Arsenene: Two-dimensional buckled and puckered honeycomb arsenic systems
aa r X i v : . [ c ond - m a t . m t r l - s c i ] O c t Arsenene: Two-dimensional buckled andpuckered honeycomb arsenic systems
C. Kamal and Motohiko Ezawa October 21, 2014 Indus Synchrotrons Utilization Division, Raja Ramanna Centre for AdvancedTechnology, Indore 452013, India, Department of Applied Physics, Universityof Tokyo, Hongo 7-3-1, 113-8656, Japan
Recently phosphorene, monolayer honeycomb structure of blackphosphorus, was experimentally manufactured and attracts rapidlygrowing interests. Here we investigate stability and electronic prop-erties of honeycomb structure of arsenic system based on first prin-ciple calculations. Two types of honeycomb structures, buckled andpuckered, are found to be stable. We call them arsenene as in thecase of phosphorene. We find that both the buckled and puckeredarsenene possess indirect gaps. We show that the band gap of thepuckered and buckled arsenene can be tuned by applying strain. Thegap closing occurs at 6% strain for puckered arsenene, where thebond angles between the nearest neighbour become nearly equal. Anindirect-to-direct gap transition occurs by applying strain. Especially, strain is enough to transform the puckered arsenene into a direct-gap semiconductor. Our results will pave a way for applications tolight-emitting diodes and solar cells. Graphene, a planar honeycomb monolayer of carbon atoms, is oneof the most fascinating materials . It has high mobility, heat conduc-tance and mechanical strength. However, it lacks an intrinsic band gap,which makes electronic applications of graphene difficult. The finding ofgraphene excites material search of other monolayer honeycomb systemswith intrinsic gaps. Recently, honeycomb structures of the carbon groupattract much attention, which are silicene, germanene and stanene . Thegeometric structures of these systems are buckled due to the hybridiza-tion of sp and sp orbitals. Accordingly we can control the band gap byapplying perpendicular electric field . These are topological insulatorsowing to spin-orbit interactions . Although silicene and germanene havealready been manufactured on substrates , their free-standing samplesare not yet available, which makes experiments difficult to reveal their ex-citing properties. Phosphorene, a monolayer of black phosphorus, wasrecently manufactured by exfoliating black phosphorus . It has alreadybeen shown that it acts as a field-effect transistor . The experimental suc-cess evokes recent flourish of studies of phosphorene . The structure ispuckered, which is different from the planar graphene and the buckled sil-icene. Furthermore, the buckled phosphorene named "blue phosphorene"is shown to be stable by first principle calculations .In this paper, motivated by recent studies on phosphorene, we have in-vestigated stability and electronic properties of arsenene, which is a honey-comb monolayer of arsenic, by employing density functional theory (DFT)based electronic structure calculations. First we show two types of honey-comb structures, namely buckled and puckered, are stable by investigat-ing phonon spectrum and cohesive energy. Our calculations show thatthe buckled arsenene is slightly more stable than the puckered arsenene.Though both these two systems possess indirect band gaps, it is possibleto make a transition from an indirect to direct band gap by applying strain or external electric field. Puckered arsenene is transformed into a direct-gap semiconductor by applying only strain, and the gap nearly closesat strain. The band gap of the buckled arsenene can be tuned by electricfield, while the band gap change is negligible for the puckered arsenene. RESULTS
Stability of Arsenene.
Graphene forms a planar honeycomb structure since it exhibits purelysp hybridization. On the other hand, other elemental honeycomb systemsso far found are not planar but form either buckled or puckered structure.For example, a honeycomb structure of group IV element such as silicene,germanene and stanene form a buckled structure. Additionally, phospho-rene made of phosphorus belonging to group V is known experimentallyto have a puckered structure. It has theoretically been shown that there isalso a buckled structure of phosphorene named blue phosphorene . Theseobservations make it important to study if there is a stable honeycombstructure made of arsenic - another group V element. For this purpose, wechoose three different possible honeycomb geometric structures, namely(i) puckered, (ii) planar and (iii) buckled for arsenene. We show the opti-mized geometric structures for these three cases in Figure 1(a),(b),(c). Theresults of optimized geometric structures are also summarized in Table 1.The puckered angle of arsenene is 100.80 ◦ , which is slightly smaller thanthat of phosphorene 103.69 ◦ . In the case of the buckled structure, thebuckling height and angle are found to be 1.388 Å and 92.22 ◦ , respec-tively.In order to study the stability of arsenene, we have carried out thecohesive energy as well as phonon dispersion calculations for the abovementioned three possible structures. The cohesive energy of -2.952, -2.391and -2.989 eV/atom for the puckered, planar and buckled arsenene, respec-tively. Among the three two-dimensional structures, the buckled arseneneis the minimum energy configuration. However, the cohesive energy dif-ference between the buckled and puckered systems is very small and it iscomparable with the thermal energy at the room temperature. On the otherhand, the cohesive energy of planar structure is about 400 meV less ascompared to those of the other two structures.Furthermore, we have performed the phonon dispersion calculationsfor these three systems. The results of phonon dispersion along the highsymmetric points in the Brillouin zone (See Figure 1(d), (e), (f)) for thesethree systems are given in Figure 1(g), (h), (i). From the phonon spec-trum, it is possible to compare the stability and structural rigidity of thesesystems. Puckered arsenene is globally stable since the global energy min-imum exists, and the phonon dispersion is completely positive and lineararound the Γ point . In the case of buckled arsenene, all the modes containpositive values of frequencies except the transverse acoustic mode near the Γ point. This mode gets negative frequencies due the softening of phononsand a similar situation has been reported in the literature for the buckledgermanene , where a strong dependence of frequency of this mode on the1 able 1 | The results for optimized geometries of arsenene obtained by DFT with PBE exchange-correlations functional.
Structure Space Cohesive Lattice constants (Å) Bond Bondgroup energy (eV/atom) a b or c length (Å) angle ( ◦ )Puckered Pmna -2.952 3.677 4.765 ( b ) 2.501, 2.485 100.80, 94.64Planar P6/mmm -2.391 4.366 - 2.521 120.00Buckled P3m1 -2.989 3.607 - 2.503 92.22Bulk R-3m -2.986 3.820 10.752 ( c ) 2.556 96.72(3.7598) (10.5475) computational parameters is also observed. On the other hand, the pla-nar arsenene is not stable since it possesses a few modes with imaginaryfrequencies in a large region of the Brillouin zone, which corresponds tonegative values in Figure 1(h). From the detailed analysis of the phononspectra, we infer that, among the 12 phonon modes of the puckered ar-senene, half of them are Raman active and they are 97, 112, 215, 217, 247and 253 cm − with the C h point group symmetry at the Γ point. In thecase of the buckled arsenene, all the three modes of optical branch are Ra-man active. They are 236 cm − (doubly degenerate) and 305 cm − withthe D d point group symmetry at the Γ point. Band Structures.
We show the electronic band structures for the puckered, planar andbuckled arsenene in Figure 1(j),(k),(l). We find that the planar arseneneis metallic. We shall not continue to discuss any of its properties since itdoes not correspond to a stable structure. Both the puckered and buckledarsenene are semiconductors with indirect band gap of 0.831 and 1.635eV, respectively. An indirect band gap in the buckled arsenene resemblesthat of the buckled (blue) phosphorene . However, there are certain dif-ferences in the band structures of the buckled phosphorene and arsenene.In the case of the buckled arsenene (see Figure 1(i)), the valence bandmaximum lies at the Γ point and the conduction band minimum occursalong the Γ -M direction, whereas in the buckled phosphorene, neither theconduction band minimum nor the valence band maximum lies at the highsymmetry k -points in the Brillouin zone . Moreover, the difference be-tween the indirect band gap ( . eV) and the direct gap ( . eV) at the Γ point is quite large ( . eV) for buckled arsenene.On the other hand, the indirect-gap semiconducting character of thepuckered arsenene is distinctly different from the direct band gap of thepuckered phosphorene. We note that, in the puckered arsenene, two sepa-rate valence and conduction band edges exist near the Fermi energy. Thecompetition between the energies of these edges crucially determines thenature of the semiconducting behavior. In the puckered arsenene, the max-imum of valence and the minimum of conduction bands occur along the Γ -Y direction and at the Γ point, respectively. This causes the puckeredarsenene to behave as an indirect-gap semiconductor. This is in contrastto the direct gap present at the Γ point in the puckered phosphorene .Moreover, we clearly see from Figure 1(j) that the difference in energiesbetween two valence band edges near the Fermi level is very small (only85 meV) as compared to that in the puckered phosphorene (more than 500meV) . The difference is of the order of thermal energy at room tempera-ture. In the next section, we analyze the effect of mechanical strain on theelectronic structures of the puckered arsenene, and show that it is possibleto transform puckered arsenene to a direct-gap semiconductor by applyingstrain. Strain induced band gap change.
Puckered Arsenene
Applying mechanical strain to the sample is a powerful method tomodulate the electronic properties of materials. There are several reportswhich suggest that the band structure of phosphorene can be modified by applying strain . In the present case, we study the evolution ofelectronic properties of the puckered arsenene when it is subjected to me-chanical strain, both tensile and compressive, along the two separate lat-tice vectors a and b . The application of mechanical strain is simulated byfreezing one of the lattice constants, which is different from the optimizedvalue and then vary the other lattice constant as well as internal degrees offreedom of each atom during the geometric optimization. Thus, the effectof strain is translated into the difference ( ∆ a or ∆ b) between the frozenand globally optimized lattice constant. For this purpose, we choose therange of ∆ a and ∆ b from − to of the optimized lattice constantswith the spacing of . We assign the positive and negative values forcompressive and tensile strains, respectively. First we evaluate the totalenergy of the puckered structure when strain is applied and the results areshown in Figure 2(a). Puckered and buckled arsenene are energeticallystable under very strong compressive and tensile strains. The total energywith strain along the b -axis is lower than that with strain along the a -axis.It is natural that we can easily compress or expand the puckered structurealong the b -axis by way of changing the puckered angle θ . On the otherhand, the structure is planar along the a -axis, which makes it difficult tochange the structure along the a -axis. In Figure 2(b), we present the opti-mized lattice constants a and b during the compressive and tensile strains.For strain along the a -axis, we first fix the lattice constant a and then op-timize the lattice constant b . Similarly, we perform the optimization of thelattice constant a with fixed value of the lattice constant b for the strainalong the b -axis.We also carry out detailed analysis of geometric structure of all thestrained puckered arsenene. The results of this analysis are plotted in Fig-ure 2(c) and (d) for strains along the a and b axes, respectively. In the caseof the puckered structure, there are two types of bond lengths ( d and d )and bond angles ( θ and θ ). Around the optimized structures, both thebond lengths and the bond angles vary linearly with the amount of strains.The increase in one of the bond lengths (or angles) results in decrease inthe other bond lengths (or angles). This is due to the fact that the compres-sion in one of the lattice directions leads to relaxation of atoms in the otherdirection.Now, we discuss the modulations in the band structures of the puck-ered arsenene by applying strain along lattice vectors a (in Figure 3(a))and b (in Figure 3(b)). We first investigate the band structures with strainalong the a -axis. We find from Figure 3(a) that there is an indirect-to-direct gap transition due to both compressive and tensile strain along the a -axis. However, the locations of the direct band gap in k -vector for thesetwo strains are different. In the case of compressive strain, the location ofthe direct band gap occurs at the Γ point whereas for tensile strain, the di-rect band gap lies along the Γ -Y direction. It is remarkable that the systemremains as a direct-gap semiconductor for a wide values of strains rangingfrom − to except for the vicinity of no strain. This is a signifi-cantly important result from application point of view since it can accom-modate possible structural deformations, which may arise during growthor device manufacturing, while retaining its direct gap semiconducting be-havior.Other important observations from Figure 3(a) are the gap closing and2he emergence of a linear dispersion around the Fermi energy along the Γ -Y direction for the tensile strain of . In this situation, the system pos-sesses a strong anisotropy in the electronic band structure; the Dirac-likedispersion along the Γ -Y directions and the Schrödinger-like dispersion inother direction. In Figure 2(e) and (f), we plot the variation of the bandgap as a function of strain. We observe that the band gap of the puckeredarsenene becomes smaller when we apply tensile strain along the a -axis.The gap nearly closes at strain and then the band gap increases. On theother hand, for the compressive strain along the a -axis, the band gap ini-tially decreases and becomes metallic around − due to the significantoverlap between the conduction and the valence bands.Next we investigate the band structures with strain along the b -axis.We find from Figure 3(b) that the application of strain along the b -axisproduces nearly similar effects as in the case of strain along the a -axis, butin the opposite direction. It is natural because if we apply tensile strainalong the b -axis, the system is elongated along the b -axis and shortenedalong the a -axis. This kind of deformation also occurs when we applycompressive strain along the a -axis. Here also we observe an indirect-to-direct band gap transition due to strain. Furthermore, the band gap ofthe puckered arsenene becomes smaller and then the gap nearly closesat − due to compressive strain. We note that the band structure ofthe puckered arsenene with − compressive strain along the b -axis isalmost similar to that with tensile strain along the a -axis.We find a strong correlation between the emergence of a linear dis-persion in the band structure and the geometric structure of the puckeredarsenene. A closer look at Figure 2(c) and (d) reveals that when the bondangles between the nearest neighbour become nearly equal ( θ ≈ θ ), thesystem possesses a nearly linear dispersion in the electronic band struc-ture. This can be understood as follows. When the two angles becomeequal, each arsenic atom is surrounded by three nearest neighbours withsame angle. It makes the local environment more symmetric in spite ofhaving non-hexagonal or non-trigonal crystal symmetries, which results inthe gap closing with a nearly linear dispersion.Our DFT based calculations predict that it is possible to produce thefollowing modifications in the puckered arsenene by applying mechanicalstrains: (i) indirect-to-direct band gap transition, (ii) semiconductor-semimetal transition and (iii) semiconducting-metallic transition.Furthermore, the band gap of the puckered arsenene can also be tunedover wide range. These results suggest that the puckered arsenene canbe choosen as one of promising nanomaterials for several applications,including optoelectronic devices. Buckled Arsenene
Similar to the puckered arsenene, we have also performed the stud-ies on the effect of strain on the properties of the buckled arsenene. Inthis case, we apply compressive and tensile strains symmetrically along itsprimitive lattice vectors. Then, the amount of strain is directly quantifiedin terms of change in the lattice constant ( ∆ a ). Around the equilibriumgeometric structure, the total energy of the system shows a parabolic be-haviour, while the bond length and angle show nearly linear variations.The band structure by varying strain is shown in Figure 4. The buckledarsenene mostly remains as an indirect-gap semiconductor for both com-pressive and tensile strains. The variation in indirect band gap with strainis plotted in Figure 2(f). The band gap slowly decreases with increase ineither compressive or tensile strains. Then, the system goes from semicon-ductor to metallic for the values of strains beyond − and . Electric field induced band gap change.
Applying perpendicular electric field to the buckled honeycomb struc-ture such as silicene is shown to be an effective way to directly control theband gap . In the buckled honeycomb structure, there exists a separationbetween the A and B sublattices. Then the perpendicular electric field actsas the staggered potential for the honeycomb system. It is an interesting problem to investigate how the band structure of the buckled arsenene ismodified under electric field. We have performed calculations with thestrength of perpendicular electric field ranging from 0.0 to 6.0 V/nm. It isfound that there is no change in the band gap of the buckled arsenene foran electric field strength up to of 4.2 V/nm. The resultant band structuresfor some of the field strengths from 4.2 V/nm to 5.8 V/nm are shown inFigure 5. As discussed earlier, without electric field, the buckled arseneneis an indirect semiconductor. There is an indirect-to-direct gap transitionat 4.2 V/nm. We show the band gap as a function of electric field in Figure5(b). For . V/nm < E < . V/nm, the band gap decreases linearlywith the strength of electric field. Based on the linear fit, we find that theband gap closes at the critical electric field E = 5 . V/nm. Above thecritical field, the conduction band starts to overlap with the valence bandand makes the system metallic. We note that the electric field requiredfor the indirect-to-direct transition is quite high, which makes experimentsdifficult.
DISCUSSIONS
We find that the bond lengths of these two-dimensional structures areless than that in bulk arsenic. In order to compare the stability of arsenene,we have also carried out the calculation of the stability on bulk grey ar-senic. The buckling height is 1.291 Å and angle is 96.72 ◦ for bulk greyarsenic. These values are very close to those of buckled arsenene. It isvery important to note that the cohesive energy of the puckered and buck-led structures are quite close to that of bulk arsenic (-2.986 eV/atom). SeeTable 1. Hence, the growth of these two stable structures of arsenene areenergetically favourable.Graphene is manufactured by exfoliating graphite. Recently phospho-rene has also been manufactured by exfoliating black phosphorus. Thereare a few reports on the existence of layered buckled arsenene in nature,which is called grey arsenic . Thus, it is possible to obtain the buckledarsenene by exfoliating grey arsenic as in the case of graphene and phos-phorene. Since the cohesive energy of the puckered arsenene is very closeto both buckled arsenene and bulk grey arsenic, there is also a possibilityof manufacturing the puckered arsenene experimentally. Our results willmotivate experimentalists to grow arsenene.We predict that the puckered and buckled structures of arsenene arestable from both the energetics and structural rigidity point of view basedon the DFT calculations. These two structures are semiconductors withindirect band gaps. Interestingly, the puckered arsenene goes from anindirect-gap to direct-gap semiconductor due to structural deformationalong any of its lattice vectors. Furthermore, the onset of this transitionoccurs at very small amount of lattice deformation of . It is also pos-sible to tune the band gaps of this system over wide range while keepingits direct-gap semiconducting behavior by applying compressive and ten-sile strain. Another important observation is the presence of the Dirac-likedispersion along the Γ -Y direction when the system is subjected to eithercompressive or tensile strain along its lattice vectors. For larger compres-sive strain, the system is transformed from a semiconductor to a metal dueto a strong overlap of orbitals corresponding to the valence and conductionbands. Experimentally, it is possible to induce a strain by the beam bend-ing apparatus , STM tips for tensile strain and substrates, and hencethe results predicted can be verified once arsenene is grown on substrateor exfoliated from its bulk counterpart. The indirect-to-direct band gaptransition found in puckered arsenene may open up a possibility of usingthis two-dimensional system in several optoelectronic devices such as alight-emitting diode and solar cell. METHODS
Computational Details
We use Quantum ESPRESSO package for performing a fullyself-consistent density functional theory (DFT) calculations by solv-ing the standard Kohn-Sham (KS) equations. For exchange-correlation3XC) potential, the generalized gradient approximation given by Perdew-Burke-Ernzerhof has been utilized. We use Vanderbilt ultrasoftpseudopotential for As atom that includes the scalar-relativistic effect .Kinetic energy cutoffs of 30 Ry and 120 Ry have been used for electronicwave functions and charge densities, respectively. We adopt Monkhorst-Pack scheme for k -point sampling of Brillouin zone integrations with 31 × × × × − Ry. The geometric structures are optimized by minimizingthe forces on individual atoms with the criterion that the total force oneach atom is below 10 − Ry/Bohr. In order to mimic the two-dimensionalsystem, we employ a super cell geometry with a vacuum of about 18 Åin the z-direction (direction perpendicular to the plane of arsenene) so thatthe interaction between two adjacent unit cells in the periodic arrange-ment is negligible. The geometric structures are drawn using XCrySDensoftware References
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Contributions
C.K performed the electronic structure calculations.Both authors co-analysed the numerical results and co-wrote themanuscript.
Competing Interests
The authors declare that they have no com-peting financial interests.
Correspondence
Correspondence and requests for materials shouldbe addressed to C. Kamal ([email protected]) or Motohiko Ezawa([email protected]). 5 igure 1 | Optimized geometric structures, Phonon dispersion curves, Electronic band structure of puckered, planar and buckled arsenene.(a),(b),(c) : Fully optimized structure of (a) puckered, (b) planar and (c) buckled arsenene. The length of arrow in red color indicates the lattice constant. (d) , (e) , (f) : Brillouin zone of (g) puckered, (h) planar, and (i) buckled arsenene. The Brillouin zone of puckered arsenene is rectangular, while those of planerand buckled arsenene are hexagonal. We mark the high symmetric points. (g) , (h) , (i) : Phonon dispersion curves for (g) puckered, (h) planar, and (i) buckledarsenene. The puckered arsenene is globally stable since the global minimum exists at the Γ point. The planar arsenene is unstable since it possesses a fewmodes with negative frequency. In the buckled arsenene, all the modes contain positive values of frequency except transverse acoustic mode near the Γ point. (j) , (k) , (l) : Electronic band structure of (j) puckered, (k) planar, and (l) buckled arsenene. Indirect band gap (direct band gap at Γ ) is indicated by green (blue)arrow. The puckered and buckled arsenene are indirect semiconductors, while the planar arsenene is a metal. igure 2 | Effect of strain on energy, geometric structure and band structure. (a) : Variation of the total energy with strain along lattice vectors a and b forpuckered arsenene. The total energy is parabolic, where the bottom is at strain. The total energy with strain along lattice vectors a is higher than that alonglattice vectors b . (b) : Intersection of two curves represents the globally optimized lattice constants a and b . Black circles (red squares) show the optimizedlattice constant b ( a ) by fixing the lattice constant a ( b ). (c),(d) : Variation of bond lengths and bond angles with strain along lattice vectors a and b . Around theequilibrium structure, the bond length and angle vary linearly with strain. The angles θ and θ become the same at ( − ) strain along lattice vector a ( b ), where the band gap nearly closes. See Figure 3. (e) : The band gap for puckered arsenene. The band gap reaches minimum at ( − ) strain alonglattice vector a ( b ), while it takes maximum at − ( ) strain along lattice vector a ( b ). The band gap is zero beyond − strain along lattice vector a ,where the system becomes metallic. (f) : The band gap for buckled arsenene. The band gap attains the maximum value at strain. The system becomesmetallic beyond and − strain due to the overlap between the valence and conduction bands. igure 3 | Variation of electronic band structures with strain along lattice vectors a and b. (a) : The band gap nearly closes at strain. The system ismetallic beyond − strain. Indirect to direct gap transition occurs at and − strain. (b) : The band gap nearly closes at − strain. Indirect to directgap transition occurs at and − strain. igure 4 | Variation of electronic band structures as function of strain for buckled arsenene.