional theory from first-principles calculations, in this work, the electronic properties and Schottky contact of the Graphene/InSe heterostructure, together with the effect of strain, are investigated systematically. Our results show that in the graphene/InSe heterostructure, graphene is very weakly bound to the InSe monolayer. Furthermore, we find that due to the sublattice symmetry breaking, a tiny band gap of 5 meV is opened in the graphene/InSe heterostructure, making it suitable for applications in electronic and optoelectronic devices. Moreover, we also find that the n-type Schottky contact is formed in the graphene/InSe heterostructure with a very small Schottky barrier height of 0.05 eV. The Schottky barrier height as well as Schottky contact types in the graphene/InSe heterostructure could be controlled by vertical strain applied perpendicularly to the heterostructure. When the interlayer distance between graphene and the topmost InSe monolayer is smaller than 2.40 A, one can observe a transformation of the Schottky contact of the graphene/InSe heterostructure. Our results may provide helpful information for designing novel high-performance graphene-based van der Waals heterostructures and explore their potential applications in future nanoelectronic and optoelectronic devices.

In this paper, we design novel ultra-thin graphene/MoSeS and graphene/MoSSe heterostructures and investigate systematically their structural and electronic properties as well as the effect due to perpendicularly applied electric field on the heterostructure. Our results show that the electronic properties of both the graphene (Gr) and Janus MoSeS monolayer are well kept in the Gr/MoSeS and Gr/MoSSe heterostructures due to weak interaction between them. The interlayer distance between the Gr and Janus MoSeS monolayer is derived to be 3.34 A, whereas the binding energy in the heterostructure is found to be - 3 meV per carbon atom, indicating the weak interactions between the Gr and Janus MoSeS layers. We find that in both Gr/MoSeS and Gr/MoSSe heterostructures, the Gr becomes a semiconductor with a tiny band gap of about 3 meV, forming between the π and π ∗ bands at the high symmetry K point. The appearance of the fundamental band gap in the Gr makes it suitable for application in electronics and optoelectronics like as field effect transistors. Furthermore, the Gr/MoSeS heterostructure forms an n-type Schottky contact with the Schottky barrier height of 0.53 eV at the equilibrium state. Our results also indicate that the electric field applied perpendicularly to the heterostructure could control not only the Schottky barrier height, but also the Schottky contact type from the n-type to p-type. Based on these extraordinary electronic properties of ultra-thin Gr/MoSeS heterostructures, which are expected to be with applications in nanoelectronic and optoelectronic devices in the future experiments.

The influences of an external electric field with uniform or modulated potential on the electronic and optical properties of armchair graphene nanoribbons (GNRs) are explored using the multi-orbital tight-binding Hamiltonian. The interplay between an electric field and interaction between (s, p x , p y , p z ) orbitals remarkably enriches the main features of band structures and absorption spectra. The applied electric field can notably alter the energy dispersions of π and σ bands, leading to the deformation of band-edge states, open and close of a band gap, and modification of the Fermi energy. The vertical optical excitations happen among the π bands, while their available channels depend on the Fermi level which is controlled by the σ-edge bands and a finite potential. With the rich and unique properties, GNRs are suitable candidates for applications in the fields of photodetectors, nanoelectronics, and spintronics. The calculated results are expected to be examined by the angle-resolved photoemission spectroscopies and optical spectroscopies.

Two-dimensional graphene-based van der Waals heterostructures have received considerable interest because of their intriguing characteristics compared with the constituent single-layer two-dimensional materials. Here, we investigate the interfacial characteristics, Schottky contact, and optical performance of $\mathrm{graphene}/{\mathrm{Ga}}_{2}\mathrm{SSe}$ van der Waals (vdW) heterostructure using first-principles calculations. The effects of stacking patterns, electric gating, and interlayer coupling on the interfacial properties of $\mathrm{graphene}/{\mathrm{Ga}}_{2}\mathrm{SSe}$ heterostructures are also examined. Our results demonstrate that the Dirac cone of graphene is well preserved at the $\mathrm{\ensuremath{\Gamma}}$ point in all stacking patterns due to the weak vdW interactions, which keep the heterostructures feasible such that they can be obtained in further experiments. Moreover, depending on the stacking patterns, a small band gap of about 13--17 meV opens in graphene and has a high carrier mobility, indicating that the $\mathrm{graphene}/{\mathrm{Ga}}_{2}\mathrm{SSe}$ heterostructures are potential candidates for future high-speed nanoelectronic applications. In the ground state, the $\mathrm{graphene}/{\mathrm{Ga}}_{2}\mathrm{SSe}$ heterostructures form an $n$-type Schottky contact. The transformation from an $n$-type to a $p$-type Schottky contact or to an Ohmic contact can be forced by electric gating or by varying the interlayer coupling. Our findings could provide physical guidance for designing controllable Schottky nanodevices with high electronic and optical performances.

In this paper, detailed investigations of the electronic and optical properties of a Janus SnSSe monolayer under a biaxial strain and electric field using ab initio methods are presented. Our calculations indicate that the Janus SnSSe monolayer is a semiconductor with an indirect band gap larger/lower than that of the SnSe2/SnS2 monolayer. To obtain accurate estimates of the band gap, both Perdew–Burke–Ernzerhof (PBE) and Heyd–Scuseria–Ernzerhof (HSE06) hybrid functionals have been used and the effect of spin–orbit coupling has also been included. While the influence of the electric field on the electronic and optical properties of the Janus SnSSe monolayer is quite weak, biaxial strain plays a key role in controlling these properties. The Janus SnSSe monolayer has a wide absorption spectrum, from visible light to the ultraviolet region. At equilibrium, the maximum absorption coefficient of the monolayer is up to 11.152 × 104 cm−1 in the ultraviolet region and it can be increased by strain engineering. With high absorption intensity in the visible light area and being able to tune the absorbance by strain, the Janus SnSSe monolayer becomes a promising material for applications in optoelectronic devices.

In this work, we consider the electronic and optical properties of chemically functionalized InN monolayers with F and Cl atoms (i.e., F–InN–F, F–InN–Cl, Cl–InN–F, Cl–InN–Cl monolayers) using first-principles calculations. The adsorption of the F and Cl atoms on the InN monolayer is determined to be chemically stable and the F–InN–F monolayer is most likely to occur. Our calculations show that the chemical functionalization with Cl and F atoms not only breaks the planar structure of InN monolayer but also increases its band gap. By using both Perdew, Burke, and Ernzerhof (PBE) and the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functionals, all four models of chemically functionalized InN monolayers are found to be semiconductors with direct energy gaps and these gaps depend on the constituent species. When the spin–orbit coupling (SOC) was included, the energy gap of these monolayers was reduced and an energy splitting was found at the Γ-point in the valence band. Chemically functionalized InN monolayers can absorb light in a wide region, especially the F–InN–F and Cl–InN–F monolayers have a strong ability to absorb the visible light. Our findings reveal that the chemically functionalized InN monolayers have potential applications in next-generation optoelectronic devices.

We study the optical transport properties of the monolayer transition metal dichalcogenides (TMDCs) such as ${\mathrm{MoS}}_{2}$, ${\mathrm{WS}}_{2}$, ${\mathrm{MoSe}}_{2}$, and ${\mathrm{WSe}}_{2}$ in the presence of a magnetic field. The TMDCs band structures are obtained and discussed by using the effective massive Dirac model, in which the spin and valley Zeeman effects as well as an external electric field are included. The magneto-optical absorption coefficient (MOAC) is derived as a function of absorbed photon energy when the carriers are scattered by random impurities combined with the intrinsic acoustic and optical phonons in TMDCs and the surface optical (SO) phonons of substrates. Our result shows that the spin-splitting feature appeared in all four TMDC materials. The combination of strong spin-orbit coupling (SOC) and Zeeman fields has doubled the Landau levels but has not changed the energy gap of the TMDCs monolayer, which can be controlled by the electric field. Because of their strong SOC effect, the absorption spectrum in monolayer TMDCs is separated into two separate peaks caused by spin up and down. At the low temperature, the MOAC intensity via impurity scattering is the biggest followed by that of the SO phonons while the intrinsic acoustic and optical phonon scatterings display the smallest. For the monolayer TMDCs on substrates, ${\mathrm{SiO}}_{2}$ always shows its superiority in comparison with the others. Among the four TMDC materials, ${\mathrm{MoSe}}_{2}$ shows the biggest MOAC intensity, while ${\mathrm{WS}}_{2}$ has the biggest value of the absorbed photon energy. The full-width at half-maximum (FWHM) via impurity scattering achieves its highest value in ${\mathrm{WS}}_{2}$, while this occurs in ${\mathrm{MoSe}}_{2}$ and ${\mathrm{MoS}}_{2}$ via intrinsic acoustic and optical phonon scatterings, respectively. Our estimation of mobility from FWHM gives good agreement with the experimental results in ${\mathrm{WS}}_{2}$.

In this work, we systematically investigate the electronic and optical properties of surface-functionalized GeC monolayer with F and Cl using density functional theory. Our calculations indicate that the surface functionalization of the GeC with F and C atoms leads to the disruption of the planar structure of the GeC monolayer and the surface-functionalized GeC monolayer has a low-bucking structure. At equilibrium, all four configurations of surface-functionalized GeC monolayer with F and Cl, i.e., F–GeC–F, F–GeC–Cl, Cl–GeC–F, and Cl–GeC–Cl, are direct semiconductors. Their band gaps vary from 2.839 eV to 3.175 eV which are calculated using Heyd–Scuseria–Ernzerhof (HSE) hybrid functional. Compared to the other configurations, the formation energy of F–GeC–F is the smallest, − 9 . 097 eV , which implies that this configuration is the most likely to occur. We also used the Mulliken population analysis to estimate the internal charge distribution and transferred charge in the systems. The functionalization of the surface leads to the shifting the first optical gap of the material. The fully chlorination of GeC causes its absorption coefficient to increase significantly, up to 14 . 912 × 1 0 4 cm−1 at the incident light energy of 13.173 eV. Besides, surface-functionalized GeC monolayer with F and Cl strongly absorbs light in the near ultraviolet region. Our calculation results provide detailed information on how to change the electronic and optical properties of monolayer GeC by surface functionalization, which has promising applications in opto-electronic devices.

In this work, by means of density functional theory, we systematically investigate the geometric structure and electronic properties of the vertical heterostructure by stacking graphene on top of single-layered hexagonal boron nitride and molybdenum diselenide (Gr/h-BN/MoSe2). Our results show that the interlayer coupling in the heterostructure is mainly governed by the weak van der Waals interactions. We find that in the heterostructure, a tiny band gap of 82 meV is opened around the Dirac K point of graphene due to sublattice symmetry breaking, and a minigap of 39 meV is opened between the π band of graphene and the vertical orbitals of MoSe2 due to their hybridization. This band gap opening in graphene makes it suitable for application in novel high-performance nanoeclectronic devices. Furthermore, the Gr/h-BN/MoSe2 heterostructure with inserting insulated h-BN layer forms an n-type Schottky contact with a small Schottky barrier height of 0.1 eV. These findings could provide helpful information for designing novel nanoelectronic devices by stacking graphene on top of single-layered h-BN and MoSe2.

In this work, we consider the effect of biaxial ɛb and uniaxial ɛac∕zz strains on electronic properties and optical parameters of monolayer SnS using first-principles calculations. Our calculations show that the monolayer SnS is a semiconductor with an indirect energy gap of 1.63 eV at the equilibrium state. While an effect of tensile strains on bandgap is quite small, the bandgap of monolayer SnS depends strongly on the compressive strains, especially a semiconductor-metal phase transition is occurred due to the uniform compressive biaxial strain at −14% elongation. The optical spectra of the monolayer are high anisotropic, and the absorption coefficient of monolayer SnS tends to increase in the presence of compression strains, while the tensile strains reduce the absorption coefficient of the monolayer SnS. We believe that the phase transition and extraordinary optical properties of the strained monolayer SnS will make it become a useful material in nanoelectromechanical devices and optoelectronic applications.

The effect of strain on the structural and electronic properties of monolayer phosphorene is studied by using first-principle calculations based on the density functional theory. The intra- and inter-bond length and bond angle for monolayer phosphorene is also evaluated. The intra- and inter-bond length and the bond angle for phosphorene show an opposite tendency under different directions of the applied strain. At the equilibrium state, monolayer phosphorene is a semiconductor with a direct band gap at the Γ -point of 0.91 eV. A direct-indirect band gap transition is found in monolayer phosphorene when both the compression and tensile strain are simultaneously applied along both zigzag and armchair directions. Under the applied compression strain, a semiconductor-metal transition for monolayer phosphorene is observed at −13% and −10% along armchair and zigzag direction, respectively. The direct-indirect and phase transition will largely constrain application of monolayer phosphorene to electronic and optical devices.

Graphene-based van der Waals heterostructures are expected recently to design and fabricate many novel electronic and optoelectronic devices. The combination of the electronic structures of graphene and graphene-like GaSe monolayer (g-GaSe) in an ultrathin heterostructure has been realized experimentally, such as graphene/g-GaSe field effect transistor and dual Schottky diode device. In the present work, we investigate the electronic properties of the graphene/g-GaSe heterostructures under the applied electric field, in-plane strains, and interlayer coupling. Our results show that the electronic properties of the graphene/g-GaSe heterostructures are well preserved owing to a weak vdW interaction. Especially, a tiny band gap of 13 meV has opened in the presence of the g-GaSe monolayer. We found that the n-type Schottky contact is formed in the graphene/g-GaSe heterostructure with a Schottky barrier height of 0.86 eV, which can be efficiently modulated by applying the electric field, in-plane strains, and interlayer coupling. Furthermore, a transformation from the n-type to p-type Schottky contact is observed when the applied electric field is larger than 0.1 V/A or the interlayer distance is smaller than 3.2 A. Our results may provide helpful information to design and fabricate the future graphene-based vdW heterostructures, such as graphene/g-GaSe heterostructure and understand the physics mechanism in the graphene-based 2D vdW heterostructures.

Using density functional theory, we have studied the structural, electronic and optical properties of two-dimensional graphene-like $$\hbox {C}_2\hbox {N}$$ nanosheet under in-plane strains. Our results indicate that the $$\hbox {C}_2\hbox {N}$$ nanosheet is a semiconductor with a direct band gap of 1.70 eV at the equilibrium state opening between the highest valence band and lowest conduction band located at the $$\varGamma $$ point. The band gap of the $$\hbox {C}_2\hbox {N}$$ nanosheet decreases with the increasing of both uniaxial/biaxial strains. In the presence of the strain, we found band shift and band splitting of the occupied and unoccupied energy states of the valence and conduction bands, resulting in a decrease of the band gap. Furthermore, the absorption and reflectance spectra for the $$\hbox {C}_2\hbox {N}$$ nanosheet have a broad peak around 2.6 eV, where a maximum absorption value is up to $$3.2 \times 10^{-5}\,\hbox {cm}^{-1}$$ and reflectance is about 0.27%. Moreover, our calculations also show that the optical properties of the $$\hbox {C}_2\hbox {N}$$ nanosheets can be controlled by applying the biaxial and uniaxial strains. The obtained results might provide potential applications for the $$\hbox {C}_2\hbox {N}$$ nanosheets in nanoelectronics and optoelectronics.

In this paper, we study the electronic properties of graphene/phosphorene (G/P) heterostructure under applied electric field. The interlayer distance between graphene and topmost phosphorene is 3.50 A and the binding energy per carbon atom is 28.2 meV, which is indicated that graphene is bound to phosphorene via vdW interaction. The appearance of an energy gap of 33 meV in graphene is due to the dominant influence exerted by the phosphorene on graphene and sublattice symmetry broken between graphene and substrate. The G/P heterostructure forms a p-type Schottky contact with Φ B p = 0.34 eV. By applying the negative electric field, the G/P heterostructure keeps a p-type Schottky contact. Whereas with the positive electric field of E ≥ +0.25 V/A, Φ B p becomes larger than Φ B n , resulting in a transformation from p-type to n-type Schottky contact. The present results may open up a new avenue for application of the G/P vdW heterostructure in electronic devices.

In this work, the influence of biaxial strain on electronic, optical, and effective masses characteristics of Janus MSSe (M = Mo, W) have been investigated through first-principles calculations as implemented in WIEN2k package. From the obtained results, we remark that MoSSe and WSSe monolayers exhibit, respectively, a direct and indirect bandgap transition at equilibrium. Our achieved results demonstrate that the biaxial strain fundamentally alters the electronic states of Janus MSSe monolayers, and mainly, a semiconductor-metal transition phase has been determined to occur at a biaxial strain ratio of 12%. Moreover, it has been revealed that both electrons and holes effective masses of MSSe monolayers can be tuned by biaxial strain. For the optical properties of Janus monolayers, the polarization direction of the incident light plays a vital role in defining the light absorption domain. The MSSe Janus monolayers are shown to have a wide range of absorption spectrum , including the visible light domain with perpendicular polarized light . Furthermore, our computations of the dielectric function indicate that the optical responses of Janus monolayers MoSSe and WSSe strongly depend on the applied strain ratio; particularly, for the high photon energy domain. Overall, the findings revealed that both Janus MoSSe and WSSe monolayers could be potential materials for applications in optoelectronics.

In this work, we consider the effect of out-plane strain on the electronic properties of AB-stacked bilayer armchair graphene nanoribbons (BAGNRs) using density functional theory. At equilibrium, the interlayer distance of BAGNRs is $$d_0=3.326$$ A. Our DFT calculations show that while the dependence of the band gap of 11-BAGNR on interlayer distance d is insignificant, especially in the case of the $$d

We investigated the effects of biaxial strain on electronic structure of ZrS2, ZrSe2, HfS2, HfSe2, ZrSSe and HfSSe monolayers. Similar to ZrS2, ZrSe2, HfS2, HfSe2 monolayers, Janus ZrSSe and HfSSe monolayers are indirect bandgap semiconductors. Tensile strain of 6(8)% transform ZrSSe(HfSSe) monolayer to direct bandgap semiconductor. Based on the calculation of binding energies and interlayer distance staking-(c) is found to be the most stable configuration for ZrSSe/HfSSe vdW heterostructure. Unstrained ZrSSe/HfSSe vdW heterostructure in staking-(c) is a type-II indirect bandgap semiconductor. Valence and conduction band edges show that under tensile strain ZrSSe, HfSSe and ZrSSe/HfSSe vdW heterostructure are efficient photocatalysts.

We investigate the peculiar electronic and optical properties of zigzag graphene nanoribbons (GNRs) under the effects of uniform and modulated electric fields. The hybridization between the four atomic orbitals ( s , p x , p y , p z ) is considered by means of the tight-binding model calculations. Both the π bands originating from the p z orbital and σ bands arising from the ( s , p x , p y ) orbitals play critical roles in the electronic structure and thus the absorption spectra. They determine the Fermi level and the available excitation channels between the occupied and unoccupied states. We show that an in-plane electric field in the form of modulated potential can significantly modify the electronic and optical properties of zigzag GNRs. The field-induced modification in energy dispersion, band-edge states, and band gap gives rise to rich absorption spectra with diverse structures. Our theoretical prediction could be verified by angle-resolved photoemission spectroscopies and optical spectroscopies.

Motivated by the successful experimental fabrication of Janus structures recently, a systematic study of the structural, electronic, and optical properties of the Janus Al2SSe monolayer has been done through first-principles approach. Through phonon spectrum and ab initio molecular dynamics analysis, Al2SSe was confirmed to be dynamically and thermally stable. The Janus Al2SSe monolayer exhibits a semiconducting characteristics with indirect band gap of 2.079 eV at equilibrium. While biaxial strain can significantly alter band gap, the influence of electric field on electronic as well as optical properties is negligible. The optical absorbance of Al2SSe is activated in the visible light region and its intensity can be enhanced by strain. Our findings only highlight the physical properties but also provide an effective way for tuning the electronic and optical properties of Al2SSe monolayer by strain engineering.

In this work, the effect of Peierls distortion on the electronic properties of armchair graphene nanoribbons is theoretically studied in a tight-binding approximation. As a consequence of Peierls distortion, when the Kekule-type bond alternation is introduced, the band gap of armchair nanoribbons strongly depends on the difference in bond length between short and long bonds in the honeycomb lattice. We can control the band gap of a nanoribbon by its uniaxial strain and a semiconductor–metal phase transition can occur at certain elongations.

In the present work, we consider systematically the electronic and optical properties of two-dimensional monolayer germanium monosulfide (GeS) under uniaxial strains along armchair (AC-strain) and zigzag (ZZ-strain) directions. Our calculations show that, at the equilibrium state, the monolayer GeS is a semiconductor with an indirect band gap of 1.82 eV. While monolayer GeS is still an indirect band gap semiconductor under ZZ-strain, an indirect–direct energy gap transition can be found in the monolayer GeS when the AC-strain is applied. The optical spectra of the monolayer GeS have strong anisotropy in the investigated energy range from 0 eV to 8 eV. Based on optical properties, we believe that the monolayer GeS is a potential candidate for applications in energy conversion and optoelectronic technologies. This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 103.01-2017.309 and the Belarusian Scientific Program ‘‘Convergence’’.

Combining van der Waals heterostructures by stacking different two-dimensional materials on top of each other layer-by-layer can enhance their desired properties and greatly extend the applications of the parent materials. In this work, by means of first principles calculations, we investigate systematically the structural and electronic properties of six different stacking configurations of a Si/GaSe heterostructure. The effect of biaxial strain and electric field on the electronic properties of the most energetically stable configuration of the Si/GaSe heterostructure has also been discussed. At the equilibrium state, the electronic properties of the Si/GaSe heterostructure in all its stacking configurations are well kept as compared with that of single layers owing to their weak van der Waals interactions. Interestingly, we find that a sizable band gap is opened at the Dirac K point of silicene in the Si/GaSe heterostructure, which could be further controlled by biaxial strain or electric field. These findings open up a possibility for designing silicene-based electronic devices, which exhibit a controllable band gap. Furthermore, the Si/GaSe heterostructure forms an n-type Schottky contact with a small Schottky barrier height of 0.23 eV. A transformation from the n-type Schottky contact to a p-type one, or from the Schottky contact to an ohmic contact may occur in the Si/GaSe heterostructure when strain or an electric field is applied.

In this work, the doping effects of rare-earth La and Ce atoms on electronic and optical properties of Janus MoSSe monolayer are investigated by means of first principles calculations. Our results imply that when one La and Ce doped to one S or Se side of Janus MoSSe monoalayer, it leads to a decrease in the band gap and results in the transition from direct to indirect. With increasing the La and Ce doping concentration, the Janus MoSSe monolayer switched from semiconductor to metal. Moreover, we find that effective masses of all the La and Ce doped Janus MoSSe systems are decreased as compared to pristine state, rendering their high carrier mobility. Furthermore, all the La and Ce doped MoSSe systems have red shift and possess high absorption ability in the visible and infrared regions. These findings suggest that rare-earth La and Ce doped MoSSe monolayer are potential candidate for spintronics, nanoelectronics and optoelectronics.

In this paper, the electronic, optical, and photocatalytic properties of GaSe/HfS2 heterostructure are studied via first-principles calculations. The stability of the vertically stacked heterobilayers is validated by the binding energy, phonon spectrum, and ab initio molecular dynamics simulation. The results reveal that the most stable GaSe/HfS2 heterobilayer retains a type-II alignment with an indirect bandgap 1.40 eV. As well, the results also show strong optical absorption intensity in the studied heterostructure (1.8 × 105 cm−1). The calculated hole mobility is 1376 cm2 V−1 s−1, while electron mobility reaches 911 cm2 V−1 s−1 along the armchair and zigzag directions. By applying an external electric field, the bandgap and band offset of the designed heterostructure can be effectively modified. Remarkably, a stronger external electric field can create nearly free electron states in the vicinity of the bottom of the conduction band, which induces indirect-to-direct bandgap transition as well as a semiconductor-to-metal transition. In contrast, the electronic properties of GaSe/HfS2 heterostructure are predicted to be insensitive to biaxial strain. The current work reveals that GaSe/HfS2 heterostructure is a promising candidate as a novel photocatalytic material for hydrogen generation in the visible range.

In present work, we study the electronic, optical and photocatalytic properties of strained MoSSe monolayer through first-principles study. A single layer Janus MoSSe possesses a semiconducting character with a direct band gap of 1.59/2.09 eV obtained by PBE/HSE06 method. The valence band maximum (VBM) of Janus MoSSe monolayer is mainly contributed by the S-p orbital, whereas the conduction band minimum (CBM) comes from the Mo- d x 2 . Furthermore, Janus MoSSe monolayer has been proved to be energetically stable with no imaginary frequency in its phonon spectrum. Interesting, both the tensile and compressive strains can transform Janus MoSSe monolayer from direct to indirect band gap nature as well as tune its band gap. The compressive strain tends to an increase in the band gap, whereas the tensile strain leads to decrease in the band gap. Optical absorption of Janus MoSSe monolayer demonstrates that the tensile strain gives rise to an existence of blue shift, while compressive strain is responsible for the formation of a red shift. Photocatalytic properties show that Janus MoSSe monolayer with 4% or 6% strained could be a catalyst for the H2O oxidation, making it suitable for water splitting applications.

The effect of biaxial strains e b and electric field E on the electronic structure and optical properties of Janus monolayer PtSSe was studied by Density Functional Theory (DFT). A reasonable band gap of PtSSe was found to be 1.547 eV. In the infrared region, both biaxial strains and electric fields result in noticeable enhancement of the electronic structure as well as optical properties of PtSSe. Especially, under biaxial strains, the change of PtSSe band gap obeys the form of an asymmetric concave down parabola. This result confirms the existence of a maximum PtSSe band gap under biaxial strains e b and the possibility of tuning PtSSe band gap to fit the requirement of the optoelectronic devices. The absorption rate in the visible light region of Janus monolayer PtSSe increases sharply and can be altered by strain engineering. Biaxial strain not only alters the absorption intensity but can also significantly shift the position of these absorption peaks. The present study provides additional information about the strain and electric field-induced electronic structure and optical properties of Janus monolayer PtSSe, which should be taken into account for better PtSSe-based devices.

In this work, detailed investigations of the electronic and optical properties of a Janus Ga2STe monolayer under a biaxial strain and electric field have been performed using density functional theory. Via the phonon spectrum and ab-initio molecular dynamics simulations, the dynamical and thermal stabilities of the Janus Ga2STe monolayer are verified. Our obtained results showed that the Janus Ga2STe exhibits a direct semiconducting characteristic and its band gap depends greatly on the biaxial strain. While both the electronic and optical properties are very weakly dependent on the electric field, strain engineering can cause a direct–indirect band gap transitions in the Janus Ga2STe. At equilibrium, the optical absorbance of the Janus Ga2STe monolayer is activated in the infrared light region of about 0.9 eV, which is close to its band gap value. The main peak of the optical absorbance spectrum is located in the ultraviolet light region with an absorbance intensity of 11.914 × 104 cm−1 may be increased by compression strain. In particular, the absorbance intensity of the Janus Ga2STe monolayer increases rapidly in the visible light region, reaching 4.810 × 104 cm−1 and can be altered by strain. Our results not only show that the Janus Ga2STe monolayer has many promising applications in opto-electronic devices but also motivates experimental works on Janus structures in near future.

In this paper, we study the effect of uniaxial and biaxial strain on the structural and electronic properties of MoS monolayers by first-principle calculations based on density functional theory. Our calculations show that the bond length between Mo and S atoms depends linearly on the strain. At the equilibrium state, MoS has a direct band gap of 1.72 eV opening at the K-point. However, an indirect–direct band gap transition has been found in MoS monolayer when the strain is introduced. MoS becomes a semiconductor with an indirect band gap when the uniaxial strain or the biaxial strain . Under biaxial strain, a metal–semiconductor transition occurs at of elongation. The indirect character and phase transition will largely constrain application of MoS monolayer to electronic and optical devices.

In this work, we investigate band-gap tuning in bilayer MoS2 by an external electric field and by applied biaxial strain. Our calculations show that the band gaps of bilayer MoS2 can be tuned by the perpendicular electric field or biaxial strain. The band gaps of bilayer MoS2 decrease with increasing applied electric field or biaxial strain. When the electric field was introduced, electronic levels are split due to the separation of the valence sub-band and the conduction sub-band states. Our calculations also show that the change in the band gap of bilayer MoS2 is due to the separation of electronic levels by electric field via the Stark effect. At the electric field $$E_{\mathrm{Field}} = 5.5$$ V/nm or biaxial strain $$\varepsilon = 15\%,$$ bilayer MoS2 becomes metallic. The semiconductor–metal phase transition in bilayer MoS2 plays an important role in its application for nanodevices.

In this work, making use of density functional theory (DFT) computations, we systematically investigate the effect of biaxial strain engineering and external electric field applied perpendicular to the layers on the band gaps and electronic properties of monolayer MoS 2 . The direct-to-indirect band gaps and semiconductor-to-metal transition are observed in monolayer MoS 2 when strain and electric field are applied in our calculation. We show that when the biaxial strain and external electric field are introduced, the electronic properties including band gaps of monolayer MoS 2 can be reduced to zero. Our results provide many useful insights for the wide applications of monolayer MoS 2 in electronics and optoelectronics.

In this work, we investigate the electronic and optical properties of two configurations of haft-hydrogenated indium nitride monolayers H–InN and 2H–InN using first-principles calculations. Both H–InN and 2H–InN monolayers are semiconductors with indirect bandgap quite larger than that of pure InN monolayer. When the spin–orbit coupling was included, their bandgap is significantly reduced. Upon the hydrogenation, charge transfers from InN plane to functionalized species H in H–InN while a small amount of charge has been transferred from H atoms to InN plane in 2H–InN monolayer. Haft-hydrogenated InN monolayers can strongly absorb light in a wide range from visible light to infrared which opens possibilities for their application in optoelectronic devices.

In this work, we investigate the low-energy bands of monolayer WS2 under external electric and magnetic fields using an effective low-energy Hamiltonian. Our calculations indicate that band gap of monolayer WS2 increases linearly with an external perpendicular electric field and when the electric field energy Δ z is equal to the size of spin splitting, the band gap including spin–orbit interaction of the monolayer increases to its band gap as the case of without spin–orbit interaction. In the presence of the magnetic field, spin splitting energy in the conduction and the valence bands at the valleys depends strongly on the magnetic field. In this work, the optical properties of monolayer WS2 are also calculated by using the Ehrenreich–Cohen formula. Our estimation for the square of the interband matrix element for transitions near the K points is in good agreement with previous calculations.