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GaAs monolayer: Excellent SHG responses and semi metallic to metallic transition modulated by vacancy effect
Accepted Manuscript Full Length Article GaAs monolayer: excellent SHG responses and semi metallic to metallic transition modulated by vacancy effect Ilmira Rozahun, Tohtiaji Bahti, Guijie He, Yasenjan Ghupur, Abduleziz Ablat, Mamatrishat Mamat PII: DOI: Reference:
S0169-4332(18)30388-X https://doi.org/10.1016/j.apsusc.2018.02.045 APSUSC 38503
To appear in:
Applied Surface Science
Received Date: Revised Date: Accepted Date:
20 November 2017 9 January 2018 4 February 2018
Please cite this article as: I. Rozahun, T. Bahti, G. He, Y. Ghupur, A. Ablat, M. Mamat, GaAs monolayer: excellent SHG responses and semi metallic to metallic transition modulated by vacancy effect, Applied Surface Science (2018), doi: https://doi.org/10.1016/j.apsusc.2018.02.045
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
GaAs monolayer: excellent SHG responses and semi metallic to metallic transition modulated by vacancy effect Ilmira Rozahun a, Tohtiaji Bahti b, Guijie He a, Yasenjan Ghupur a, Abduleziz Ablat a, and Mamatrishat Mamat*a a
b
School of Physics and technology, Xinjiang University, 666 Victory Road, Urumqi 830046, China Xinjiang Technical Institute of physics & chemistry of CAS, 40-1 south Beijing Road, Urumqi 830011,
China
Abstract Monolayer materials are considered as a promising candidate for novel applications due to their attractive magnetic, electronic and optical properties. Investigation on nonlinear optical (NLO) properties and effect of vacancy on monolayer materials are vital to property modulations of monolayers and extending their applications. In this work, with the aid of first-principles calculations, the crystal structure, electronic, magnetic, and optical properties of GaAs monolayers with the vacancy were investigated. The result shows gallium arsenic (GaAs) monolayer produces a strong second harmonic generation (SHG) response. Meanwhile, the vacancy strongly affects structural, electronic, magnetic and optical properties of GaAs monolayers. Furthermore, arsenic vacancy (VAs) brings semi metallic to metallic transition, while gallium vacancy (VGa) causes nonmagnetic to magnetic conversion. Our result reveals that GaAs monolayer possesses application potentials in Nano-amplifying modulator and Nano-optoelectronic devices, and may provide useful guidance in designing new generation of Nano-electronic devices. Key words First-principles calculation; GaAs monolayer; SHG response; Vacancy Introduction The exploration of two-dimensional (2D) monolayer materials have received considerable attentions owing to their unique electronic, magnetic, and optical
properties
[1-5],
and
promising
applications
such
as
Nano-electronic,
Nano-optoelectronic and topological insulator devices [6, 7]. During the past decades dozens of excellent 2D monolayer materials such as graphene [8-11], 2D oxides [12, 13], and 2D chalcogenide structure [14-16] etc. have been found and designed. However, the research on 2D materials with outstanding property still continues. Among these materials the 2D monolayers with III–V elements have considered as leading members for potential applications [17, 18]. Nonlinear optical (NLO) materials have attracted much attention due to their ability to extend the spectral range of lasers. For NLO materials, SHG is one of the crucial properties[19, 20], which was observed in 1961 when a beam of ruby laser pointed into a quartz crystal [21]. Usually SHG response of materials investigated to check their optical fields [22-25], and it was commonly believed that materials could obtain SHG if the material structure was non-centrosymmetric [26-28]. 2D systems that possesses non-centrosymmetric structure can exhibits such strong nonlinear optical behavior [29-31], therefore they are becoming interesting research hotspots [31, 32]. In recent years, there have been intensive research efforts regarding structural and electronic properties of 2D monolayers of III–V elements[14, 33]. Although, III–V monolayer materials are intensively explored [8, 20], reports on investigation of nonlinear optical properties of GaAs monolayer are relatively scarce. Previous reports are mainly including investigation of linear optical properties [18, 34-36], quantum effects [37, 38] and electronic property etc. Nevertheless, GaAs monolayer belongs to the non-centrosymmetric crystal symmetry group, and SHG response of GaAs monolayer did not reported yet. In addition, when it comes to property modulation of 2D monolayer materials, doping methods has been widely used for identifying the influence of doping induced defects on monolayer materials [14, 16, 38, 39], and it was concluded that defects can strongly effect on the electronic, magnetic and optical properties of the monolayer materials. Take MoS2 monolayer as an example [39] , the research shows that vacancy can induce magnetic moment, lower the formation energy, and cause direct to indirect band gap transition. The above research backgrounds inspired us to explore the SHG
response of 2D monolayers and study the effects of vacancy on properties of GaAs monolayers. In this work, by employing the first-principles calculations, firstly, to find out the potential applications, we studied the previously unreported SHG response of pure GaAs monolayer, and calculated the SHG coefficients and explained the source of the SHG response. Secondly, we examined the vacancy effects on the electric and magnetic properties of GaAs monolayer after the involvement of As atom vacancy (VAs) and Ga atom vacancy (VGa). Calculation method To identify the effects of structure on properties, the optical property calculations of 2D monolayers were carried out by applying the plane-wave pseudopotential based density functional theory (DFT) with Cambridge serial total energy package (CASTEP) [40]. DFT calculation with the Hybrid functional PBE0 [41] can give excellent band gap value that is in good agreement with the experimental band gap (within the error of 1.5%), but calculated optical properties from PBE0 are not excellent as compared to GGA function [42]. Therefore, for calculating the energy bands, we applied PBE0, and for other structural, electronic, magnetic, and optical properties calculation we applied GGA with Perdew-Burke-Erenzerhof (PBE) function [43]. The kinetic energy cutoff is set as 500 eV with the Ultrasoft pseudopotentials for wave function expansion. For the case of electronic relaxation, the system energy is iterated until a tolerance 2 × 10 – 6 eV/atom is attained. Our structure model consists of a 4×3 monolayer GaAs supercell and containing one impurity atom in its lattice structure. Brillouin zone is involved 5×5×1 Monkhorst-pack k-point sampling, and Fermi level smearing is taken as 0.05 eV for geometry optimization and other calculations. The other parameters were set as default values of CASTEP calculations. In addition, under the zero frequency limit with use of length-gauge formalism which derived by Aversa and Sipe [44], the SHG coefficients were calculated.
Results and discussion 1. Electronic structure of GaAs Top view and side view of the primitive cell of pure GaAs monolayer are shown in fig. 1. The fig. 1 shows that 2D honeycombs GaAs monolayer structure is formed by repeating six membered Ga3As3 rings. The Ga-As bond length of 2.409 Å well matches with other previous works [38]. The GaAs monolayer was positioned at X-Y plane with a vacuum in Z direction. As seen from the calculated result of phonon dispersion presented in fig. 1(c), for GaAs monolayer, phonon dispersion spectra show no imaginary frequency, the result indicates that GaAs monolayer is structurally and dynamically stable [45]. As depicted in the fig. 2, in the repeating ring, the Ga atoms hold covalent bonds with As atoms. Band gap of monolayers with different vacuum thicknesses are calculated by GGA, as presented in Table 1, the band gap values converged around thickness value of 21 Å. Therefore, entire work completed via using GaAs monolayer with the vacuum thickness of 21 Å. Fig. 3 illustrates the band structure that calculated from PBE0 and GGA, and also shows the density of state (DOS) and partial density of state (PDOS) for GaAs monolayers. From the fig. 3 (a) it can be noticed that by PBE0 the calculated band gap (2.568 eV) is larger than the calculated bad gap by GGA (1.027 eV). Our obtained band gap value from PBE0 is larger than the band gap for bulk GaAs (1.53 eV). Fig. 3(a) shows the band structures for the both cases, it is seen that the band dispersions are along G - K - M - G dierections, Fermi energy level is setted as default value of 0 eV, and conduction band minimum is located at G point and the valence band maximum is located at K point. Fig. 3 (b) shows the DOS of pure GaAs monolayer, it is clear that the both lower conduction bands and higher valence bands are contribution of hybridization of As - p and Ga - p orbits. In lower conduction band As - p orbits play an important role, while in higher valence bands major player is Ga - p orbits, and the results indicates that the difference on vacancy responsible for property alterations. 2. SHG response For a nonlinear material, when incident light irradiates the material, the induced polarization is calculated as
,
(1)
In the above equation, E is the electric field of the incident radiation,
is
polarization without incident electric fields. Second order polarization that related to SHG responses can be obtained by
； ，
,
(2)
In this work, in order to compare the results with other 2D materials, we use the sheet optical susceptibility via following equation
.
(3)
In eq. (3), L defined as
, where 3.4 is van der Waals thickness, d is
thickness of 2D material [46]. Since GaAs monolayer belongs to the point group 3m, therefor among the 10 reduced SHG coefficients, it has only four independent SHG coefficients (
). In this work, SHG coefficients are
estimated at zero frequency limit, and the obtained result is , (
which
is
larger
than
the
maximum
SHG
coefficient
) of BN monolayer, and larger than SHG coefficient ( ) of MoS2 monolayer. When it comes to origins of SHG responses, both
virtual-electron (VE) and virtual-hole (VH) processes make contributions to the total SHG coefficient [47], the contribution of VH can be ignored compare to contribution of VE. To investigate the origin of the SHG, in fig.4 and fig.5, we depicted SHG density [48] profile for VE process of the largest SHG tensors d11 and electron localization function (ELF) for pure GaAs monolayer, respectively. Fig. 4 illustrates that Ga atom takes a major role in occupied states, and As atoms have dominant contribution to the unoccupied states. Fig.5 implies that electron localization is not
symmetric and this non-symmetrical electron localization is main reason of large SHG response [19]. 3.
Sami metallic to metallic by vacancy effect Here we discussed the electronic, magnetic, and optical properties of GaAs
monolayer with Ga vacancy (VGa) and As vacancy (VAs). The structural analysis where given at first, fig. 6 shows the atomic structure of GaAs monolayer with V Ga and VAs after geometry optimization. In order to make GaAs monolayer with vacancy, one gallium or one arsenic atom removed from 4 ×3 pure GaAs monolayer, therefore, VGa monolayer which containing of 11 Ga and 12 As atoms, and VAs monolayer which containing of 12 Ga and 11 As atoms are designed. After geometrical optimization, it was found that, structural symmetry of both V Ga and VAs monolayers where damaged; for VGa monolayer, changes in bond length was not obvious, while for VAs monolayer, bond length becomes longer. Main reason for this difference is electronegativity, that is, electronegativity of As ( χ p: 2.18) larger than that of Ga (χ p: 1.81). In VGa monolayer, electron-absorption capability in between As - As atoms that are nearest to the defect positions larger than the one in between As - Ga atoms that are next nearest neighbor to the defect positions. While in VAs monolayer, electron-attracting capability in between Ga - Ga atoms, which nearest to the defect positions, weaker than the ones in between Ga - As atoms, that next nearest neighbor to the defect positions. Next, we discussed the effects of vacancy on the electronic and magnetic properties of GaAs monolayer. Fig. 7 illustrates the spin polarized TDOS for GaAs monolayer with vacancy, and PDOS of As and Ga atom nearest to the vacancy position. The result implies that VGa monolayer is semiconductor and VAs monolayer is conductor. The impurity status appeared in the band gap of both VGa and VAs monolayers. In the band gap, impurity status of VGa monolayer is mainly formed by mixing 4p state of Ga atoms and 4p state of As atoms closest to VGa. Therefore, it can be seen that different spin states have different band gap values, for the up spin the band gap value is 1.05 eV, whereas, for the down spin the band gap value is 0.24 eV. The spin dependent property may enable the monolayer to apply as spin filtering device. Here,
we introduced the spin density plots for VGa and VAs monolayers to discuss the origin of the magnetic property. From fig. 8 it can be noticed that spin polarization mainly localized around the atoms neighboring with the vacancy, and the spin density of V Ga monolayer larger than the spin density of VAs monolayer. The calculated magnetic moment value is 2.89 μB for VGa monolayer, and 0.716 × 10 - 3μB for VAs monolayer. Major explanation for this phenomenon is that, generating of Ga vacancy creates disconnected As atoms which possess half occupied 4p orbits, and the large number of half-filled high symmetric 4p orbital electrons (electrons with same spin direction) trigger the magnetic property. Whereas, when As vacancy was generated, a number of free electrons are increased, but due to the anisotropic spins these electrons unable to create magnetic property. Finally, we analyzed the optical property of GaAs monolayer with vacancy. The reflectivity spectra and absorption curves are important features in estimating the optical properties and predicting the application field of the materials. The dielectric constant which is related to the electronic property of the external field described as
,
where real part
(4)
can be obtained by the Kramers – Kronig transformation [49]
and given as
,
(5)
where P is the principle value of the integral
. (6)
The imaginary part
originated from real transition between the occupied and
unoccupied states and given as [50]
.
Where, e is the electric charge,
is dipole matrix,
is eigen value of wave
function that corresponding to conduction (valence) band. E and Fermi
distribution
function,
respectively.
By
(7)
applying
are energy and Kramers – Kronig
transformation, one can get the absorption and reflectivity as follow [35]
,
.
(8)
(9)
Fig. 9 shows the reflectivity curves of pure GaAs monolayer, VGa and VAs monolayers for both parallel and perpendicular to the electric field. As depicted in the fig. 9, when electric field applied parallel to monolayer plane, higher reflectivity emerged in the low energy region, and for the pure GaAs monolayer the maximum reflectivity peak localized at the energy of 7.3 eV; while for VGa and VAs monolayers, the maximum reflectivity values occur around 0 eV. When the electric field applied perpendicular to the monolayer surface, for pure GaAs monolayer the maximum peak for the reflectivity appeared at the energy of 9.1 eV, and for the VGa and VAs monolayers the maximum reflectivity peaks appeared at the energy of 7.6 eV. When the vacancies are generated, the reflective intensities at the energy region from 0 to 8.01 eV have increased and red shifted. Fig. 10 presents the absorption coefficient curves for the pure GaAa monolayer, VGa and VAs monolayers respectively. The absorption curves show that the vacancy affects both the intensity and position of the absorption peaks. In the parallel polarization (E//X) the absorption spectrum for pure GaAs monolayer have two main peaks locating at the energy of 3.95 eV and 6.74 eV respectively. First absorption sub peaks located at 1.6 eV for the pure GaAs
monolayer and 0.8 eV for VGa monolayer. In the vertical polarization (E//Z), for the pure GaAs monolayer the maximum absorption peak resided at 8.7 eV, while for the monolayer with the vacancy, the maximum absorption peaks localized at 7.2 eV. With the generation of vacancies, in the energy region from 0 to 8.2 eV the absorption coefficients have increased and red shifted. Conclusion Contribution of this work can be seen from two major points. First, we estimated SHG response of GaAs monolayer. Second, we investigated vacancy effects on the structural, electronic, magnetic and optical properties of GaAs monolayer. SHG density of the pure GaAs monolayer suggests that the both Ga and As atoms contributes to their SHG responses. Furthermore, strong SHG responses suggest that GaAs monolayer presents many appealing features such as, Nano-amplifying modulator, and topological insulator. For vacancy effects, the calculated result revealed that GaAs monolayer is sensitive to the type of vacancy. From the structural property of view, vacancy damages the structural symmetry; while, from the electronic property of view, VGa monolayer exhibits the semi metallic behavior, and VAs exhibits the metallic behavior. In the view of magnetic property, VGa monolayer is spin polarized and behaves as magnetic, and the calculated total magnetic moment is 2.89 μB; while, VAs monolayer is spin-unpolarized, and behaves as nonmagnetic. From the optical aspect of view, for the both types of vacancy monolayers (VGa and VAs) their reflectivity intensities and absorption coefficients have increased and red shifted. These results will provide helpful guidance for designing of outstanding Nano-materials in real experiments.
Acknowledgments This research successfully completed in Xinjiang Technical Institute of physics & chemistry of CAS, and the author Ilmira Rozahun would like thanks to Bingbing Zhang, Cong Hu, Zhonglei Wei, and other group members to their helpful discussions and keen assistance. This work is supported by the National Natural Science Foundation of China (Grant Nos. 61366001 and 61604126), and Xinjiang autonomous regional research innovation found for postgraduate students (Grant No. XJGRI 2017031).
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Figure captions Fig. 1 (a) Top view and (b) side view of optimized atomic structure of pure 4×3 monolayer GaAs supercell (c) The phonon spectra of GaAs monolayer Fig. 2 Electron density difference of pure 4×3 monolayer GaAs Fig. 3 (a) Band structure of GaAs monolayer (b) DOS of GaAs monolayer Fig. 4 The SHG-density of the virtual-electron of the largest SHG tensors of GaAs with (a) occupied state (b) unoccupied state Fig. 5 Electron localization function of pure GaAs monolayer Fig. 6 Top view of the atomic structure of GaAs monolayer with VGa and VAs after geometry optimization (a) top view of VGa monolayer (b) top view of V As monolayer, Light blue and light gray bolls represents Ga, and As atoms, respectively Fig. 7 TDOS and PDOS of VGa and VAs in monolayer GaAs (a) is TDOS (b) and (C) are PDOS of As and Ga atom nearest to the vacancy, respectively. The black, blue, and pink lines represent the s, p, and d orbit, respectively Fig. 8 Spin density for isosurfaces of GaAs monolayers with (a) vacancy VGa and (b) vacancy VAs Fig. 9 Reflectivity curves for the electric field (a) parallel and (b) perpendicular to the GaAs monolayer surface Fig. 10 Absorption coefficient curves for the electric field (a) parallel and (b) perpendicular to GaAs monolayer
(a)
(C)
(b)
Fig. 1 (a) Top view and (b) side view of optimized atomic structure of pure 4×3 monolayer GaAs supercell (c) The phonon spectra of GaAs monolayer
Fig. 2 Electron density difference of pure 4×3 monolayer GaAs
(a)
(b)
Fig. 3 (a) Band structure of GaAs monolayer (b) DOS of GaAs monolayer
Fig. 4 The SHG-density of the virtual-electron of the largest SHG tensors of GaAs with (a) occupied state (b) unoccupied state
Fig. 5 Electron localization function of pure GaAs monolayer
Fig. 6 Top view of the atomic structure of GaAs monolayer with V Ga and VAs after geometry optimization (a) top view of VGa monolayer (b) top view of V As monolayer, light blue and light gray bolls represents Ga, and As atoms, respectively.
Fig. 7 TDOS and PDOS of VGa and VAs in monolayer GaAs (a) is TDOS (b) and (C) are PDOS of As and Ga atom nearest to the vacancy, respectively. The black, blue, and pink lines represent the s, p, and d orbits, respectively.
Fig. 8 Spin density for isosurfaces of GaAs monolayers with (a) vacancy VGa and (b) vacancy VAs
Fig. 9 Reflectivity curves for the electric field (a) parallel and (b) perpendicular to the GaAs monolayer surface
Fig. 10 Absorption coefficient curves for the electric field (a) parallel and (b) perpendicular to GaAs monolayer
Table 1 Band gap of GaAs monolayer with different vacuum thickness
Table 1 Band gap of GaAs monolayer with different vacuum thickness Vacuum
10
15
18
21
23
25
0.569
0.814
0.997
1.027
1.02
1.02
6
8
thickness (Å) ΔE (eV)
Graphical abstract
Highlights:
GaAs monolayer produces a strong SHG response.
Vacancy strongly affects structural, electronic, magnetic and optical properties of GaAs monola ye.
Arsenic vacancy (VAs) causes semi metallic to metallic transition, while Gallium vacancy (VGa) causes nonmagnetic to magnetic transition.
S0169-4332(18)30388-X https://doi.org/10.1016/j.apsusc.2018.02.045 APSUSC 38503
To appear in:
Applied Surface Science
Received Date: Revised Date: Accepted Date:
20 November 2017 9 January 2018 4 February 2018
Please cite this article as: I. Rozahun, T. Bahti, G. He, Y. Ghupur, A. Ablat, M. Mamat, GaAs monolayer: excellent SHG responses and semi metallic to metallic transition modulated by vacancy effect, Applied Surface Science (2018), doi: https://doi.org/10.1016/j.apsusc.2018.02.045
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
GaAs monolayer: excellent SHG responses and semi metallic to metallic transition modulated by vacancy effect Ilmira Rozahun a, Tohtiaji Bahti b, Guijie He a, Yasenjan Ghupur a, Abduleziz Ablat a, and Mamatrishat Mamat*a a
b
School of Physics and technology, Xinjiang University, 666 Victory Road, Urumqi 830046, China Xinjiang Technical Institute of physics & chemistry of CAS, 40-1 south Beijing Road, Urumqi 830011,
China
Abstract Monolayer materials are considered as a promising candidate for novel applications due to their attractive magnetic, electronic and optical properties. Investigation on nonlinear optical (NLO) properties and effect of vacancy on monolayer materials are vital to property modulations of monolayers and extending their applications. In this work, with the aid of first-principles calculations, the crystal structure, electronic, magnetic, and optical properties of GaAs monolayers with the vacancy were investigated. The result shows gallium arsenic (GaAs) monolayer produces a strong second harmonic generation (SHG) response. Meanwhile, the vacancy strongly affects structural, electronic, magnetic and optical properties of GaAs monolayers. Furthermore, arsenic vacancy (VAs) brings semi metallic to metallic transition, while gallium vacancy (VGa) causes nonmagnetic to magnetic conversion. Our result reveals that GaAs monolayer possesses application potentials in Nano-amplifying modulator and Nano-optoelectronic devices, and may provide useful guidance in designing new generation of Nano-electronic devices. Key words First-principles calculation; GaAs monolayer; SHG response; Vacancy Introduction The exploration of two-dimensional (2D) monolayer materials have received considerable attentions owing to their unique electronic, magnetic, and optical
properties
[1-5],
and
promising
applications
such
as
Nano-electronic,
Nano-optoelectronic and topological insulator devices [6, 7]. During the past decades dozens of excellent 2D monolayer materials such as graphene [8-11], 2D oxides [12, 13], and 2D chalcogenide structure [14-16] etc. have been found and designed. However, the research on 2D materials with outstanding property still continues. Among these materials the 2D monolayers with III–V elements have considered as leading members for potential applications [17, 18]. Nonlinear optical (NLO) materials have attracted much attention due to their ability to extend the spectral range of lasers. For NLO materials, SHG is one of the crucial properties[19, 20], which was observed in 1961 when a beam of ruby laser pointed into a quartz crystal [21]. Usually SHG response of materials investigated to check their optical fields [22-25], and it was commonly believed that materials could obtain SHG if the material structure was non-centrosymmetric [26-28]. 2D systems that possesses non-centrosymmetric structure can exhibits such strong nonlinear optical behavior [29-31], therefore they are becoming interesting research hotspots [31, 32]. In recent years, there have been intensive research efforts regarding structural and electronic properties of 2D monolayers of III–V elements[14, 33]. Although, III–V monolayer materials are intensively explored [8, 20], reports on investigation of nonlinear optical properties of GaAs monolayer are relatively scarce. Previous reports are mainly including investigation of linear optical properties [18, 34-36], quantum effects [37, 38] and electronic property etc. Nevertheless, GaAs monolayer belongs to the non-centrosymmetric crystal symmetry group, and SHG response of GaAs monolayer did not reported yet. In addition, when it comes to property modulation of 2D monolayer materials, doping methods has been widely used for identifying the influence of doping induced defects on monolayer materials [14, 16, 38, 39], and it was concluded that defects can strongly effect on the electronic, magnetic and optical properties of the monolayer materials. Take MoS2 monolayer as an example [39] , the research shows that vacancy can induce magnetic moment, lower the formation energy, and cause direct to indirect band gap transition. The above research backgrounds inspired us to explore the SHG
response of 2D monolayers and study the effects of vacancy on properties of GaAs monolayers. In this work, by employing the first-principles calculations, firstly, to find out the potential applications, we studied the previously unreported SHG response of pure GaAs monolayer, and calculated the SHG coefficients and explained the source of the SHG response. Secondly, we examined the vacancy effects on the electric and magnetic properties of GaAs monolayer after the involvement of As atom vacancy (VAs) and Ga atom vacancy (VGa). Calculation method To identify the effects of structure on properties, the optical property calculations of 2D monolayers were carried out by applying the plane-wave pseudopotential based density functional theory (DFT) with Cambridge serial total energy package (CASTEP) [40]. DFT calculation with the Hybrid functional PBE0 [41] can give excellent band gap value that is in good agreement with the experimental band gap (within the error of 1.5%), but calculated optical properties from PBE0 are not excellent as compared to GGA function [42]. Therefore, for calculating the energy bands, we applied PBE0, and for other structural, electronic, magnetic, and optical properties calculation we applied GGA with Perdew-Burke-Erenzerhof (PBE) function [43]. The kinetic energy cutoff is set as 500 eV with the Ultrasoft pseudopotentials for wave function expansion. For the case of electronic relaxation, the system energy is iterated until a tolerance 2 × 10 – 6 eV/atom is attained. Our structure model consists of a 4×3 monolayer GaAs supercell and containing one impurity atom in its lattice structure. Brillouin zone is involved 5×5×1 Monkhorst-pack k-point sampling, and Fermi level smearing is taken as 0.05 eV for geometry optimization and other calculations. The other parameters were set as default values of CASTEP calculations. In addition, under the zero frequency limit with use of length-gauge formalism which derived by Aversa and Sipe [44], the SHG coefficients were calculated.
Results and discussion 1. Electronic structure of GaAs Top view and side view of the primitive cell of pure GaAs monolayer are shown in fig. 1. The fig. 1 shows that 2D honeycombs GaAs monolayer structure is formed by repeating six membered Ga3As3 rings. The Ga-As bond length of 2.409 Å well matches with other previous works [38]. The GaAs monolayer was positioned at X-Y plane with a vacuum in Z direction. As seen from the calculated result of phonon dispersion presented in fig. 1(c), for GaAs monolayer, phonon dispersion spectra show no imaginary frequency, the result indicates that GaAs monolayer is structurally and dynamically stable [45]. As depicted in the fig. 2, in the repeating ring, the Ga atoms hold covalent bonds with As atoms. Band gap of monolayers with different vacuum thicknesses are calculated by GGA, as presented in Table 1, the band gap values converged around thickness value of 21 Å. Therefore, entire work completed via using GaAs monolayer with the vacuum thickness of 21 Å. Fig. 3 illustrates the band structure that calculated from PBE0 and GGA, and also shows the density of state (DOS) and partial density of state (PDOS) for GaAs monolayers. From the fig. 3 (a) it can be noticed that by PBE0 the calculated band gap (2.568 eV) is larger than the calculated bad gap by GGA (1.027 eV). Our obtained band gap value from PBE0 is larger than the band gap for bulk GaAs (1.53 eV). Fig. 3(a) shows the band structures for the both cases, it is seen that the band dispersions are along G - K - M - G dierections, Fermi energy level is setted as default value of 0 eV, and conduction band minimum is located at G point and the valence band maximum is located at K point. Fig. 3 (b) shows the DOS of pure GaAs monolayer, it is clear that the both lower conduction bands and higher valence bands are contribution of hybridization of As - p and Ga - p orbits. In lower conduction band As - p orbits play an important role, while in higher valence bands major player is Ga - p orbits, and the results indicates that the difference on vacancy responsible for property alterations. 2. SHG response For a nonlinear material, when incident light irradiates the material, the induced polarization is calculated as
,
(1)
In the above equation, E is the electric field of the incident radiation,
is
polarization without incident electric fields. Second order polarization that related to SHG responses can be obtained by
； ，
,
(2)
In this work, in order to compare the results with other 2D materials, we use the sheet optical susceptibility via following equation
.
(3)
In eq. (3), L defined as
, where 3.4 is van der Waals thickness, d is
thickness of 2D material [46]. Since GaAs monolayer belongs to the point group 3m, therefor among the 10 reduced SHG coefficients, it has only four independent SHG coefficients (
). In this work, SHG coefficients are
estimated at zero frequency limit, and the obtained result is , (
which
is
larger
than
the
maximum
SHG
coefficient
) of BN monolayer, and larger than SHG coefficient ( ) of MoS2 monolayer. When it comes to origins of SHG responses, both
virtual-electron (VE) and virtual-hole (VH) processes make contributions to the total SHG coefficient [47], the contribution of VH can be ignored compare to contribution of VE. To investigate the origin of the SHG, in fig.4 and fig.5, we depicted SHG density [48] profile for VE process of the largest SHG tensors d11 and electron localization function (ELF) for pure GaAs monolayer, respectively. Fig. 4 illustrates that Ga atom takes a major role in occupied states, and As atoms have dominant contribution to the unoccupied states. Fig.5 implies that electron localization is not
symmetric and this non-symmetrical electron localization is main reason of large SHG response [19]. 3.
Sami metallic to metallic by vacancy effect Here we discussed the electronic, magnetic, and optical properties of GaAs
monolayer with Ga vacancy (VGa) and As vacancy (VAs). The structural analysis where given at first, fig. 6 shows the atomic structure of GaAs monolayer with V Ga and VAs after geometry optimization. In order to make GaAs monolayer with vacancy, one gallium or one arsenic atom removed from 4 ×3 pure GaAs monolayer, therefore, VGa monolayer which containing of 11 Ga and 12 As atoms, and VAs monolayer which containing of 12 Ga and 11 As atoms are designed. After geometrical optimization, it was found that, structural symmetry of both V Ga and VAs monolayers where damaged; for VGa monolayer, changes in bond length was not obvious, while for VAs monolayer, bond length becomes longer. Main reason for this difference is electronegativity, that is, electronegativity of As ( χ p: 2.18) larger than that of Ga (χ p: 1.81). In VGa monolayer, electron-absorption capability in between As - As atoms that are nearest to the defect positions larger than the one in between As - Ga atoms that are next nearest neighbor to the defect positions. While in VAs monolayer, electron-attracting capability in between Ga - Ga atoms, which nearest to the defect positions, weaker than the ones in between Ga - As atoms, that next nearest neighbor to the defect positions. Next, we discussed the effects of vacancy on the electronic and magnetic properties of GaAs monolayer. Fig. 7 illustrates the spin polarized TDOS for GaAs monolayer with vacancy, and PDOS of As and Ga atom nearest to the vacancy position. The result implies that VGa monolayer is semiconductor and VAs monolayer is conductor. The impurity status appeared in the band gap of both VGa and VAs monolayers. In the band gap, impurity status of VGa monolayer is mainly formed by mixing 4p state of Ga atoms and 4p state of As atoms closest to VGa. Therefore, it can be seen that different spin states have different band gap values, for the up spin the band gap value is 1.05 eV, whereas, for the down spin the band gap value is 0.24 eV. The spin dependent property may enable the monolayer to apply as spin filtering device. Here,
we introduced the spin density plots for VGa and VAs monolayers to discuss the origin of the magnetic property. From fig. 8 it can be noticed that spin polarization mainly localized around the atoms neighboring with the vacancy, and the spin density of V Ga monolayer larger than the spin density of VAs monolayer. The calculated magnetic moment value is 2.89 μB for VGa monolayer, and 0.716 × 10 - 3μB for VAs monolayer. Major explanation for this phenomenon is that, generating of Ga vacancy creates disconnected As atoms which possess half occupied 4p orbits, and the large number of half-filled high symmetric 4p orbital electrons (electrons with same spin direction) trigger the magnetic property. Whereas, when As vacancy was generated, a number of free electrons are increased, but due to the anisotropic spins these electrons unable to create magnetic property. Finally, we analyzed the optical property of GaAs monolayer with vacancy. The reflectivity spectra and absorption curves are important features in estimating the optical properties and predicting the application field of the materials. The dielectric constant which is related to the electronic property of the external field described as
,
where real part
(4)
can be obtained by the Kramers – Kronig transformation [49]
and given as
,
(5)
where P is the principle value of the integral
. (6)
The imaginary part
originated from real transition between the occupied and
unoccupied states and given as [50]
.
Where, e is the electric charge,
is dipole matrix,
is eigen value of wave
function that corresponding to conduction (valence) band. E and Fermi
distribution
function,
respectively.
By
(7)
applying
are energy and Kramers – Kronig
transformation, one can get the absorption and reflectivity as follow [35]
,
.
(8)
(9)
Fig. 9 shows the reflectivity curves of pure GaAs monolayer, VGa and VAs monolayers for both parallel and perpendicular to the electric field. As depicted in the fig. 9, when electric field applied parallel to monolayer plane, higher reflectivity emerged in the low energy region, and for the pure GaAs monolayer the maximum reflectivity peak localized at the energy of 7.3 eV; while for VGa and VAs monolayers, the maximum reflectivity values occur around 0 eV. When the electric field applied perpendicular to the monolayer surface, for pure GaAs monolayer the maximum peak for the reflectivity appeared at the energy of 9.1 eV, and for the VGa and VAs monolayers the maximum reflectivity peaks appeared at the energy of 7.6 eV. When the vacancies are generated, the reflective intensities at the energy region from 0 to 8.01 eV have increased and red shifted. Fig. 10 presents the absorption coefficient curves for the pure GaAa monolayer, VGa and VAs monolayers respectively. The absorption curves show that the vacancy affects both the intensity and position of the absorption peaks. In the parallel polarization (E//X) the absorption spectrum for pure GaAs monolayer have two main peaks locating at the energy of 3.95 eV and 6.74 eV respectively. First absorption sub peaks located at 1.6 eV for the pure GaAs
monolayer and 0.8 eV for VGa monolayer. In the vertical polarization (E//Z), for the pure GaAs monolayer the maximum absorption peak resided at 8.7 eV, while for the monolayer with the vacancy, the maximum absorption peaks localized at 7.2 eV. With the generation of vacancies, in the energy region from 0 to 8.2 eV the absorption coefficients have increased and red shifted. Conclusion Contribution of this work can be seen from two major points. First, we estimated SHG response of GaAs monolayer. Second, we investigated vacancy effects on the structural, electronic, magnetic and optical properties of GaAs monolayer. SHG density of the pure GaAs monolayer suggests that the both Ga and As atoms contributes to their SHG responses. Furthermore, strong SHG responses suggest that GaAs monolayer presents many appealing features such as, Nano-amplifying modulator, and topological insulator. For vacancy effects, the calculated result revealed that GaAs monolayer is sensitive to the type of vacancy. From the structural property of view, vacancy damages the structural symmetry; while, from the electronic property of view, VGa monolayer exhibits the semi metallic behavior, and VAs exhibits the metallic behavior. In the view of magnetic property, VGa monolayer is spin polarized and behaves as magnetic, and the calculated total magnetic moment is 2.89 μB; while, VAs monolayer is spin-unpolarized, and behaves as nonmagnetic. From the optical aspect of view, for the both types of vacancy monolayers (VGa and VAs) their reflectivity intensities and absorption coefficients have increased and red shifted. These results will provide helpful guidance for designing of outstanding Nano-materials in real experiments.
Acknowledgments This research successfully completed in Xinjiang Technical Institute of physics & chemistry of CAS, and the author Ilmira Rozahun would like thanks to Bingbing Zhang, Cong Hu, Zhonglei Wei, and other group members to their helpful discussions and keen assistance. This work is supported by the National Natural Science Foundation of China (Grant Nos. 61366001 and 61604126), and Xinjiang autonomous regional research innovation found for postgraduate students (Grant No. XJGRI 2017031).
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Figure captions Fig. 1 (a) Top view and (b) side view of optimized atomic structure of pure 4×3 monolayer GaAs supercell (c) The phonon spectra of GaAs monolayer Fig. 2 Electron density difference of pure 4×3 monolayer GaAs Fig. 3 (a) Band structure of GaAs monolayer (b) DOS of GaAs monolayer Fig. 4 The SHG-density of the virtual-electron of the largest SHG tensors of GaAs with (a) occupied state (b) unoccupied state Fig. 5 Electron localization function of pure GaAs monolayer Fig. 6 Top view of the atomic structure of GaAs monolayer with VGa and VAs after geometry optimization (a) top view of VGa monolayer (b) top view of V As monolayer, Light blue and light gray bolls represents Ga, and As atoms, respectively Fig. 7 TDOS and PDOS of VGa and VAs in monolayer GaAs (a) is TDOS (b) and (C) are PDOS of As and Ga atom nearest to the vacancy, respectively. The black, blue, and pink lines represent the s, p, and d orbit, respectively Fig. 8 Spin density for isosurfaces of GaAs monolayers with (a) vacancy VGa and (b) vacancy VAs Fig. 9 Reflectivity curves for the electric field (a) parallel and (b) perpendicular to the GaAs monolayer surface Fig. 10 Absorption coefficient curves for the electric field (a) parallel and (b) perpendicular to GaAs monolayer
(a)
(C)
(b)
Fig. 1 (a) Top view and (b) side view of optimized atomic structure of pure 4×3 monolayer GaAs supercell (c) The phonon spectra of GaAs monolayer
Fig. 2 Electron density difference of pure 4×3 monolayer GaAs
(a)
(b)
Fig. 3 (a) Band structure of GaAs monolayer (b) DOS of GaAs monolayer
Fig. 4 The SHG-density of the virtual-electron of the largest SHG tensors of GaAs with (a) occupied state (b) unoccupied state
Fig. 5 Electron localization function of pure GaAs monolayer
Fig. 6 Top view of the atomic structure of GaAs monolayer with V Ga and VAs after geometry optimization (a) top view of VGa monolayer (b) top view of V As monolayer, light blue and light gray bolls represents Ga, and As atoms, respectively.
Fig. 7 TDOS and PDOS of VGa and VAs in monolayer GaAs (a) is TDOS (b) and (C) are PDOS of As and Ga atom nearest to the vacancy, respectively. The black, blue, and pink lines represent the s, p, and d orbits, respectively.
Fig. 8 Spin density for isosurfaces of GaAs monolayers with (a) vacancy VGa and (b) vacancy VAs
Fig. 9 Reflectivity curves for the electric field (a) parallel and (b) perpendicular to the GaAs monolayer surface
Fig. 10 Absorption coefficient curves for the electric field (a) parallel and (b) perpendicular to GaAs monolayer
Table 1 Band gap of GaAs monolayer with different vacuum thickness
Table 1 Band gap of GaAs monolayer with different vacuum thickness Vacuum
10
15
18
21
23
25
0.569
0.814
0.997
1.027
1.02
1.02
6
8
thickness (Å) ΔE (eV)
Graphical abstract
Highlights:
GaAs monolayer produces a strong SHG response.
Vacancy strongly affects structural, electronic, magnetic and optical properties of GaAs monola ye.
Arsenic vacancy (VAs) causes semi metallic to metallic transition, while Gallium vacancy (VGa) causes nonmagnetic to magnetic transition.