Tunable Topological State, High Hole-Carrier Mobility, and Prominent

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Cite This: J. Phys. Chem. Lett. 2019, 10, 761−767

Tunable Topological State, High Hole-Carrier Mobility, and Prominent Sunlight Absorbance in Monolayered Calcium Triarsenide Feng Li,† Hong Wu,† Zhaoshun Meng,† Ruifeng Lu,*,‡ and Yong Pu*,† †

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New Energy Technology Engineering Laboratory of Jiangsu Provence & School of Science, Nanjing University of Posts and Telecommunications (NUPT), Nanjing 210046, China ‡ Department of Applied Physics, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, P.R. China S Supporting Information *

ABSTRACT: Designing novel two-dimensional (2D) materials is highly desirable for material innovation. Here, we propose monolayered calcium triarsenide (1L CaAs3) as a new 2D semiconductor with a series of encouraging functionalities. In contrast to the ∼33 meV small band gap in bulk CaAs3, 1L CaAs3 possesses a large direct band gap of 0.92 eV with a high hole mobility of ∼104 cm2 V−1 s−1. The electronic properties of 2D CaAs3 can be manipulated significantly by the layer thickness and external strains. Remarkably, 2D CaAs3 suggests a topologically nontrivial−trivial state transition under thickness reduction and strain engineering, which is attributed to the drastic surface relaxation and pinch effect under compression. A semiconductor−semimetal transition is also revealed when the layer thickness is greater than 3L. Furthermore, 1L CaAs3 exhibits prominent visible-light absorption compared with the crystalline silicon. All these desired properties render 2D CaAs3 a promising candidate for use in electronic and photovoltaic devices.

T

GeP3, InP3, and SnP3 are in the symmetry group of P-3M1, while 2D BP3 is in a symmetry group of PM; 2D CaP3 is P-1. These different structures resulted in diverse electronic properties in comparison with pristine phosphorene, e.g., direct/indirect band gap, n-/p- doping semiconductors. Here, we extend the phosphorene derivatives to the arsenene derivatives because As has the similar outermost electrons to P. Surprisingly, arsenene derivatives are different from those of phosphorene derivatives, for example calcium triarsenide (CaAs3) is predicted as a topological insulator in theory.24 As a representative arsenide, CaAs3 is a layered compound and was first prepared through reaction of gaseous arsenic with calcium metal at 800−900 °C in a sealed silica tube in 1976.25 Remarkably, bulk CaAs3 has two isomers with space groups of P1̅ and C1̅, respectively. Their symmetries are lowered by distortion compared with those of SrAs3, BaAs3, and EuAs3 (in space of C2/m), making it different from other XAs3 (X = Sr, Ba, Eu). The geometric structure of bulk CaAs3 (Figure 1) is quite similar to that of arsenene. By removing 1/4 of the As atoms from the puckered polyanionic As32− nets, arsenene is changed to CaAs3. To date, the monolayered (1L) CaAs3 crystal, expected from its bulk counterpart, is yet to be prepared, and a comprehensive understanding of its electronic and topological properties is still lacking.

he physics of two-dimensional (2D) materials are intriguing in their own right. Since the discovery of graphene,1,2 a zoo of 2D materials has been experimentally realized,3−5 such as silicene,6 borophene,7,8 phosphene,9,10 transition-metal chalcogenides,11,12 etc. These 2D materials, exhibiting novel physical properties not seen in their bulk counterparts,13 are widely applied in field-effect transistors, light-emitting devices, photovoltaic solar cells, photocatalysts, and many other areas. Recently, 2D topological insulators have been intensively investigated in electronics,14−17 where the electrons traveling on the surface are insensitive to impurity scattering. More recently, the notion has been developed for light and microwaves, which is expected to be useful for building optical and electromagnetic waveguides immune to backscattering.18 To control the behavior of the electronic transport, a flexible way to turn on/off the topological states is highly desired. However, despite various proposed strategies, a tunable topological state still remains a big challenge. In addition, direct band gap semiconductors in 2D materials with band gap comparable to that of silicon (∼1.16 eV) and sufficiently large (105 cm−1) visible-light absorption are still in high demand for nanodevices. Among 2D materials, phosphorene is attractive in particular because of its high conductivity, moderate band gap, and prominent light-harvesting properties. Recently, a series of phosphorene derivatives have been proposed in theory, including 2D GeP3,19 InP3,20 SnP3,21 BP3,22 and CaP3.23 Despite the apparent similarity in their chemical formulas, these 2D materials are very different in their geometrics: 2D © XXXX American Chemical Society

Received: January 7, 2019 Accepted: February 4, 2019 Published: February 4, 2019 761

DOI: 10.1021/acs.jpclett.9b00033 J. Phys. Chem. Lett. 2019, 10, 761−767

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The Journal of Physical Chemistry Letters

Figure 1. Crystal structures of bulk calcium triphosphide in space groups of P1̅ and C1̅. (a and d) Top view of 3 × 3 supercell along the c axis and (b and e) side view of 3 × 3 supercell from the b axis. Big green and small purple balls represent Ca and As atoms, respectively. (c and f) Calculated electronic band structures of bulk P1̅- and C1̅-CaAs3 at the HSE06 level. The Fermi level is set at 0 eV.

(AIMD) was performed at 298, 500, and 1000 K within 20 ps by the Nosé−Hoover method.34 Geometric Structures. Bulk calcium triarsenide (CaAs3), first discovered in 1981,35 is a natural pseudo-two-dimensional crystal with a metallic luster. It has two experimental structures in space groups of P1̅ and C1̅. As shown in Figure 1, both bulk CaAs3 possess similar 2D networks of puckered configurations in plane and different van der Waals layers stacking out of plane. The puckered polyanionic As32− nets are derivatives of the arsenene structure by removing 1/4 of the As atoms. The D3-Grimme optimized lattice parameters of bulk P1̅- and C1̅CaAs3 are a = 5.92 Å, b = 5.90 Å, c = 5.84 Å and a = 9.24 Å, b = 7.49 Å, c = 5.79 Å, respectively, which match well with the experimental data of a = 5.92 Å, b = 5.86 Å, c = 5.83 Å and a = 9.02 Å, b = 7.59 Å, c = 5.83 Å, respectively.35 The structural details are summarized in Table S1, certifying the accuracy and reliability of our prediction. When exfoliating from bulk phases to monolayer, 1L CaAs3 has the same geometric structures with high stability in theory. The lattice constants are optimized to be a = b = 5.98 Å, θ = 100.1°, with the internal atomic positions seen in Table S2. Compared with the bulk phases, we found a significant distortion for the As−As bond lengths and angles in the 1L form. Without the strong vdw interactions, the positions of the Ca atoms are getting much closer to the plane of the CaAs3 sheet, resulting in the shortest nonbonding Ca−Ca interlayer distance of 3.26 Å (shortest, 3.99 Å reported to date35). This remarkable geometric distortion, induced by the surface relaxation, finally leads to large enchantment of band gap and topologically nontrivial− trivial state transition on 1L CaAs3 compared to its bulk form. According to the experiments, bulk CaAs3 is a semiconductor with a very small energy gap,35 as Ca element does not have four valence electrons to retain an electron octet on arsenide. As shown in Figure 1c,f, bulk P1̅- and C1̅-CaAs3 are both direct band gap semiconductors (including spin−orbit coupling effect), with small HSE06 gaps of 33 and 20 meV, respectively, in which the valence and conduction bands are meeting at one point along the Y−Γ directions. For the 1L CaAs3, the band gap is obviously opened and enlarged ∼28 times bigger to 0.92 eV (as shown in Figure 2b). Such huge

In this work, we theoretically demonstrated the 1L CaAs3 as a new 2D semiconductor with a HSE06 band gap of 0.92 eV, in which hole conduction is predominant. We systematically investigated the electronic properties of the bulk and freestanding 1L CaAs3. Remarkably, we showed that the topological state of the bulk CaAs3 can be tuned from nontrivial to trivial by exfoliating the layered bulk counterpart to a few layers, including 2L and 3L CaAs3. Besides, the topologically nontrivial state can be recovered in 1L CaAs3 by strain engineering. We then presented a remarkable optical absorption coefficient of 1L CaAs3 that is comparable to intrinsic silicon and proposed its potential applications in photovoltaics. Furthermore, the high kinetic and thermodynamic stabilities of 1L CaAs3 were confirmed according to no imaginary phonon modes in the phonon dispersion and stable configurations at room temperature. Finally, we explored the feasibility of preparing 2D CaAs3 from its bulk form that is practical in experiment. All the calculations of bulk and 2D CaAs3 are obtained from the first-principles calculations on the basis of density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP).26 The electron configurations of Ca and As are 3p64s2 and 4s24p3, respectively. The projector-augmented wave (PAW)27,28 potentials were used along with the generalized gradient approximation (GGA29). An accurate Heyd−Scuseria−Ernzerhof (HSE06)30 screened hybrid functional including van der Waals corrections is adopted with the density functional dispersion correction (D3Grimme31). The spin−orbit coupling (SOC) is included to consider the topological properties. A cutoff energy of 650 eV is chosen for plane wave basis, and the vacuum layer of 20 Å is used to avoid the interlayer interactions under the periodic boundary condition. The convergence criteria in electronic self-consistence and the ionic residual forces are 10−6 eV and 10−3 eV/Å, respectively. K-meshes of 6 × 6 × 6 and 6 × 6 × 1 were used for bulk and few-layer CaAs3, respectively. The phonon calculations were performed using a 2 × 2 × 1 supercell with the density functional perturbation theory (DFPT)32 as implemented in phonopy codes.33 To assess the thermal stability of 1L CaAs3, ab initio molecular dynamics 762


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Figure 2. 1L CaAs3. (a) Optimized geometric structure, (b) electronic band structure and projected density of states, (c) electron localization functions (ELF) of top and middle layers, and (d) charge densities of the valence band maximum (VBM) and conduction band minimum (CBM). The iso-value is 0.005 e Å−3, and the Fermi energy (Ef) is set at 0 eV (dashed line).

Figure 3. Electronic band gap as a function of (a) the number of thickness and (b) strains using the HSE06 functional. Wannier charge centers (WCCs) as a function of k in (c) bulk, (d) 1L, (e) 2L, and (f) 4.5% compressed 1L CaAs3, respectively.

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therefore, 2D CaAs3 could be a potential building block in constructing nanoelectronics of vdw heterostructures.40 Strain engineering has been proven as one of the most effective strategies to tune the electronic structure in semiconductors. The calculated electronic band gaps under various strains are shown in Figure 3b. A monotonic response of band gap to the strains is found for the 1L CaAs3, in which the band gaps can be tuned in a wide range, from 1.42 eV to zero, which is highly desired in electronic and optoelectronic devices. Remarkably, a topologically trivial−nontrivial transition is observed under a biaxial compression of 4.5% (Figure 3f), with a transition of Z2 from 0 to 1 compared with the intrinsic 1L form. This topological state transition is attributed to the new forming of the covalent bonds of Ca−As compared in the insets in Figure 3a,b. The band gap of −4.5% 1L CaAs3 is identified as 49 meV, between those of 5 QL (41 meV) and 4 QL (70 meV) Bi2Se3.41 The geometric and band structures of 4.5% compressed 1L CaAs3 are shown in the inset of Figure 3b. Unlike the topological state found in strained graphene,42 the transition of the topologically trivial−nontrivial states are attributed to the pinch effect that the Ca atoms are forced 0.13 Å away from the plane of the CaAs3 sheet under compression, making the 1L configuration closer to that of the bulk phase. Therefore, the electronic properties and topology of CaAs3 nanosheets are quite sensitive to the thickness and external strains. By carefully selecting the thickness and strains, it is promising to turn on/off the topological states for new architecture and functionality in future electronic and spintronic devices. Carrier Mobility. From the electronic band structure of 1L CaAs3 (Figure 2b), it can be clearly seen that the top of the valence band is more dispersive than the flat conduction band, which indicates a higher carrier mobility for the holes. For simplicity, our analysis is focused on the intrinsic scattering with longitudinal acoustic phonons. As other scattering mechanisms may also affect the transport, e.g., optical phonon scattering, the computed carrier mobility here should be considered as upper limits to the actual mobility. Because the accurate electron−phonon scattering terms can be computed from first-principles,43 the carrier mobility and relaxation time of 1L CaAs3 can be estimated in the deformation-potential theory (DP).44 The effective carrier masses and in-plane stiffness are summarized in Table 1. All the computations were

band gap enhancement from bulk to monolayer form is rare in other reported 2D materials, for example, the band gaps of bulk and 1L MoS2 are 1.2 and 1.9 eV, respectively.36,37 Rather than the quantum confinement effect, the prominent enhancement of the band gap is mainly contributed to the surface relaxation for 1L CaAs3 (in Figure 2a), as there is an obvious difference in the bond lengths and angles between the bulk and 1L forms. Electronic Structure. The computed electronic properties of the 1L CaAs3 at the HSE06 level are shown in Figure 2. Clearly, the 1L CaAs3 is a direct band gap semiconductor, as the valence band maximum (VBM) and the conduction band minimum (CBM) are both shifted to the Γ point compared to the bulk phase. The band gap of 1L CaAs3 is 0.13 eV at the GGA-PBE level, which is 0.92 eV by using the more accurate HSE06 functional. This band gap is closer to that of bulk silicon (1.16 eV),38 which makes 1L CaAs3 highly desired for photovoltaic and infrared applications. The valence bands are dominated by Ca atoms and partly contributed by As atoms in As−Ca bonds, which are overlapping in the full energy range (Figure 2b). This result indicates the ionic and covalent characters for the Ca−As and As−As bonds, respectively, as further evidenced by the analysis of the electron localization function (ELF, Figure 2c). The nonbonding Ca−Ca character is evidenced by the zero ELF value in the middle of two neighboring Ca−Ca atoms. The investigation of the charge densities (Figure 2d) also predicts the same trend, in which no charge density is located between two nearby Ca atoms, and the VBM and CBM are mainly distributed at the Ca−As and As−As bonds. In addition, Bader charge analysis confirmed ∼1.38 |e| charge on average is transferred from Ca atoms to the neighboring As atoms (∼0.64 |e|), while the As atoms in the As−As bonds are almost neutral (∼0.08 |e|). The migration of charge density from Ca to As atoms indicates the ionic bonding character of Ca−As bonds. The chemical bonding patterns were analyzed by the SSAdNDP software and shown in Figure S2.39 In a primitive cell, there are 7 two-center-two-electron (2c−2e) As−As σbonds, which require 14 electrons, as well as 10 one-centertwo-electron (1c−2e) ones, which require 20 electrons. The sum of the electrons is equal to the outer 34 valence electrons in 1L CaAs3. As a whole, the hybrid of ionic and covalent bonds between Ca and As atoms are jointly responsible for the formation and stability of the 1L CaAs3. 2D Topology. The CaAs3 family of materials are strong topological insulators. The topological invariant Z2 (1; 010) of bulk P1̅- and C̅ 1̅-CaAs3 are further evidenced by the Wannier charge centers (WCC) as a function of k computed in this work, as shown in Figures 3c and S1. When exfoliating the bulk CaAs3 powders into single- or few-layer nanosheets (Figure 3a), 1L CaAs3 exhibits a semiconducting property with a HSE06 band gap of 0.92 eV, while that of 2L CaAs3 is 0.28 eV. For 3L and more layered CaAs3, the band gaps are close to zero, where the middle Ca atoms are pulled out because of the strong vdw interlayer interactions, resulting in a very short intralayer Ca−Ca nonbonding length of 4.04 Å. Remarkably, the topological states Z2 for 1L and 2L CaAs3 are 0, in contrast to that of Z2 = 1 in bulk CaAs3, as shown in Figure 3d,e. The topologically nontrivial−trivial transition is attributed to the drastic surface relaxation in 1L and 2L CaAs3. 1L CaAs3 could be well combined with pristine phosphorene or arsenene with a moderate lattice mismatchment of −4% and 1%, respectively;

Table 1. Carrier Effective Masses (m*), 2D In-Plane Stiffness (C), Deformation Potential Constant (El), Carrier Mobility (μ), and Relaxation Time (τ) of the Investigated 1L and 2L CaAs3 type

carrier

m*/ m0

C (J m−2)

El (eV)

1L

electron (a) hole (a) electron (a) hole (a)

2.04 0.31 0.89 0.34

60.0 60.0 109.7 109.7

6.63 0.86 7.40 0.23

2L

μ (cm2 V−1 s−1)

τ (fs)

× × × ×

5.4 2119 18.2 49949

0.01 1.21 0.04 2.61

103 104 103 105

computed using the HSE06 functional. The effective mass of a hole in 1L CaAs3 is only 0.31 m0, which is much smaller than that of an electron (2.04 m0). As a result, the hole mobility in 1L CaAs3 is computed to be 1.21 × 104 cm2 V−1 s−1 at room temperature, 4 orders of magnitude larger than that of the electrons. This value is also larger than that of phosphorene 764


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The Journal of Physical Chemistry Letters (80−1140 cm2 V−1 s−1),45 which indicates 1L CaAs3 has potential as a hole-transporting layer (HTL) in solar cells. Because the shielding of the electron clouds of the As atoms allows the As layers to come closer together, the vdw interaction between intralayers becomes the most important factor for the transport properties. Interestingly, our computations confirmed that the hole-carrier mobility in 2L CaAs3 has been significantly enhanced to 2.61 × 105 cm2 V−1 s−1, which is 1 order of magnitude higher than that of 1L CaAs3. While for phosphorene, the carrier mobility decreases rapidly from its monolayer to bilayer. This result revealed another advantage of CaAs3 nanosheets: that the characters of carriers can be well tuned by the thickness selection. Meanwhile, the hole-carrier lifetime is also increased from ∼2 ps in 1L to ∼50 ps in 2L CaAs3. In conclusion, nconduction is dominant in 2D CaAs3, and the high hole-carrier mobilities suggest the great potential for nanoelectronics. The computations of the deformation potential constants of 1L and 2L CaAs3 are shown in Figure S3. Light Harvesting. Bulk CaAs3 is a graphite-like black mineral with a metallic luster. Because the predicted one-atom-thick CaAs3 has a direct band gap of 0.92 eV close to that of silicon (∼1.16 eV), 1L CaAs3 has potential application in photovoltaics. The light absorption coefficients of 1L CaAs3 is computed by the frequency-dependent microscopic polarizability matrix in the projector-augmented wave (PAW) methodology,46 and the absorbance of silicon is also given for comparison. As shown in Figure 4, the predicted in-plane

Exfoliation. To evaluate the feasibility of exfoliating the oneatom-thick CaAs3 sheet from its layered bulk crystal, we simulated the mechanical cleavage process for bulk CaAs3 P1̅ and C1̅. The energies as a function of the separation distance (d) are shown in Figure 5. The computed cleavage energies are

Figure 5. Computed cleavage energy as a funciton of the separation distance for calcium triphosphide in P1̅ and C1̅ space compared with black phosphorus and GeS, where zero distance refers to the balance distance between adjacent layers in bulk crystal.

1.36 and 1.41 J/m2, respectively, which are larger than the experimentally determined value of graphite (0.37 J/m2)48 but in the same range of Ga2N (1.09 J/m2).49 This result suggests that 1L CaAs3 crystal could be prepared experimentally from its bulk counterpart using mechanical cleavage or liquid phase exfoliation, making it practical for experimental study and industrial application. Stability. The stability of 2D crystals is crucial for experimental fabrication and practical applications. To check the structural stability of 1L CaAs3, the dynamical stability was assessed by calculating the phonon dispersions based on the density functional perturbation theory. As shown in Figure 6a, no imaginary phonon modes are identified, indicating that 1L CaAs3 is dynamically stable. The highest phonon mode of 1L CaAs3 is 243 cm−1; although this is much smaller than that of graphene (1600 cm−1), it is comparable to those of 1L GeSe (240 cm−1) and 1L GeS (350 cm−1),50 indicating a good kinetic stability. Furthermore, the thermodynamic stability of 1L CaAs3 was assessed by performing AIMD simulations (Figure S5). As pointed out by the structural snapshots in Figure 6b, the quasi-planar puckered networks of 1L CaAs3 are well maintained at 290 and 500 K within 20 ps, with all the atoms vibrating around their equilibrium positions. The analysis of the pair correlation functions at different temperatures confirmed that the 1L CaAs3 can keep its configuration up to 500 K. In addition, the water stability of 2D CaAs3 is also confirmed by performing AIMD simulations at room temperature, as shown in Figure S6. Thus, 1L CaAs3 has moderate cohesive energies, all positive phonon modes, and good thermal stability, which indicate great promise for experimental realization. In summary, we have theoretically predicted a new 2D semiconductor CaAs3 that shows various exceptional electronic properties. The monolayered CaAs3 has a direct HSE06 band gap of 0.92 eV and exhibits dominant n-conducting with a hole mobility of ∼104 cm2 V−1 s−1 at room temperature. A monotonic electronic response to the uniaxial and biaxial

Figure 4. Optical in-plane absorption coefficients of P1̅- and C1̅- 1L CaAs3 at the HSE06 method, compared with the experimental and theoretical spectrum of intrinsic silicon in the visible-light range (400−770 nm). The gray background indicates the reference solar spectral irradiance (Air Mass 1.5). The spectral power density P (right-hand y-axis) is depicted as gray bars.

absorption coefficients of 1L CaAs3 is observably larger than that of the intrinsic silicon.47 The light absorbance of silicon descends dramatically above the wavelength of ∼400 nm, while the in-plane light absorption coefficients of 1L CaAs3 drop gradually. Compared to the narrow window of light absorption of silicon, the 1L CaAs3 shows remarkably light-harvesting ability in the entire visible solar spectrum from 400 to 770 nm. This outstanding optical performance suggests the 1L CaAs3 is a very promising material for efficient photovoltaic solar cells. Details of dielectric constants of CaAs3 monolayers are provided in Figure S4. 765


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Figure 6. Stability of 1L CaAs3. (a) Phonon spectrum without any imaginary phonon modes. (b) Snapshots of the equilibrium structures after 20 ps in ab initio molecular dynamics (AIMD) simulation at 298 K. (c) Pair correlation function g(r) of final structures at 298, 500, and 1000 K.

ORCID

strains was found in the 2D CaAs3. Remarkably, the topologically trivial state for bulk CaAs3 disappears when the layer thickness is reduced to few- or monolayer, which is attributed to the drastic surface relaxation without the strong vdw interlayer interactions. Because of the pinch effect under compression, the topologically trivial state of 1L CaAs3 can be induced and tuned under strain engineering. Thus, the tunable ability of the topologically trivial state for 2D CaAs3 could be achieved readily from experiments by controlling the layer thickness and external strains. A semiconductor−semimetal transition is also revealed in the 1L CaAs3 when the layer thickness is more than 3L or a biaxial compression is larger than 4.5%. Furthmore, monolayered CaAs3 exhibits pronounced visible-light absorption comparable to that of silicon. Finally, the proposed CaAs3 monolayer has good kinetic and thermodynamic stabilities and is expected to be experimentally cleaved from its layered bulk crystal because of its moderate exfoliating energy. These favorable features are expected to promote the experimental realization of monolayered CaAs3 and potential applications in the fields of electronics and photovoltaics.

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Feng Li: 0000-0003-2638-2185 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China (Nos. 61704083, 61605087, and 61874060), Natural Science Foundation of Jiangsu Province (Nos. BK20160881 and BK20181388). The authors gratefully acknowledge the computing time granted by the VSR commission on the supercomputer JURECA at Forschungszentrum Jülich.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.9b00033.

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REFERENCES

Structural properties of bulk P1̅- and C1̅- CaAs3; geometric structures and atomic coordinates of 1L CaAs3; WCCs as a function of k for bulk C1̅-CaAs3; snapshots of the equilibrium structures of 1L CaAs3 monolayers at different temperatures after 20 ps in ab initio AIMD simulations; DP constant and dielectric constants of 1L CaAs3 (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: rfl[email protected]. *E-mail: [email protected]. 766


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Tunable Topological State, High Hole-Carrier Mobility, and Prominent

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