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Article

Strain and Layer Modulations of Optical Absorbance and Complex Photoconductivity of Two-Dimensional InSe: A Study Based on GW0+BSE Calculations

by
Chuanghua Yang
1,*,
Yuan Jiang
1,
Wendeng Huang
1 and
Feng Pan
1,2
1
School of Physics and Telecommunication Engineering, Shaanxi University of Technology, Hanzhong 723001, China
2
Shaanxi Key Laboratory of Catalysis, School of Physics and Telecommunication Engineering, Shaanxi University of Technology, Hanzhong 723001, China
*
Author to whom correspondence should be addressed.
Crystals 2025, 15(7), 666; https://doi.org/10.3390/cryst15070666
Submission received: 16 June 2025 / Revised: 13 July 2025 / Accepted: 17 July 2025 / Published: 21 July 2025
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Abstract

Since the definitions of the two-dimensional (2D) optical absorption coefficient and photoconductivity are independent of the thickness of 2D materials, they are more suitable than the dielectric function to describe the optical properties of 2D materials. Based on the many-body GW method and the Bethe–Salpeter equation, we calculated the quasiparticle electronic structure, optical absorbance, and complex photoconductivity of 2D InSe from a single layer (1L) to three layers (3L). The calculation results show that the energy difference between the direct and indirect band gaps in 1L, 2L, and 3L InSe is so small that strain can readily tune its electronic structure. The 2D optical absorbance results calculated taking into account exciton effects show that light absorption increases rapidly near the band gap. Strain modulation of 1L InSe shows that it transforms from an indirect bandgap semiconductor to a direct bandgap semiconductor in the biaxial compressive strain range of −1.66 to −3.60%. The biaxial compressive strain causes a slight blueshift in the energy positions of the first and second absorption peaks in monolayer InSe while inducing a measurable redshift in the energy positions of the third and fourth absorption peaks.

1. Introduction

Two-dimensional (2D) materials refer to materials with several-atom-thick layers peeled off from three-dimensional layered crystal materials. Two-dimensional materials are stable due to the weak interactions between the layers of three-dimensional layered materials. Many 2D materials have been synthesized, including boron nitride (h-BN), transition metal dichalcogenides, and metal monochalcogenides. Many studies have shown that 2D materials have significantly different properties from their bulk counterparts. Many of the transition metal dichalcogenides and metal monochalcogenides have been proven by research to have good optical properties and are suitable for use in optoelectronic devices such as photodetectors.
Currently, the layered hexagonal metal chalcogenide InSe is attracting great attention from researchers due to its high photoresponsivity, layer-dependent electronic and optical properties, high carrier mobility, and stability in the air [1,2,3,4,5]. Bulk InSe crystallizes in a layered structure and has three crystallographic structures, β, γ, and ε, according to different stacking arrangements. γ-InSe, the most studied structure and monolayer, and few-layer γ-InSe have exhibited high electron mobility (103 cm2 V−1 S−1) [4,5], a high current on/off ratio (108) [1,2], good metal ohmic contact, and an applicable bandgap range [6]. However, the instability of γ-InSe itself has a negative influence [1] on its practical application in microelectronics and optoelectronics. Experimental studies show that few-layered InSe is a semiconductor with an indirect band gap of 1.4 eV, a strong photoresponse rate of 34.7 mA/W, and a fast response time of 488 μs [7]. Due to the stacking arrangement of ABAB, bulk β-InSe is the most stable of the three structures [8,9]. The symmetry groups of γ-InSe and ε-InSe are C 3 v 5 and D 3 h 1 , respectively. Compared with the other two structures, the advantage of monolayer or few-layer β-InSe is that the layered hexagonal structure can be directly peeled from the bulk β-InSe [9]. β-InSe belongs to the asymmetrical point Γ roup, which presents a better anisotropy of optical properties than γ-InSe and ε-InSe. This feature can be used to make polarization-sensitive photodetectors, which can be applied to night vision devices, remote sensing images, and biological images. Guo with his collaborators [10] has synthesized stable p-type 2D layered β-InSe and has built polarization-sensitive photodetectors with a photocurrent anisotropic ratio of 0.70. Dai and his collaborators [11] summarized the recent research progress of layered InSe in their review article, including device performance, synthetic methods, and future development opportunities and challenges. Magorrian et al. [12] studied the electronic structure and optical properties of 2D InSe based on DFT but did not give a specific light absorption spectrum and did not consider the exciton effect.
Optical properties are key basic characteristics for optoelectronic materials. Several studies [13,14,15] have reported that the dielectric function, which effectively describes the optical properties of bulk materials, fails to accurately characterize the optical behavior of two-dimensional (2D) materials due to the thickness problem. For 2D materials, photoconductivity and absorbance can define their optical properties well [13,14]. So far, there are no related reports on the photoconductivity and absorptivity of 2D InSe. Generally, the exciton effect in 2D materials is relatively strong and greatly affects their optical properties [13], so it must be considered in the calculation of optical properties. Sang et al. have calculated the dielectric function of layered β-InSe based on the HSE06 functional [9], which cannot accurately and comprehensively describe the optical properties of 2D materials.
Several approaches have been proposed for modulating the electronic structures and optical properties of two-dimensional materials, including alloying [16] and applied electric fields (Stark effect) [17]. Beyond these control mechanisms, strain engineering is a common and effective means to modulate the electronic structure and optical properties of 2D semiconductors. Previous experiments demonstrated that graphene and MoS2 can withstand a maximum strain of 15% and 11% [18,19,20], respectively. However, it should be noted that material defects and imperfections reduce the strain limit [21]. Ni et al. successfully opened the 300 meV band gap of graphene by applying 1% uniaxial tensile strain [22]. Previous calculations [23,24,25] have reported the effect of strain on the electronic structure of 2D MoS2 and phosphorene by applying tensile or compressive strain. For 2D materials, strain is easily implemented by stretching, adding a substrate, or exerting pressure [26,27,28]. Hu et al. [29] reported that single-layer InSe can withstand 27% of the strain in the armchair direction and can sustain 25% of the strain in the z-shaped direction (an A phase change will occur if the strain is greater than this). Song et al. tuned the band structure of few-layer γ-InSe by applying uniaxial strain and observed the shift of the PL spectrum with the strain and number of layers [30]. Wu et al. studied the effects of strain on the electronic structure, mobility, and optical properties of one-to-five-layer γ-InSe [31]. Their results show that the indirect band gap can be converted into a direct band gap by applying compressive strain, which significantly increases the PL intensity.
Few-layer β-InSe has huge application prospects in manufacturing polarization-sensitive photodetectors [10]. At present, there are no related reports on the 2D light absorption and complex photoconductivity of 2D β-InSe optical properties, which are critical to the manufacture of optoelectronic devices. These two properties not only accurately describe the optical properties of 2D materials but also facilitate direct comparison with experimental data [32,33]. In this work, we employ first-principles calculations within density functional theory (DFT), the many-body GW0 method [34,35,36], and the Bethe–Salpeter equation (BSE) [37,38] to investigate the electronic structure, optical absorbance, and complex photoconductivity of 1L-to-3L β-InSe and the modulation effect of strain on them.

2. Materials and Methods

Our calculation method uses a combination of first principles and many-body perturbation theory. All the first-principles calculations were implemented in the Vienna ab initio simulation package (VASP) [39,40] based on DFT with the projector augmented wave (PAW) [41] method. The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) [42] functional is adopted for the exchange–correlation potential. We sampled the Brillouin zone using a shifted k-point Γ rid of 12 × 12 × 1 based on the Monkhorst–Pack model [43]. The vacuum thickness along the z-axis is set to 15 Å to prevent the interaction between periodically repeated lattices.
Based on the DFT calculations, the GW0 method and random phase approximation (RPA) [44,45] are used, as implemented in the VASP, to calculate the quasiparticle electronic structure and optical properties. Quasiparticle electronic structures were interpolated with the maximally localized Wannier function method [46]. Quasiparticle electronic structures were generated on Brillouin zone grids with up to 50 × 50 × 50 points with the maximally localized Wannier function method interpolation. The In-5s and In-5p states forming the conduction band, along with the Se-4p states constituting the valence band, were included in the basis set for Wannier function construction for the construction and the final accuracy of the interpolation. The optical properties including exciton effects were determined using the BSE with Tamm–Dancoff approximation. The cutoff energy for the response function expansion was set to 1.3 × the electronic wavefunction cutoff (ENCUT = 300 eV). Convergence testing confirmed energy shifts < 0.05 eV when increasing to 450 eV. One hundred forty-four empty conduction bands are included in the summation to calculate the dielectric function and GW self-energy. The BSE calculation utilized a 16 × 16 × 1 Gamma-centered grid, as exciton wavefunctions require denser sampling. The optical properties including exciton effects were determined by solving the BSE equation with Tamm–Dancoff approximation [47], including 24 highest valence bands and 24 lowest conduction bands as the basis of exciton states.
The 2D optical absorbance and 2D photoconductivity have been defined and derived in previous studies [13,14].

3. Results and Discussion

3.1. Geometric Structure

The top views and side views of few-layer β-InSe are displayed in Figure 1. The hexagonal primitive cell is used to calculate the properties of pristine and biaxially strained β-InSe. For comparison with experimental data, the optimized equilibrium geometric structures of bulk β-InSe are summarized in Table 1 using different pseudopotentials (PPs). The d and sv PPs, respectively, represent the semi-core d states and s states, serving as the valence electrons of Ga and Se atom PPs. As can be seen from Table 1, the lattice constants obtained using three pseudopotential optimizations are all larger than the experimental values. The reason is that the PBE pseudopotential always underestimates the band gap but overestimates the lattice constant. Among the results of the three pseudopotentials, sv PPs have the best result, with the largest error compared to the experimental value being only 1.67%. Therefore, in all calculations below, sv PPs will be adopted.

3.2. Computational Analysis of the Electronic and Optical Characteristics of Bulk β-InSe

The quasiparticle band structure of bulk β-InSe is depicted in Figure 2. The calculated result shows that bulk InSe is a direct bandgap semiconductor with a band gap of 1.30 eV, and this result is in good agreement with the experimentally measured value [48,49] at about 100 K. The maximum value of the valence band and the minimum value of the conduction band are both at the Γ point. The accurate prediction of the electronic structure of bulk InSe lays a good foundation for the following calculation of the strain- and layer-modulated 2D InSe.
The imaginary parts ε2(ω) of bulk β-InSe along the xx (a) and zz (b) polarization directions are depicted in Figure 3. In this paper, all the optical functions and spectra are calculated along the directions of xx and zz polarization and are presented relative to the hexagonal axis as extraordinary E || c and ordinary E ⊥ c waves, respectively. It can be clearly seen from Figure 3 that the optical properties of polarization in the xx and zz directions are anisotropic. By comparing the GW spectrum and the BSE spectrum, the exciton effect is investigated. In comparison with RPA, the BSE spectra show a small redshift. The exciton binding energies are 18 meV and 21 meV for the xx and zz polarization directions, respectively, which accords with the experimental value of 14.4 meV [50] very well. Our calculated value is slightly larger than the experimental value in the literature at a temperature of 4.2 K. This is because the calculated value is the result at absolute temperature. For the xx polarization direction, the BSE spectrum including the exciton effect is significantly enhanced in the energy range of 0 to 4.84 eV and drops rapidly above 4.84 eV compared to the GW spectrum. For the zz polarization direction, the BSE spectrum is obviously reshaped relative to the GW spectrum. The accurate prediction of the optical properties of bulk β-InSe provides a good guarantee for the subsequent study of the optical properties of 2D InSe.
The quasiparticle band structures of 1L, 2L, and 3L β-InSe are displayed in Figure 4. As can be seen in Figure 4, they are all indirect bandgap semiconductors. Their indirect band gaps are 2.905 eV, 2.323 eV, and 2.017 eV, respectively. The band gap of layered β-InSe is larger than that of its bulk counterpart and increases as the number of layers decreases, which can be attributed to the quantum confinement effect. Their band structures exhibit similar shapes, but as the number of layers increases, additional band splitting occurs due to reduced energy band degeneracy caused by interlayer interactions. The minimum conduction bands of 1L, 2L, and 3L InSe band structures are all at point Γ. For 1L-to-3L β-InSe, the maximum valence bands are all in the G-to-K direction. For instance, in the case of 1L β-InSe (as shown in Figure 3a), the direct band gap at the Γ-point is 3.010 eV, while the indirect band gap along the Γ-K path is 2.905 eV. The negligible energy difference between them thus qualifies it as a quasi-direct bandgap semiconductor. It is very interesting that the valence band becomes quite flat for the 3L film. Flattening of the valence band implies that the energy levels within that band are nearly the same across a significant portion of the material’s Brillouin zone. This flattening primarily arises from enhanced orbital interactions as the number of layers increases.
The 2D optical absorbance of 1L-to-3L β-InSe is presented in Figure 5a Due to quantum confinement and weak dielectric screening, 2D materials exhibit strongly bound excitons with large oscillator strengths. Therefore, we investigate the excitonic effects in few-layer β-InSe using the GW+BSE approach. Previous studies [13,14,15,29] have shown that the dielectric function, which describes the optical properties of bulk (3D) materials, is ill-defined for 2D materials due to their vanishing thickness. Consequently, it cannot be directly applied to characterize the optical response of 2D systems. In contrast, 2D absorbance [13] and complex photoconductivity provide a robust description of the optical properties of 2D materials, circumventing the thickness dependence issue. To systematically investigate the screening properties of few-layer β-InSe and address the thickness dependence issue, we calculate its 2D absorbance and complex photoconductivity using both the GW+RPA and GW+BSE approaches. For the 2D photoconductivity analysis, we focus exclusively on the BSE calculation results. Due to significant depolarization effects normal to the plane, we focus exclusively on the optical response for in-plane (xx-direction) polarization. For the RPA spectrum of 1L–3L β-InSe, the shape of the absorption spectrum is roughly the same, and the absorption rate gradually increases from the edge of the absorption band. The absorption peaks increase progressively from 25.4% (1L) to 39.8% (2L) and 46.0% (3L), revealing a strong thickness dependence. For the RPA absorption peaks, all absorption peaks are the result of the direct electron transition from the top of the valence band to the bottom of the conduction band. The BSE spectra arising from the electron–hole interaction are found to be redshifted relative to the RPA spectra. In the energy range lower than the energy band gap, several absorption peaks appear, which indicates that there is a strong exciton effect in 2D β-InSe. The existence of the exciton state makes the absorption peak in the low energy range significantly stronger than the RPA spectrum. The binding energy of excitons corresponds to the energy offset between the fundamental quasiparticle band gap and the optical gap determined by the lowest excitonic state in BSE calculations. Remarkably, the exciton binding energies (200, 110, and 50 meV for 1L–3L β-InSe, respectively) show a dramatic layer-number dependence and are substantially larger than the bulk counterpart (18 meV). The exciton binding energy reported for 2L β-InSe in another theoretical work by Ceferino et al. [51] is approximately 60 meV, which was calculated by considering the material’s dielectric properties. Due to the ultra-thin nature of two-dimensional materials, computational approaches based on dielectric functions face significant challenges in determining exciton binding energies. Moreover, these methods often rely heavily on empirical parameters. Experimental work by Zultak et al. [52] using photoluminescence excitation spectroscopy reports ~50 meV for bilayer (2L) InSe. Our calculated value of 110 meV for 2L InSe is higher than the experimentally reported ~50 meV, which may be attributed to the ideal nature of our calculation on a freestanding layer in a vacuum, which does not account for environmental screening effects present in the experimental setup. As the spatial overlap probability of electron and hole wave functions in β-InSe increases, the exciton binding energy increases. So, the excitons in few-layer β-InSe are more thermally stable at room temperature than those in bulk InSe, which further affects the optical properties of the few-layer β-InSe. For atomically thin 2D materials, the exciton binding energy generally increases as the thickness decreases due to confinement and the weakening of screening.
The 2D complex photoconductivity of 1L-to-3L β-InSe is shown in Figure 5b. The 2D photoconductivity not only provides a robust description of the optical properties of 2D materials but also serves as a critical parameter for optoelectronic device fabrication. Notably, the real part of the complex photoconductivity can be readily measured via transmission electron microscopy (TEM) and reflection spectroscopy. Although the imaginary part cannot be directly measured by experiments, Chang et al. [29] have realized its extraction by spectroscopic ellipsometry. From the definition of 2D complex photoconductivity [13], we know that the real part of the photoconductivity is proportional to the absorption rate, and the absorption peaks also show a corresponding relationship. Comparing the real part of the photoconductivity of 1L-to-3L β-InSe, we find that the number of absorption peaks in the low energy range increases as the number of layers increases, which is caused by the reduction in energy band degeneracy and splitting due to the interaction between the layers. From 1L to 3L, the maximum absorption peaks reach 17.5%, 37.0%, and 43.8%, respectively. When the energy is lower than 4.2 eV, 4.4 eV, and 4.9 eV, the imaginary part of the complex photoconductivity of 1L, 2L, and 3L InSe becomes negative. Leveraging this unique property, 2D β-InSe can be employed in the design and fabrication of metamaterial devices.
As can be seen from Figure 4a, the direct band gap of unstrained 1L InSe is 3.010 eV, and the indirect band gap is 2.905 eV. The difference between them is only 105 meV. Such band structure characteristics provide great convenience for strain-controlled electronic structure. Figure 6 shows the band structures of 1L β-InSe under different biaxial compressive strains from −1.4% to −2.4%. As the compressive strain increases, both the direct and indirect band gaps increase. But the indirect band gap increases faster than the direct band gap.
In Figure 7, the band structures of 1L β-InSe under different biaxial compressive strains from −3.0 to −4.0 are plotted. It can be seen from the figure that as the compressive strain further increases, the direct band gap corresponding to point Γ continues to increase, but the band gap from the top of the valence band at point Γ to the bottom of the conduction band at point K continues to decrease.
As shown in Figure 8a the transition of the band structure from the indirect band gap to the direct band gap occurs at a strain of approximately 1.66%. In another theoretical computation study [53], the authors employed first-principles calculations and found this transition to occur at a much larger compressive strain of −6.7%. The observed discrepancy stems from the authors’ use of DFT-based methodology, which not only underestimates the fundamental band gap of 2D β-InSe but also overestimates the energy separation between the valence band maximum and the secondary valence peak at the point Γ.
The crossover from the direct band gap to the indirect band gap occurs at approximately −3.6% strain, which is shown in Figure 8b.
To sum up the above, a biaxial compressive strain of −1.66% to −3.60% can be applied to 1L InSe, causing it to transform from an indirect bandgap semiconductor to a direct bandgap semiconductor. The range of the direct band gap at the point Γ corresponds to 3.405 eV to 3.426 eV. This is a very narrow range, which provides great convenience for strain control.
As can be seen from the previous section, 2D InSe changes from a direct band gap to a direct band gap under the action of −1.66% to −3.60% biaxial compressive strain. In order to study the relationship between the optical properties of 2D InSe as a function of strain, the 2D absorbance of 2D InSe under −2.4%, −2.8%, −3.2%, and −3.6% compressive strains was calculated. The relationship is shown in Figure 9. It can be seen from Figure 9 that as the compressive strain increases, the first and second peaks of the 2D absorption coefficient undergo a weak blueshift, but the third and fourth peaks undergo a relatively large redshift.

4. Conclusions

In summary, we investigate the quasiparticle band structures and optical properties of 1L, 2L, 3L, and bulk InSe. Among them, 1L, 2L, and 3L InSe are quasi-direct bandgap semiconductors. We mainly focus on the regulation of the electronic structure and optical properties of 1L InSe by applying biaxial compressive strain, because it can transform 1L InSe from an indirect bandgap semiconductor to a direct bandgap semiconductor more efficiently than other types of strain. For 1L InSe, applying a biaxial compressive strain of −1.66% to −3.60% transforms it from an indirect bandgap semiconductor to a direct bandgap semiconductor. The band gap value of 1L InSe after strain adjustment remains in a very small range of 3.405 eV to 3.426 eV. This will provide great convenience for manufacturing semiconductor optoelectronic devices using strain-regulated 1L InSe. The 2D optical absorbance and complex photoconductivity of 1L-to-3L β-InSe are studied based on GW+RPA and GW+BSE. The calculated exciton binding energies are 200 meV, 110 meV, and 50 meV, respectively, which indicates that they are thermally stable at room temperature. The calculation of the 2D absorbance of 1L InSe with different biaxial compressive strains shows that as the compressive strain increases, the first and second absorption peaks undergo a weak blueshift, while the third and fourth absorption peaks undergo larger redshifts.

Author Contributions

Conceptualization, C.Y. and W.H.; methodology, Y.J.; software, C.Y.; validation, C.Y., Y.J., and F.P.; formal analysis, F.P.; investigation, W.H.; resources, W.H.; data curation, Y.J.; writing—original draft preparation, C.Y.; writing—review and editing, W.H.; visualization, C.Y.; supervision, C.Y.; project administration, C.Y.; funding acquisition, Y.J. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China for Theoretical Physics special fund “cooperation program”(No. 11547039), the Shaanxi Provincial Natural Science Foundation key research and development program (No. 2024SF-YBXM-587), the Natural Science Basic Research Program of Shaanxi, China (Program No. 2022JM-051), the Shaanxi Institute of Scientific Research Plan projects (No. SLGKYQD2-05), and the Research Foundation of Education Bureau of Shaanxi Province, China (No. 19JS009).

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.

Conflicts of Interest

The authors declare no conflicts of interest.

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Crystals 15 00666 g001
Figure 1. Atomic structure arrangements of few-layer β-InSe. (a) Top views of 1L–3L β-InSe. In (a), the black diamond represents the hexagonal primitive cell, the rectangular lattice is a 2 × 1 unit cell, and the AC and ZZ arrows represent the armchair and zigzag directions, respectively. Side views of (b) 1L, (c) 2L, and (d) 3L β-InSe. Uniformly, a 15 Å vacuum buffer was implemented in the z-direction for every system configuration.
Figure 1. Atomic structure arrangements of few-layer β-InSe. (a) Top views of 1L–3L β-InSe. In (a), the black diamond represents the hexagonal primitive cell, the rectangular lattice is a 2 × 1 unit cell, and the AC and ZZ arrows represent the armchair and zigzag directions, respectively. Side views of (b) 1L, (c) 2L, and (d) 3L β-InSe. Uniformly, a 15 Å vacuum buffer was implemented in the z-direction for every system configuration.
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Figure 2. GW0-calculated band structure of bulk β-InSe along high-symmetry paths.
Figure 2. GW0-calculated band structure of bulk β-InSe along high-symmetry paths.
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Figure 3. Optical properties of bulk β-InSe. Calculated imaginary parts ε2(ω) of bulk β-InSe along the xx (E⊥c) polarization direction (a) and zz (E||c) polarization direction (b) with (GW+BSE) and without (GW+RPA) the electron–hole (e–h) interaction. Due to the crystal symmetry of InSe, its optical properties along the xx and yy polarization directions are isotropic.
Figure 3. Optical properties of bulk β-InSe. Calculated imaginary parts ε2(ω) of bulk β-InSe along the xx (E⊥c) polarization direction (a) and zz (E||c) polarization direction (b) with (GW+BSE) and without (GW+RPA) the electron–hole (e–h) interaction. Due to the crystal symmetry of InSe, its optical properties along the xx and yy polarization directions are isotropic.
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Figure 4. Calculated band structure of 1L (a), 2L (b), and 3L (c) β-InSe along M–Γ–K–M direction in the Brillouin zone with GW0 method.
Figure 4. Calculated band structure of 1L (a), 2L (b), and 3L (c) β-InSe along M–Γ–K–M direction in the Brillouin zone with GW0 method.
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Figure 5. The 2D optical absorbance (a) and 2D complex photoconductivity (b) of 1L-to-3L β-InSe along the xx (E||c) polarization direction with (GW+BSE) and without (GW+RPA) the electron–hole (e–h) interaction. For 2D complex photoconductivity, only BSE results are shown.
Figure 5. The 2D optical absorbance (a) and 2D complex photoconductivity (b) of 1L-to-3L β-InSe along the xx (E||c) polarization direction with (GW+BSE) and without (GW+RPA) the electron–hole (e–h) interaction. For 2D complex photoconductivity, only BSE results are shown.
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Figure 6. Band structures of 1L β-InSe under different biaxial compressive strains from 1.4% to 2.4% calculated by accurate GW0 method.
Figure 6. Band structures of 1L β-InSe under different biaxial compressive strains from 1.4% to 2.4% calculated by accurate GW0 method.
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Figure 7. Band structures of 1L β-InSe under different biaxial compressive strains from −3.0 to −4.0 calculated by accurate GW0 method.
Figure 7. Band structures of 1L β-InSe under different biaxial compressive strains from −3.0 to −4.0 calculated by accurate GW0 method.
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Figure 8. Calculated dependence of Eg, dir, Eg, ind of 1L β-InSe as a function of biaxial compressive strain. Eg, dir and Eg, ind represent the direct and indirect band gaps, respectively. (a) For the biaxially compressively strained 1L β-InSe, the crossover from direct to indirect band gap occurs at a strain of approximately −1.66%. (b) However, as the compressive strain continues to increase, its energy band changes from a direct band gap to an indirect band gap when the strain is approximately −3.6%.
Figure 8. Calculated dependence of Eg, dir, Eg, ind of 1L β-InSe as a function of biaxial compressive strain. Eg, dir and Eg, ind represent the direct and indirect band gaps, respectively. (a) For the biaxially compressively strained 1L β-InSe, the crossover from direct to indirect band gap occurs at a strain of approximately −1.66%. (b) However, as the compressive strain continues to increase, its energy band changes from a direct band gap to an indirect band gap when the strain is approximately −3.6%.
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Figure 9. The 2D absorbance of 1L InSe under −2.4%, −2.8%, −3.2%, and −3.6% compressive strains based on the calculation of GW+BSE.
Figure 9. The 2D absorbance of 1L InSe under −2.4%, −2.8%, −3.2%, and −3.6% compressive strains based on the calculation of GW+BSE.
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Table 1. Optimized equilibrium geometric structures using different pseudopotentials and errors relative to the experiment. In all calculations, the plane-wave energy cutoff was set to 1.3 times the highest energy value of the employed pseudopotentials. The Brillouin zone integration was performed using a Γ-centered Monkhorst–Pack grid with 16 × 16 × 4 k-points for all systems.
Table 1. Optimized equilibrium geometric structures using different pseudopotentials and errors relative to the experiment. In all calculations, the plane-wave energy cutoff was set to 1.3 times the highest energy value of the employed pseudopotentials. The Brillouin zone integration was performed using a Γ-centered Monkhorst–Pack grid with 16 × 16 × 4 k-points for all systems.
Encut (eV)a = b (Å)Relative Error (%)c (Å)Relative Error (%)
General PP3004.0981.18518.3838.582
d PP5004.0880.93818.0826.804
sv PP6204.0620.29617.2131.672
Experiment 4.050 16.930
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Yang, C.; Jiang, Y.; Huang, W.; Pan, F. Strain and Layer Modulations of Optical Absorbance and Complex Photoconductivity of Two-Dimensional InSe: A Study Based on GW0+BSE Calculations. Crystals 2025, 15, 666. https://doi.org/10.3390/cryst15070666

AMA Style

Yang C, Jiang Y, Huang W, Pan F. Strain and Layer Modulations of Optical Absorbance and Complex Photoconductivity of Two-Dimensional InSe: A Study Based on GW0+BSE Calculations. Crystals. 2025; 15(7):666. https://doi.org/10.3390/cryst15070666

Chicago/Turabian Style

Yang, Chuanghua, Yuan Jiang, Wendeng Huang, and Feng Pan. 2025. "Strain and Layer Modulations of Optical Absorbance and Complex Photoconductivity of Two-Dimensional InSe: A Study Based on GW0+BSE Calculations" Crystals 15, no. 7: 666. https://doi.org/10.3390/cryst15070666

APA Style

Yang, C., Jiang, Y., Huang, W., & Pan, F. (2025). Strain and Layer Modulations of Optical Absorbance and Complex Photoconductivity of Two-Dimensional InSe: A Study Based on GW0+BSE Calculations. Crystals, 15(7), 666. https://doi.org/10.3390/cryst15070666

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