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Unexpected buckled structures and tunable electronic properties in arsenic nanosheets: insights from first-principles calculations
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 225304 (10pp)
doi:10.1088/0953-8984/27/22/225304
Unexpected buckled structures and tunable electronic properties in arsenic nanosheets: insights from first-principles calculations Yanli Wang1 and Yi Ding2 1
Department of Physics, Center for Optoelectronics Materials and Devices, Zhejiang Sci-Tech University, Xiasha College Park, Hangzhou, Zhejiang 310018, People’s Republic of China 2 Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, People’s Republic of China E-mail: [email protected] and [email protected] Received 25 January 2015, revised 6 April 2015 Accepted for publication 16 April 2015 Published 18 May 2015 Abstract
Using dispersion-corrected density functional theory calculations, we investigate the structural and electronic properties of arsenic (As) nanosheet, which is a cousin of phosphorene. We find that the black-phosphorus like structure is dynamically unstable for As, which has an out-of-plane soft mode from its flat As zigzag lines. Hence different from phosphorene, the stable As monolayer possesses a unique buckling along the zigzag direction, which leads to a surface corrugation of 0.20 Å and a robust dynamic stability. The zigzag buckling alters the band feature of As nanosheet, transforming it from an indirect band gap semiconductor to a direct one for the buckled structure. Strain engineering can further tune the surface corrugation and band structure of As nanosheet, for which the direct or indirect gap feature can be switched by the zigzag-directional strains, while the strains along armchair direction could modulate the band gap and induce a metallic behaviour. Prominent anisotropic Dirac-like electronic structures and orientation-dependent elastic behaviours with a remarkable negative Poisson ratio are both found in the As nanosheets, enabling the system promising applications for nano-electrics and devices. Keywords: group-V nanostructure, tunable semiconducting properties, dynamical stability, negative Poisson ratio, DFT+D calculations (Some figures may appear in colour only in the online journal)
that along x direction [14, 15]. Similarly, anisotropic elastic behaviours are also obtained in phosphorene, whose Young moduli are smallest/largest along the x/y axis [16]. It results in a good ductility against the x-axial tension, which can cause a semiconductor-to-metal transition for phosphorene, while the y-axial tension would induce an unconventional one-dimensional (1D) metallic characteristic in it [17, 18]. Such a tunable semiconducting feature enables phosphorene fascinating applications in nano-electronics and nano-devices [19–22]. As a neighbour of P in the periodic table, the As element is normally expected to share similar structures and properties to the P one. From a structural search on Pearson’s crystal database [23], layered hR6 and oS8 structures, which are
1. Introduction
Since the discovery of phosphorene, two-dimensional (2D) group-V nanosheets have attracted lots of interest from physicists, chemists, and material scientists [1–11]. Distinct from graphene and other group-IV nanosheets, phosphorene, the black-phosphorus (black-P) monolayer, is a pseudohoneycomb lattice with a high pucker along the armchair direction [12]. It brings peculiar anisotropic electronic and mechanical properties into phosphorene. For example, it has an extremely high hole-mobility up to 104 cm2 V−1 s−1 along zigzag (y) direction, which is one order of magnitude larger than the value along armchair (x) direction [13]. The thermal conductance of phosphorene is also orientationdependent, which is more favourable along y direction than 0953-8984/15/225304+10$33.00
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J. Phys.: Condens. Matter 27 (2015) 225304
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Figure 1. (a) The top view of As nanosheet. The lateral view of (b) flat-z and (c) buckled-z conformations, and (d) and (e) are the corresponding phonon dispersion curves calculated with the D3(BJ) dispersion corrections. The inset of (e) is the schematic diagram of first Brillouin zone for the As nanosheet. In (a), the distance of As atoms in the different zigzag lines is indicated by the dot line.
the parent bulk structures of blue- and black-P nanosheets, have also existed for the As element. In the experiments, the orthorhombic arsenic has been confirmed to possess the same A17 structure (i.e. oS8-type) to the black phosphorus [24, 25] 3 . It suggests that using similar preparation approach of phosphorene, such as the mechanical exfoliation technique, the As nanosheet may also be fabricated in the experiments. Contrary to phosphorene, the blue-P like As nanosheet is a little more energetically favourable than the black-P like one [26]. However, the transition between different buckled structures would be hindered by the energy barrier, which results in the coexistence of several stable phases for the group-V nanosheets [27–29]. Theoretical studies have shown that the blue-P like As monolayer is a wide-band-gap semiconductor [30], while the black-P like one performs similarly to phosphorene [31], so it is also referred to as arsenene in the literature [26, 31]. In this paper, we pay main attention to the black-P like As nanosheet, for which a comprehensive first-principles investigation is performed to reveal its peculiar buckled structure and tunable electronic properties in detail.
theory (DFT) calculations are performed by the VASP code [32, 33]. The Perdew–Burke–Ernzerhof (PBE) projector augmented wave pseudopotentials and plane-wave basis sets with a cutoff energy of 400 eV are used. The dispersion correction is adopted by the Grimme-D3 correction method with a Becke–Jonson damping ( D3(BJ) ) [34, 35]. The correction term is added to the Kohn–Sham DFT energies from the PBE calculations. A k-mesh of 15×18×1 and 18×25×1 is utilized in the relaxation and static calculations, respectively. All the lattice constants and atomic coordinates are optimized until the convergence of the force on each atom is less than 0.01 eV Å−1 . The cutoff energy and k-meshes have been tested with a good convergence of energy to meV. Utilizing the Phonopy code, the dynamic stability of As nanosheet is checked by phonon calculations on a 5 × 9 × 1 supercell [36]. The hybrid Heyd–Scuseria–Ernzerhof (HSE) calculations are performed by the FHIaims code [37], which adopts the HSE06 form with a screening parameter of 0.11 bohr−1 .
2. Methods
Figure 1 depicts the geometric structure of black-P like As monolayer. In the As basal plane, the As dimers are tiled along armchair (x) direction, causing a high pucker of 2.41 Å. These tiled dimers connect the As zigzag lines, which are aligned up and down alternatively in the z direction. While in the y direction, each As zigzag line is initially set to be flat as in the
3. Results and discussions
Considering the importance of van der Waals interactions for the buckled structures, dispersion-corrected density functional 3
See also SpringerMaterials—The Landolt-B¨ornstein Database (DOI: 10.1007/10681727 1118) and the references therein. 2
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case of black-P sheet. However, such flat-zigzag-line (flat-z) conformation is found to be dynamically unstable for the As case. As shown in figure 1(d), there is a noticeable imaginary frequency at the point. The eigenvector analysis shows it corresponds to an out-of-plane soft mode from the As zigzag lines. Thus, a further structural optimization along the soft mode gives a buckled-zigzag-line (buckled-z) conformation as shown in figure 1(c). The As atoms in the zigzag line become buckled one by one, which leads to a surface corrugation of 0.20 Å. Along with this zigzag buckling, the imaginary frequency is completely eliminated as shown in figure 1(e), which indicates the As nanosheet has a robust dynamic stability in the buckled-z conformation. For the As sheet, the zigzag buckling is obtained in the PBE+D3(BJ) calculation, which takes van der Waals interaction into account. Due to the high puckers along the armchair direction, the As zigzag lines are alternately located at the upper and lower planes. In each plane, the As zigzag lines are separated apart from each other, and the nearest distance between different zigzag lines is 3.28 Å as shown in figure 1. Such length is approximate to the interlayer distance of graphite, which is a typical case for the van der Waals interaction. Thus, the van der Waals effect needs to be considered in the calculations, which will affect the structural properties. It has been reported that for the graphite system, the PBE functional generally overestimates the interlayer distance, which needs to add the dispersion correction to compensate it. While the LDA functional is still lucky to obtain a proper value for the interlayer distance due to a cancellation of errors between exchange and correlation [38, 39]. For the As nanosheet, table 1 lists the structural parameters of As nanosheet by different functionals. Comparing to the experimental data of As bulks, the y-directional lattice constant b, the puckering heigh ha along the armchair direction, and As–As bond lengths Ra/z (here the subscript a/z represents the bonds orientated to the armchar/zigzag direction) are consistent among the calculated results by different functionals and the experimental values. However, the x-directional lattice constant a, which is influenced by the van der Waals interactions between the As atoms, is functional-dependent. As shown in table 1, the PBE functional overestimates the lattice parameter a too much, which fails to obtain a buckled structure. While the PBE+D3(BJ) value is reduced, which only deviates from the bulk value by 2.5%. Previous study on phosphorene shows the lattice difference between monolayer and bulk is about 2% [13]. Thus, the PBE+D3(BJ) calculated lattice parameter would be reasonable for the As nanosheet, and the As atoms are buckled under this lattice constant. Besides that, we also notice the dispersion correction should be included in the phonon calculations. Otherwise, the flat zigzag geometry will be misjudged to stable. Besides the As sheet, we have also performed the PBE+D3(BJ) calculation on the P and Sb nanosheets with black-P like structures. It is found that the zigzag lines are flat in the P sheet, but they are buckled with a 0.43 Å buckling height for the Sb sheet. Such buckling phenomenon is similar to the case of group-IV nanosheet, which is flat for graphene but buckled in silicene and germanene. A quantum chemistry study shows the bucklings
Table 1. The structural parameters of As nanosheets.
a (Å) b (Å) Ra (Å) Rz (Å) ha (Å) z (Å) E(meV unit−1 )
D3(BJ) buckled
PBE flat
LDA buckled
PBEsol buckled
Exp bulk
4.36 3.74 2.48 2.52 2.42 0.20 8
4.75 3.69 2.49 2.51 2.40 0 —
4.19 3.73 2.45 2.50 2.41 0.25 26
4.28 3.74 2.46 2.51 2.41 0.22 15
4.47 3.65 2.48 2.49 2.42 — —
Note: The D3(BJ) calculations are performed with the PBE functional. The lattice parameters a and b are the lattice constants along the armchair (x) and zigzag (y) directions in the As sheet. Ra and Rz are the lengths of As–As bonds along the armchair and zigzag directions. ha is the vertical distance between different zigzag lines, which is the puckering heigh along the armchair direction. z is the vertical distance for the As atoms in the same zigzag line, which is the buckling height along the zigzag direction. E is the energy gain of the zigzag buckling for the As nanosheet. The experimental values are adopted from the bulk structures of oS8-form (A17 phase) arsenic ( [25]).
of silicene and germanene will be attributed to a Pseudo Jahn– Teller (PJT) distortion [40]. When the energies of occupied and unoccupied states are closely spaced, they will mix by vibronic coupling, which further lowers the symmetry of structures as a PJT effect [41]. Here, our PBE+D3(BJ) calculations show the band gaps between occupied and unoccupied states follow the order of P (0.7 eV) > As (0.09 eV) > Sb (∼0 eV) nanosheets for the flat geometries. The more closely spaced the occupied and unoccupied states, the more pronounced the PJT-distortion effect, which results in the buckling phenomenon of As and Sb nanosheets. However, such zigzag buckling has not been reported yet in the experiments of As bulks. This may be attributed to the following reasons: (i) The temperature effect: as shown in figure 2(a), the energy gain from the buckling is only 8 meV unit−1 , so the zigzag buckling phenomenon is easily blurred by the thermal fluctuation at room-temperature (kB T ∼ 26 meV). (ii) The thickness influence: we find that the buckling height z varies with the layer number. Taking the 5-layered As nanosheet as an example, the outermost As layer still has a z of 0.13 Å, while in the middle layer, the z drops to 0.07 Å. Figure 2(b) depicts the minimum z in the N -layered As nanosheets√(N = 1 ∼ 5), which shows the z is roughly inverse to N . From the fitting function, we estimate that the z decreases to less than 0.05 Å when N 15. Thus, in the bulk form, the layer number N may be large enough to suppress the buckling. Such decreasing buckling with the increasing thickness also indicates a quantum confinement effect on the As nanosheets. This is further confirmed by the HSE band gap calculation, which shows the band gap is monotonically reduced from 0.70 eV of monolayer to 0.59, 0.40, 0.27, 0.18 eV for the 2–5 layers, respectively. (iii) The possible strain effect: when grown on the substrate, inplane strains may be generated in the supported nanosheets due to the lattice mismatch. Figure 2(c) depicts the z of As monolayer under different in-plane strains of (εx , εy ). Here, εx = (a − a0 )/a0 and εy = (b − b0 )/b0 . a(b) 3
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is expected that a careful low-temperature measurement on As surface, like the atomic force microscope or scanning tunneling microscope measurement, can discover the zigzag buckling in ultra-thin As films. There maybe also exist some flip–flop motions for the As atoms [42], which would hide the buckling phenomenon from the static STM/AFM images. Thus, a low temparature condition, which might freeze the atoms in the sheet, facilitates the observation of the special buckling configuration. Besides that, the sensitivity of z to the layer numbers and lattice lengths also provides a useful approach to detecting the thickness and strains of As nanosheets, which can be further used in nano-devices and sensors. Now, we discuss the buckling effects on the electronic structures of As nanosheet. As shown in figure 3(a), the flat-z conformation is an indirect band gap semiconductor, whose valence band maximum (VBM) is at the R (∼0.35,0,0) point and conduction band minimum (CBM) is at the point. The PBE calculations show the bottom conduction band at the R point is a little larger than the CBM at the point, which has been confirmed by the HSE calculations in figure 3(d). The obtained indirect characteristic for the flat-z conformation is consistent with previous studies [26, 31]. However, when the zigzag lines are buckled, the nanosheet exhibits a different band structure. As shown in figure 3(b), the buckled-z conformation becomes a direct band gap semiconductor with the VBM and CBM both at the R point. The PBE value of this direct band gap is 0.20 eV, and the HSE functional increases the gap size to 0.70 eV in figure 3(c). We have also performed the HSE calculations to investigate the buckling-dependent band gaps in As nanosheet. As shown in figure 3(e), the HSE calculations have also find the indirect-to-direct band gap transition is present at the z = 0.12 Å. The variations of band edges are similar between the PBE and HSE results, and the quantities of gap variations are also consistent with each other. Thus, although the DFT calculations would have underestimated the band gaps, the predicted variations of band gap are reliable. In order to gain more insights into the indirect-to-direct band gap transition, we investigate the evolution of band edges under different buckling heights. The absolute energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) at the R and points are plotted in figure 3(d), which adopt the vacuum level as the zero point. It can be seen that the energies of HOMO and LUMO at the R point are nearly unvaried under different buckling heights, while at the point, the HOMO and LUMO are down-shifted and up-shifted with the increasing z , respectively. When z reaches to about 0.12 Å, the HOMO at point becomes higher than that of R point, which causes a direct band gap in the buckled-z conformation. The corresponding partial charge densities of these HOMO/LUMO and orbital-resolved band structures are depicted in figure 4 for the buckled-z conformation. It shows that the bands at the R point are mainly from the As px orbitals, while the ones at the point are composed of As pz orbitals. Since the zigzag buckling of As nanosheet just causes the outof-plane structural change, its influences on the pz -character bands are more appreciable than on the px ones. Hence the energy variations of HOMO/LUMO at the R point are minor,
Figure 2. (a) The variation of energy versus the buckling height. (b)
The variation of minimum buckling height versus the As layer number, and the inset plots the distribution of different buckling heights in the 5-layered As nanosheet. (d) The buckling height of As monolayer versus the 2D strains (εx , εy ).
and a0 (b0 ) are the lattice constants along armchair(zigzag) direction at the strained and equilibrium states, respectively. Figure 2(c) shows that the buckling height z decreases with the increasing strain, which will turn to zero at small tensile strains. Therefore, since the measurements of As oS8 bulks have not been emphasized in previous studies, the possible buckling phenomenon may be ignored in the experiments. It 4
J. Phys.: Condens. Matter 27 (2015) 225304
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Figure 3. The band structures of (a) flat-z and (b) buckled-z conformations for As nanosheet. (c) The HSE band structures of flat-z and buckled-z conformations along the X − line. The Fermi level is at the 0 eV in the band structures. The horizontal dotted lines are guided to see the bottom of conduction bands, which are adopted to the values of CBM. ((d) and (e)) The variation of band edges versus the buckling height from the PBE and HSE calculations.
whereas the energies at the point are changed pronouncedly. As shown in figures 4(c) and (d), the HOMO and LUMO of point are distributed at different sublattices of the honeycomb. Thus, the increase of buckling height, which enhances the difference between two sublattices, increases the band gap at the point as shown in figure 3(c). When z becomes large, the position of CBM is transferred from the point to R point, which induces the indirect-to-direct band gap transition. This suggests that due to the existence of zigzag buckling, an outof-plane strain can easily manipulate the gap size and band feature of As nanosheet. In addition to the buckle-modulated electronic property, the band structure of As nanosheet can also be tailored by the in-plane strains akin to phosphorene. In figures 5(a) and (b), we plot the variations of gap size and band feature as a function of strains (εx , εy ). We find that the y-directional strain can effectively switch the band gap feature of As nanosheet. When εy > 0, most of the As nanosheets are direct band gap semiconductors. On the other hand, the nanosheets become indirect band gap semiconductors if εy −0.01. The typical case for such gap variation is illustrated in figure 5(c), which shows the band structures from (εx = 0.04, εy = 0.04) to (εx = 0.04, εy = −0.04). It can be seen that the band gap at the R point is substantially increased with the decreasing of εy . Due to the upshift of LUMO at the R point, the LUMO at the point becomes the CBM at εy = −0.01, which causes an indirect band gap into the As nanosheet. Besides that, we also find that the x-directional strain can
tune the gap size, which even induces a semiconductor-tometal transition in the As nanosheet. As shown in figures 5(a) and (b), there exists two possible regions for the metallic As nanosheet. One corresponds to the pronounced compressions on As nanosheet, for which the εx and εy are both negative. As shown in figure 5(d), among the X − and − Y lines, the top valence and bottom conduction bands cross the Fermi level, respectively, turning the compressed sheet into a conventional metal. Another metallic region corresponds to an appropriate tension on As nanosheet. As reported by Kamal et al, in a special configuration, where the angles between As atoms are identical, the gap at the R point would be just zero [26]. We find in such configuration, the As1 and As2 atoms make equal contributions to the HOMO and LUMO, which causes a zero band gap at the R point. Figure 5(d) depicts such typical metallic band structures for As nanosheet at the (εx = 0.05, εy = 0.02). It can be seen that there is a linear dispersion for the bands around the Fermi level, indicating a Dirac-like electronic structure in As nanosheet. The three-dimensional Dirac cone is plotted in figure 5(e), which shows the Dirac cone is quite anisotropic. The carrier in such strained As nanosheet would perform like a massless Fermion with high velocities up to 7 ∼ 8 × 105 m s−1 along the x direction, but becomes a normal electron/hole with the mass of 0.68/1.10 m0 (m0 is the mass of a free electron) along the y direction. This is an unconventional one-dimensional (1D) metallic characteristic, which has been proposed in phosphorene under large tensions 5
J. Phys.: Condens. Matter 27 (2015) 225304
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Figure 4. The orbital-resolved band structures of buckled-z conformation for As nanosheet. The corresponding partial charge densities of states near the Fermi level are depicted in the insets.
[17, 43]. For the As nanosheet, it requires smaller strains to achieve this peculiarity, which would be easier for the experimenters to realize the 1D metal in practice. In figures 5(a) and (b), we also mark the lines for the common biaxial and uniaxial strains. It shows the symmetric biaxial strain (εx = εy ) on As nanosheet can validly induce the metallic behaviour under the compression condition. While the antisymmetric biaxial strains (εx = −εy ) would cause a direct-to-indirect band gap transition in the system. Similar phenomena also occur for the uniaxial x- and ydirectional strains. It would be noted that the lines of these uniaxial strains, which allows the lattice relaxation along the perpendicular direction, are obviously tilted to the coordinate axis in figures 5(a) and (b). This suggests that the Poisson ratio of As nanosheet will be large. Thus, in figure 6, we calculate the 2D in-plane Young modulus (E) and Poisson ratio ν through the energy-versus-strain method [17]. We obtain the elastic moduli of As nanosheet are C11 = 13.3, C12 = 19.1, C22 = 70.3, C66 = 30.5, C16 = 0.2, and C26 = −0.3 N m−1 , which satisfy the mechanical stability criteria. The 2D Young moduli are 8.1 and 42.9 N m−1 for the x and y directions, respectively, which are significantly smaller than those of phosphorene (20.5 and 89.4 N m−1 ). The maximum E is up to 70.5 N m−1 , which is along the orientation about 60◦ relative to the positive x direction. The Poisson ratio is νx = 0.27 and νy = 1.43, bigger than the phosphorene ones (0.17 and 0.75). More interestingly, we find that the minimum Poisson ratio is negative, which is down to ν = −0.50 as
shown in figure 6(b). This indicates that the As nanosheet is an auxetic material, which can be stretched in one direction but become thicker in the perpendicular direction [44–46]. We find the remarkable negative Poisson ratio behaviour is mainly attributed to the buckling in As nanosheet. If we adopt the flatz conformation, the negative region is reduced significantly, whose minimum ν is only −0.10. The As nanosheet discussed above is the monolayer of A17 phase arsenic. In the arsenic bulk, the A17 phase can transform to the A7 phase, i.e. the layered hR6 structure [47]. To this end, we also briefly discuss the properties of monolayer A7 As nanosheet (A7-AsNS) in the work. As shown in figure 7, the A7-AsNS is a buckled hexagonal sheet, which has a chair-like buckling with the As atoms alternately up and down by atoms. By the PBE+D3(BJ) calculations, the lattice constant a is 3.57 Å and the buckling height h is 1.41 Å. Phonon calculations show the A7-AsNS is dynamically stable with no soft modes, which agrees well with the recent results [30, 48, 49]. For the A7-AsNS, it has an indirect band gap of 1.51 eV, whose VBM is at the point and the CBM is in the −M line. As shown in figure 7(d), the band gap of A7-AsNS can also be modulated by the strains. Owing to the structural isotropy, the variations under strains are symmetric along the line of εx = εy . The biaxial strains can effectively change the gap value of A7-AsNS, which would get to the maximum of 1.75 eV at the tensile strain of εx = εy = 0.03. While the biaxial compressions reduce the gap size rapidly, which is decreased to 0.50 eV at the strain of εx = εy = −0.06. These 6
J. Phys.: Condens. Matter 27 (2015) 225304
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Figure 5. (a) The gap size and (b) gap feature of As nanosheet under different (εx , εy ) strains. (c) The typical changes of band structures under the y-directional strain. (d) The typical band structures of metallic As nanosheet. (e) Three-dimensional plots of Dirac cones for the band structure in (d).
Figure 6. Polar diagrams for the (a) 2D Young modulus and (b) Poisson ratio of As nanosheet.
and in-plane states, akin to the case of silicene [50]. As shown in figures 8(a) and (b), due to the chair-like buckling in A7AsNS, the bands composed of pz orbitals are separated from the ones originated from the in-plane px /py orbitals. The gap
results are consistent with the findings of Kamal et al, which have shown that the further compressions up to −0.10 can close the band gap [26]. For the A7-AsNS, such gap modulations can be attributed to the competition between the out-of-plane 7
J. Phys.: Condens. Matter 27 (2015) 225304
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Figure 7. (a) The atom structures and (b) phonon dispersion curve for the A7 phase As nanosheet (A7-AsNS). (c) The band structure of A7-AsNS and (d) its tunable band gap under the different (εx , εy )strains.
size of A7-AsNS is determined by the top valence bands from the in-plane states and the bottom conduction bands from the out-of-plane ones. When a tension is applied, the sheet will become flatter and the atoms tend to be sp 2 hybridized [50]. This would enlarge the energy difference between the in-plane and out-of-plane states. Thus, with regard to the inplane states, the out-of-plane one is upper shifted under small tensile strains, which raises the band gap. Similarly, when the system is compressed, the out-of-plane states will move downward, making the gap size reduced. These behaviors are confirmed in figures 8(c) and (d). At the εx = εy = 0.03, due to the movement of out-plane state, the bottom conduction bands are up shifted and the band gap is increased to 1.75 eV. While at the the εx = εy = −0.03, the bottom conduction bands are down shifted and the gap drops to 1.14 eV. A more interesting case can be seen in the anti-symmetrical strains of εx = −εy = −0.03 in figure 8(e). Because the lattice along the x axis is compressed, only the gap along the − M line is reduced, while the one along y direction ( − M line) is not. It would be noticed that at the εx = εy = 0.03, the top valence bands are also altered from the bands of in-plane states to the out-plane ones. Thus, when biaxial tensile strains are larger than 0.03, the gap of A7-AsNS depends on the energy differences between the bonding and antibonding states of pz orbitals, which will descend due to the stretching of bonds. Thus, at the εx = εy = 0.03, the A7-AsNS has the maximum band gap.
4. Conclusion
In summary, we have investigated the structural and electronic properties of As analogue of phosphorene. We find that different from the black-P sheet, the As nanosheet possesses a unique surface corrugation along zigzag direction, which leads to a robust dynamic stability. The buckled As nanosheet is a direct-band-gap semiconductor, whose gap feature depends on the buckling height. Strain engineering can induce diverse electronic structures, such as direct- and indirect-band-gap semiconducting, normal metallic, and unconventional 1D metallic behaviours, into the As nanosheet. The buckled As nanostructure also has a prominent anisotropic elastic behaviour, which even possess a more remarkable negative Poisson ratio characteristic than phosphorene. Besides the black-P like structure, the As nanosheet with hR6 structure also possesses a strain-tunable band gap. Due to these extraordinary electronic and mechanical properties, the As nanosheet would be a promising nanomaterial for nano-electric and device applications. Acknowledgments
Authors acknowledge the supports from National Natural Science Foundation of China under Grant No. 11474081, 11104052, 11104249. Some of the calculations were performed in the Shanghai Supercomputer Center of China. 8
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Figure 8. The orbital-resolved band structures of A7-AsNS: (a) out-of-plane pz and (b) in-plane px /py ones. ((c) and (d)) The band structures under the biaxial strains as (c) εx = εy = 0.03 and (d) εx = εy = −0.03. (e) The band structures under the anti-symmetrical strains as εx = −εy = −0.03, for which used high-symmetry points are labelled in the Brillouin zone.
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[19] Xia F, Wang H and Jia Y 2014 Nat. Commun. 5 5458 [20] Buscema M, Groenendijk D J, Blanter S I, Steele G A, van der Zant H S J and Castellanos-Gomez A 2014 Nano Lett. 14 3347–52 [21] Engel M, Steiner M and Avouris P 2014 Nano Lett. 14 6414–7 [22] Wang Z, Jia H, Zheng X, Yang R, Wang Z, Ye G J, Chen X H, Shan J and Feng P X L 2015 Nanoscale 7 877 [23] Villars P and Cenzual K Pearson’s Crystal Data (Release 2013/14) (Materials Park, Ohio, USA: ASM International) [24] Krebs H, Holz W and Worms K H 1957 Chem. Ber. 90 1031–0682 [25] Smith P M, Leadbetter A J and Apling A J 1975 Phil. Mag. 31 57–64 [26] Kamal C and Ezawa M 2015 Phys. Rev. B 91 085423 [27] Zhu Z and Tom´anek D 2014 Phys. Rev. Lett. 112 176802 [28] Guan J, Zhu Z and Tom´anek D 2014 Phys. Rev. Lett. 113 046804 [29] Guan J, Zhu Z and Tomnek D 2015 ACS Nano (ASAP) [30] Zhu Z, Guan J and Tomanek D 2014 arXiv preprint (arXiv:1410.6371) [31] Zhang Z, Yang D, Xue D, Si M and Zhang G 2014 arXiv preprint (arXiv:1411.3165) [32] Kresse G and Furthmuller J 1996 ACS Nano 8 12763 [33] Kresse G and Furthmuller J 1996 Phys. Rev. B 54 11169–86 [34] Grimme S, Antony J, Ehrlich S and Krieg H 2010 J. Chem. Phys. 132 154104
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Unexpected buckled structures and tunable electronic properties in arsenic nanosheets: insights from first-principles calculations
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 225304 (10pp)
doi:10.1088/0953-8984/27/22/225304
Unexpected buckled structures and tunable electronic properties in arsenic nanosheets: insights from first-principles calculations Yanli Wang1 and Yi Ding2 1
Department of Physics, Center for Optoelectronics Materials and Devices, Zhejiang Sci-Tech University, Xiasha College Park, Hangzhou, Zhejiang 310018, People’s Republic of China 2 Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, People’s Republic of China E-mail: [email protected] and [email protected] Received 25 January 2015, revised 6 April 2015 Accepted for publication 16 April 2015 Published 18 May 2015 Abstract
Using dispersion-corrected density functional theory calculations, we investigate the structural and electronic properties of arsenic (As) nanosheet, which is a cousin of phosphorene. We find that the black-phosphorus like structure is dynamically unstable for As, which has an out-of-plane soft mode from its flat As zigzag lines. Hence different from phosphorene, the stable As monolayer possesses a unique buckling along the zigzag direction, which leads to a surface corrugation of 0.20 Å and a robust dynamic stability. The zigzag buckling alters the band feature of As nanosheet, transforming it from an indirect band gap semiconductor to a direct one for the buckled structure. Strain engineering can further tune the surface corrugation and band structure of As nanosheet, for which the direct or indirect gap feature can be switched by the zigzag-directional strains, while the strains along armchair direction could modulate the band gap and induce a metallic behaviour. Prominent anisotropic Dirac-like electronic structures and orientation-dependent elastic behaviours with a remarkable negative Poisson ratio are both found in the As nanosheets, enabling the system promising applications for nano-electrics and devices. Keywords: group-V nanostructure, tunable semiconducting properties, dynamical stability, negative Poisson ratio, DFT+D calculations (Some figures may appear in colour only in the online journal)
that along x direction [14, 15]. Similarly, anisotropic elastic behaviours are also obtained in phosphorene, whose Young moduli are smallest/largest along the x/y axis [16]. It results in a good ductility against the x-axial tension, which can cause a semiconductor-to-metal transition for phosphorene, while the y-axial tension would induce an unconventional one-dimensional (1D) metallic characteristic in it [17, 18]. Such a tunable semiconducting feature enables phosphorene fascinating applications in nano-electronics and nano-devices [19–22]. As a neighbour of P in the periodic table, the As element is normally expected to share similar structures and properties to the P one. From a structural search on Pearson’s crystal database [23], layered hR6 and oS8 structures, which are
1. Introduction
Since the discovery of phosphorene, two-dimensional (2D) group-V nanosheets have attracted lots of interest from physicists, chemists, and material scientists [1–11]. Distinct from graphene and other group-IV nanosheets, phosphorene, the black-phosphorus (black-P) monolayer, is a pseudohoneycomb lattice with a high pucker along the armchair direction [12]. It brings peculiar anisotropic electronic and mechanical properties into phosphorene. For example, it has an extremely high hole-mobility up to 104 cm2 V−1 s−1 along zigzag (y) direction, which is one order of magnitude larger than the value along armchair (x) direction [13]. The thermal conductance of phosphorene is also orientationdependent, which is more favourable along y direction than 0953-8984/15/225304+10$33.00
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Figure 1. (a) The top view of As nanosheet. The lateral view of (b) flat-z and (c) buckled-z conformations, and (d) and (e) are the corresponding phonon dispersion curves calculated with the D3(BJ) dispersion corrections. The inset of (e) is the schematic diagram of first Brillouin zone for the As nanosheet. In (a), the distance of As atoms in the different zigzag lines is indicated by the dot line.
the parent bulk structures of blue- and black-P nanosheets, have also existed for the As element. In the experiments, the orthorhombic arsenic has been confirmed to possess the same A17 structure (i.e. oS8-type) to the black phosphorus [24, 25] 3 . It suggests that using similar preparation approach of phosphorene, such as the mechanical exfoliation technique, the As nanosheet may also be fabricated in the experiments. Contrary to phosphorene, the blue-P like As nanosheet is a little more energetically favourable than the black-P like one [26]. However, the transition between different buckled structures would be hindered by the energy barrier, which results in the coexistence of several stable phases for the group-V nanosheets [27–29]. Theoretical studies have shown that the blue-P like As monolayer is a wide-band-gap semiconductor [30], while the black-P like one performs similarly to phosphorene [31], so it is also referred to as arsenene in the literature [26, 31]. In this paper, we pay main attention to the black-P like As nanosheet, for which a comprehensive first-principles investigation is performed to reveal its peculiar buckled structure and tunable electronic properties in detail.
theory (DFT) calculations are performed by the VASP code [32, 33]. The Perdew–Burke–Ernzerhof (PBE) projector augmented wave pseudopotentials and plane-wave basis sets with a cutoff energy of 400 eV are used. The dispersion correction is adopted by the Grimme-D3 correction method with a Becke–Jonson damping ( D3(BJ) ) [34, 35]. The correction term is added to the Kohn–Sham DFT energies from the PBE calculations. A k-mesh of 15×18×1 and 18×25×1 is utilized in the relaxation and static calculations, respectively. All the lattice constants and atomic coordinates are optimized until the convergence of the force on each atom is less than 0.01 eV Å−1 . The cutoff energy and k-meshes have been tested with a good convergence of energy to meV. Utilizing the Phonopy code, the dynamic stability of As nanosheet is checked by phonon calculations on a 5 × 9 × 1 supercell [36]. The hybrid Heyd–Scuseria–Ernzerhof (HSE) calculations are performed by the FHIaims code [37], which adopts the HSE06 form with a screening parameter of 0.11 bohr−1 .
2. Methods
Figure 1 depicts the geometric structure of black-P like As monolayer. In the As basal plane, the As dimers are tiled along armchair (x) direction, causing a high pucker of 2.41 Å. These tiled dimers connect the As zigzag lines, which are aligned up and down alternatively in the z direction. While in the y direction, each As zigzag line is initially set to be flat as in the
3. Results and discussions
Considering the importance of van der Waals interactions for the buckled structures, dispersion-corrected density functional 3
See also SpringerMaterials—The Landolt-B¨ornstein Database (DOI: 10.1007/10681727 1118) and the references therein. 2
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case of black-P sheet. However, such flat-zigzag-line (flat-z) conformation is found to be dynamically unstable for the As case. As shown in figure 1(d), there is a noticeable imaginary frequency at the point. The eigenvector analysis shows it corresponds to an out-of-plane soft mode from the As zigzag lines. Thus, a further structural optimization along the soft mode gives a buckled-zigzag-line (buckled-z) conformation as shown in figure 1(c). The As atoms in the zigzag line become buckled one by one, which leads to a surface corrugation of 0.20 Å. Along with this zigzag buckling, the imaginary frequency is completely eliminated as shown in figure 1(e), which indicates the As nanosheet has a robust dynamic stability in the buckled-z conformation. For the As sheet, the zigzag buckling is obtained in the PBE+D3(BJ) calculation, which takes van der Waals interaction into account. Due to the high puckers along the armchair direction, the As zigzag lines are alternately located at the upper and lower planes. In each plane, the As zigzag lines are separated apart from each other, and the nearest distance between different zigzag lines is 3.28 Å as shown in figure 1. Such length is approximate to the interlayer distance of graphite, which is a typical case for the van der Waals interaction. Thus, the van der Waals effect needs to be considered in the calculations, which will affect the structural properties. It has been reported that for the graphite system, the PBE functional generally overestimates the interlayer distance, which needs to add the dispersion correction to compensate it. While the LDA functional is still lucky to obtain a proper value for the interlayer distance due to a cancellation of errors between exchange and correlation [38, 39]. For the As nanosheet, table 1 lists the structural parameters of As nanosheet by different functionals. Comparing to the experimental data of As bulks, the y-directional lattice constant b, the puckering heigh ha along the armchair direction, and As–As bond lengths Ra/z (here the subscript a/z represents the bonds orientated to the armchar/zigzag direction) are consistent among the calculated results by different functionals and the experimental values. However, the x-directional lattice constant a, which is influenced by the van der Waals interactions between the As atoms, is functional-dependent. As shown in table 1, the PBE functional overestimates the lattice parameter a too much, which fails to obtain a buckled structure. While the PBE+D3(BJ) value is reduced, which only deviates from the bulk value by 2.5%. Previous study on phosphorene shows the lattice difference between monolayer and bulk is about 2% [13]. Thus, the PBE+D3(BJ) calculated lattice parameter would be reasonable for the As nanosheet, and the As atoms are buckled under this lattice constant. Besides that, we also notice the dispersion correction should be included in the phonon calculations. Otherwise, the flat zigzag geometry will be misjudged to stable. Besides the As sheet, we have also performed the PBE+D3(BJ) calculation on the P and Sb nanosheets with black-P like structures. It is found that the zigzag lines are flat in the P sheet, but they are buckled with a 0.43 Å buckling height for the Sb sheet. Such buckling phenomenon is similar to the case of group-IV nanosheet, which is flat for graphene but buckled in silicene and germanene. A quantum chemistry study shows the bucklings
Table 1. The structural parameters of As nanosheets.
a (Å) b (Å) Ra (Å) Rz (Å) ha (Å) z (Å) E(meV unit−1 )
D3(BJ) buckled
PBE flat
LDA buckled
PBEsol buckled
Exp bulk
4.36 3.74 2.48 2.52 2.42 0.20 8
4.75 3.69 2.49 2.51 2.40 0 —
4.19 3.73 2.45 2.50 2.41 0.25 26
4.28 3.74 2.46 2.51 2.41 0.22 15
4.47 3.65 2.48 2.49 2.42 — —
Note: The D3(BJ) calculations are performed with the PBE functional. The lattice parameters a and b are the lattice constants along the armchair (x) and zigzag (y) directions in the As sheet. Ra and Rz are the lengths of As–As bonds along the armchair and zigzag directions. ha is the vertical distance between different zigzag lines, which is the puckering heigh along the armchair direction. z is the vertical distance for the As atoms in the same zigzag line, which is the buckling height along the zigzag direction. E is the energy gain of the zigzag buckling for the As nanosheet. The experimental values are adopted from the bulk structures of oS8-form (A17 phase) arsenic ( [25]).
of silicene and germanene will be attributed to a Pseudo Jahn– Teller (PJT) distortion [40]. When the energies of occupied and unoccupied states are closely spaced, they will mix by vibronic coupling, which further lowers the symmetry of structures as a PJT effect [41]. Here, our PBE+D3(BJ) calculations show the band gaps between occupied and unoccupied states follow the order of P (0.7 eV) > As (0.09 eV) > Sb (∼0 eV) nanosheets for the flat geometries. The more closely spaced the occupied and unoccupied states, the more pronounced the PJT-distortion effect, which results in the buckling phenomenon of As and Sb nanosheets. However, such zigzag buckling has not been reported yet in the experiments of As bulks. This may be attributed to the following reasons: (i) The temperature effect: as shown in figure 2(a), the energy gain from the buckling is only 8 meV unit−1 , so the zigzag buckling phenomenon is easily blurred by the thermal fluctuation at room-temperature (kB T ∼ 26 meV). (ii) The thickness influence: we find that the buckling height z varies with the layer number. Taking the 5-layered As nanosheet as an example, the outermost As layer still has a z of 0.13 Å, while in the middle layer, the z drops to 0.07 Å. Figure 2(b) depicts the minimum z in the N -layered As nanosheets√(N = 1 ∼ 5), which shows the z is roughly inverse to N . From the fitting function, we estimate that the z decreases to less than 0.05 Å when N 15. Thus, in the bulk form, the layer number N may be large enough to suppress the buckling. Such decreasing buckling with the increasing thickness also indicates a quantum confinement effect on the As nanosheets. This is further confirmed by the HSE band gap calculation, which shows the band gap is monotonically reduced from 0.70 eV of monolayer to 0.59, 0.40, 0.27, 0.18 eV for the 2–5 layers, respectively. (iii) The possible strain effect: when grown on the substrate, inplane strains may be generated in the supported nanosheets due to the lattice mismatch. Figure 2(c) depicts the z of As monolayer under different in-plane strains of (εx , εy ). Here, εx = (a − a0 )/a0 and εy = (b − b0 )/b0 . a(b) 3
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is expected that a careful low-temperature measurement on As surface, like the atomic force microscope or scanning tunneling microscope measurement, can discover the zigzag buckling in ultra-thin As films. There maybe also exist some flip–flop motions for the As atoms [42], which would hide the buckling phenomenon from the static STM/AFM images. Thus, a low temparature condition, which might freeze the atoms in the sheet, facilitates the observation of the special buckling configuration. Besides that, the sensitivity of z to the layer numbers and lattice lengths also provides a useful approach to detecting the thickness and strains of As nanosheets, which can be further used in nano-devices and sensors. Now, we discuss the buckling effects on the electronic structures of As nanosheet. As shown in figure 3(a), the flat-z conformation is an indirect band gap semiconductor, whose valence band maximum (VBM) is at the R (∼0.35,0,0) point and conduction band minimum (CBM) is at the point. The PBE calculations show the bottom conduction band at the R point is a little larger than the CBM at the point, which has been confirmed by the HSE calculations in figure 3(d). The obtained indirect characteristic for the flat-z conformation is consistent with previous studies [26, 31]. However, when the zigzag lines are buckled, the nanosheet exhibits a different band structure. As shown in figure 3(b), the buckled-z conformation becomes a direct band gap semiconductor with the VBM and CBM both at the R point. The PBE value of this direct band gap is 0.20 eV, and the HSE functional increases the gap size to 0.70 eV in figure 3(c). We have also performed the HSE calculations to investigate the buckling-dependent band gaps in As nanosheet. As shown in figure 3(e), the HSE calculations have also find the indirect-to-direct band gap transition is present at the z = 0.12 Å. The variations of band edges are similar between the PBE and HSE results, and the quantities of gap variations are also consistent with each other. Thus, although the DFT calculations would have underestimated the band gaps, the predicted variations of band gap are reliable. In order to gain more insights into the indirect-to-direct band gap transition, we investigate the evolution of band edges under different buckling heights. The absolute energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) at the R and points are plotted in figure 3(d), which adopt the vacuum level as the zero point. It can be seen that the energies of HOMO and LUMO at the R point are nearly unvaried under different buckling heights, while at the point, the HOMO and LUMO are down-shifted and up-shifted with the increasing z , respectively. When z reaches to about 0.12 Å, the HOMO at point becomes higher than that of R point, which causes a direct band gap in the buckled-z conformation. The corresponding partial charge densities of these HOMO/LUMO and orbital-resolved band structures are depicted in figure 4 for the buckled-z conformation. It shows that the bands at the R point are mainly from the As px orbitals, while the ones at the point are composed of As pz orbitals. Since the zigzag buckling of As nanosheet just causes the outof-plane structural change, its influences on the pz -character bands are more appreciable than on the px ones. Hence the energy variations of HOMO/LUMO at the R point are minor,
Figure 2. (a) The variation of energy versus the buckling height. (b)
The variation of minimum buckling height versus the As layer number, and the inset plots the distribution of different buckling heights in the 5-layered As nanosheet. (d) The buckling height of As monolayer versus the 2D strains (εx , εy ).
and a0 (b0 ) are the lattice constants along armchair(zigzag) direction at the strained and equilibrium states, respectively. Figure 2(c) shows that the buckling height z decreases with the increasing strain, which will turn to zero at small tensile strains. Therefore, since the measurements of As oS8 bulks have not been emphasized in previous studies, the possible buckling phenomenon may be ignored in the experiments. It 4
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Figure 3. The band structures of (a) flat-z and (b) buckled-z conformations for As nanosheet. (c) The HSE band structures of flat-z and buckled-z conformations along the X − line. The Fermi level is at the 0 eV in the band structures. The horizontal dotted lines are guided to see the bottom of conduction bands, which are adopted to the values of CBM. ((d) and (e)) The variation of band edges versus the buckling height from the PBE and HSE calculations.
whereas the energies at the point are changed pronouncedly. As shown in figures 4(c) and (d), the HOMO and LUMO of point are distributed at different sublattices of the honeycomb. Thus, the increase of buckling height, which enhances the difference between two sublattices, increases the band gap at the point as shown in figure 3(c). When z becomes large, the position of CBM is transferred from the point to R point, which induces the indirect-to-direct band gap transition. This suggests that due to the existence of zigzag buckling, an outof-plane strain can easily manipulate the gap size and band feature of As nanosheet. In addition to the buckle-modulated electronic property, the band structure of As nanosheet can also be tailored by the in-plane strains akin to phosphorene. In figures 5(a) and (b), we plot the variations of gap size and band feature as a function of strains (εx , εy ). We find that the y-directional strain can effectively switch the band gap feature of As nanosheet. When εy > 0, most of the As nanosheets are direct band gap semiconductors. On the other hand, the nanosheets become indirect band gap semiconductors if εy −0.01. The typical case for such gap variation is illustrated in figure 5(c), which shows the band structures from (εx = 0.04, εy = 0.04) to (εx = 0.04, εy = −0.04). It can be seen that the band gap at the R point is substantially increased with the decreasing of εy . Due to the upshift of LUMO at the R point, the LUMO at the point becomes the CBM at εy = −0.01, which causes an indirect band gap into the As nanosheet. Besides that, we also find that the x-directional strain can
tune the gap size, which even induces a semiconductor-tometal transition in the As nanosheet. As shown in figures 5(a) and (b), there exists two possible regions for the metallic As nanosheet. One corresponds to the pronounced compressions on As nanosheet, for which the εx and εy are both negative. As shown in figure 5(d), among the X − and − Y lines, the top valence and bottom conduction bands cross the Fermi level, respectively, turning the compressed sheet into a conventional metal. Another metallic region corresponds to an appropriate tension on As nanosheet. As reported by Kamal et al, in a special configuration, where the angles between As atoms are identical, the gap at the R point would be just zero [26]. We find in such configuration, the As1 and As2 atoms make equal contributions to the HOMO and LUMO, which causes a zero band gap at the R point. Figure 5(d) depicts such typical metallic band structures for As nanosheet at the (εx = 0.05, εy = 0.02). It can be seen that there is a linear dispersion for the bands around the Fermi level, indicating a Dirac-like electronic structure in As nanosheet. The three-dimensional Dirac cone is plotted in figure 5(e), which shows the Dirac cone is quite anisotropic. The carrier in such strained As nanosheet would perform like a massless Fermion with high velocities up to 7 ∼ 8 × 105 m s−1 along the x direction, but becomes a normal electron/hole with the mass of 0.68/1.10 m0 (m0 is the mass of a free electron) along the y direction. This is an unconventional one-dimensional (1D) metallic characteristic, which has been proposed in phosphorene under large tensions 5
J. Phys.: Condens. Matter 27 (2015) 225304
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Figure 4. The orbital-resolved band structures of buckled-z conformation for As nanosheet. The corresponding partial charge densities of states near the Fermi level are depicted in the insets.
[17, 43]. For the As nanosheet, it requires smaller strains to achieve this peculiarity, which would be easier for the experimenters to realize the 1D metal in practice. In figures 5(a) and (b), we also mark the lines for the common biaxial and uniaxial strains. It shows the symmetric biaxial strain (εx = εy ) on As nanosheet can validly induce the metallic behaviour under the compression condition. While the antisymmetric biaxial strains (εx = −εy ) would cause a direct-to-indirect band gap transition in the system. Similar phenomena also occur for the uniaxial x- and ydirectional strains. It would be noted that the lines of these uniaxial strains, which allows the lattice relaxation along the perpendicular direction, are obviously tilted to the coordinate axis in figures 5(a) and (b). This suggests that the Poisson ratio of As nanosheet will be large. Thus, in figure 6, we calculate the 2D in-plane Young modulus (E) and Poisson ratio ν through the energy-versus-strain method [17]. We obtain the elastic moduli of As nanosheet are C11 = 13.3, C12 = 19.1, C22 = 70.3, C66 = 30.5, C16 = 0.2, and C26 = −0.3 N m−1 , which satisfy the mechanical stability criteria. The 2D Young moduli are 8.1 and 42.9 N m−1 for the x and y directions, respectively, which are significantly smaller than those of phosphorene (20.5 and 89.4 N m−1 ). The maximum E is up to 70.5 N m−1 , which is along the orientation about 60◦ relative to the positive x direction. The Poisson ratio is νx = 0.27 and νy = 1.43, bigger than the phosphorene ones (0.17 and 0.75). More interestingly, we find that the minimum Poisson ratio is negative, which is down to ν = −0.50 as
shown in figure 6(b). This indicates that the As nanosheet is an auxetic material, which can be stretched in one direction but become thicker in the perpendicular direction [44–46]. We find the remarkable negative Poisson ratio behaviour is mainly attributed to the buckling in As nanosheet. If we adopt the flatz conformation, the negative region is reduced significantly, whose minimum ν is only −0.10. The As nanosheet discussed above is the monolayer of A17 phase arsenic. In the arsenic bulk, the A17 phase can transform to the A7 phase, i.e. the layered hR6 structure [47]. To this end, we also briefly discuss the properties of monolayer A7 As nanosheet (A7-AsNS) in the work. As shown in figure 7, the A7-AsNS is a buckled hexagonal sheet, which has a chair-like buckling with the As atoms alternately up and down by atoms. By the PBE+D3(BJ) calculations, the lattice constant a is 3.57 Å and the buckling height h is 1.41 Å. Phonon calculations show the A7-AsNS is dynamically stable with no soft modes, which agrees well with the recent results [30, 48, 49]. For the A7-AsNS, it has an indirect band gap of 1.51 eV, whose VBM is at the point and the CBM is in the −M line. As shown in figure 7(d), the band gap of A7-AsNS can also be modulated by the strains. Owing to the structural isotropy, the variations under strains are symmetric along the line of εx = εy . The biaxial strains can effectively change the gap value of A7-AsNS, which would get to the maximum of 1.75 eV at the tensile strain of εx = εy = 0.03. While the biaxial compressions reduce the gap size rapidly, which is decreased to 0.50 eV at the strain of εx = εy = −0.06. These 6
J. Phys.: Condens. Matter 27 (2015) 225304
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Figure 5. (a) The gap size and (b) gap feature of As nanosheet under different (εx , εy ) strains. (c) The typical changes of band structures under the y-directional strain. (d) The typical band structures of metallic As nanosheet. (e) Three-dimensional plots of Dirac cones for the band structure in (d).
Figure 6. Polar diagrams for the (a) 2D Young modulus and (b) Poisson ratio of As nanosheet.
and in-plane states, akin to the case of silicene [50]. As shown in figures 8(a) and (b), due to the chair-like buckling in A7AsNS, the bands composed of pz orbitals are separated from the ones originated from the in-plane px /py orbitals. The gap
results are consistent with the findings of Kamal et al, which have shown that the further compressions up to −0.10 can close the band gap [26]. For the A7-AsNS, such gap modulations can be attributed to the competition between the out-of-plane 7
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Figure 7. (a) The atom structures and (b) phonon dispersion curve for the A7 phase As nanosheet (A7-AsNS). (c) The band structure of A7-AsNS and (d) its tunable band gap under the different (εx , εy )strains.
size of A7-AsNS is determined by the top valence bands from the in-plane states and the bottom conduction bands from the out-of-plane ones. When a tension is applied, the sheet will become flatter and the atoms tend to be sp 2 hybridized [50]. This would enlarge the energy difference between the in-plane and out-of-plane states. Thus, with regard to the inplane states, the out-of-plane one is upper shifted under small tensile strains, which raises the band gap. Similarly, when the system is compressed, the out-of-plane states will move downward, making the gap size reduced. These behaviors are confirmed in figures 8(c) and (d). At the εx = εy = 0.03, due to the movement of out-plane state, the bottom conduction bands are up shifted and the band gap is increased to 1.75 eV. While at the the εx = εy = −0.03, the bottom conduction bands are down shifted and the gap drops to 1.14 eV. A more interesting case can be seen in the anti-symmetrical strains of εx = −εy = −0.03 in figure 8(e). Because the lattice along the x axis is compressed, only the gap along the − M line is reduced, while the one along y direction ( − M line) is not. It would be noticed that at the εx = εy = 0.03, the top valence bands are also altered from the bands of in-plane states to the out-plane ones. Thus, when biaxial tensile strains are larger than 0.03, the gap of A7-AsNS depends on the energy differences between the bonding and antibonding states of pz orbitals, which will descend due to the stretching of bonds. Thus, at the εx = εy = 0.03, the A7-AsNS has the maximum band gap.
4. Conclusion
In summary, we have investigated the structural and electronic properties of As analogue of phosphorene. We find that different from the black-P sheet, the As nanosheet possesses a unique surface corrugation along zigzag direction, which leads to a robust dynamic stability. The buckled As nanosheet is a direct-band-gap semiconductor, whose gap feature depends on the buckling height. Strain engineering can induce diverse electronic structures, such as direct- and indirect-band-gap semiconducting, normal metallic, and unconventional 1D metallic behaviours, into the As nanosheet. The buckled As nanostructure also has a prominent anisotropic elastic behaviour, which even possess a more remarkable negative Poisson ratio characteristic than phosphorene. Besides the black-P like structure, the As nanosheet with hR6 structure also possesses a strain-tunable band gap. Due to these extraordinary electronic and mechanical properties, the As nanosheet would be a promising nanomaterial for nano-electric and device applications. Acknowledgments
Authors acknowledge the supports from National Natural Science Foundation of China under Grant No. 11474081, 11104052, 11104249. Some of the calculations were performed in the Shanghai Supercomputer Center of China. 8
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Figure 8. The orbital-resolved band structures of A7-AsNS: (a) out-of-plane pz and (b) in-plane px /py ones. ((c) and (d)) The band structures under the biaxial strains as (c) εx = εy = 0.03 and (d) εx = εy = −0.03. (e) The band structures under the anti-symmetrical strains as εx = −εy = −0.03, for which used high-symmetry points are labelled in the Brillouin zone.
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