First-principles prediction of two atomic-thin phosphorene allotropes with potentials for sun-light-driven water splitting

Based on first-principles, the structures, stabilities, electronic and optical properties of two new atomic-thin phosphorene allotropes, named as stair-P and zipper-P, are systematically investigated. Stair-P and zipper-P are constructed based on the previously proposed stair-graphane and zipper-graphane, respectively. They are confirmed to be dynamically stable phosphorene allotropes with energetic stabilities comparable to the experimentally synthesized black-P and blue-P. Stair-P and zipper-P are all semiconductors with indirect band gaps of 2.32 eV and 2.00 eV, respectively. These band gaps can be effectively modulated by in-layer compressive and stretching strains. The band edges of stair-P and zipper-P are proper for water splitting at both acidic (PH  =  0) and neutral (PH  =  7) environments and their sun-light adsorbing abilities are better than black-P and blue-P in the visible range.

(Some figures may appear in colour only in the online journal) Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. configuration [13,14]), ζ-P [19], ε-P [19] and green-P [20], the bi-layered θ-P [19], η-P [19], B1 [21], G1 [21] and some other interesting allotropes [22,23].
Experimentally, the black-P have been successfully fabricated through mechanically exfoliating [9,12] from its 3D counterpart black phosphorus or other chemical deposition method [24][25][26] and the blue-P can be fabricated on Au(1 1 1) by molecular beam epitaxial growth with black phosphorus as precursor [27]. The black-P and blue-P based heterostructures, such as MXene/blue phosphorene, BSe/blue phosphorene and black phosphorene, were confirmed as excellent photocatalysts [28][29][30][31] for sun-light-driven water splitting. Previous literature [23] has also shown that both the CBM and VBM positions of phosphorene allotropes match well with the chemical reaction potential of H 2 /H + and O 2 /H 2 O, showing potential ability in sun-light-driven water splitting as photocatalysts. These works show that phosphorus based nano-materials have desirable potentials in photocatalysts.
In this letter, we predict two new phosphorene allotropes, named as stair-P and zipper-P, with crystalline structures based on the previously proposed stair-graphane and zipper-graphane [32]. The structures, stabilities, electronic and optical properties, as well as their photocatalystic properties of stair-P and zipper-P were systematically investigated through the density functional theory (DFT) based first-principles calculations. They are confirmed to be dynamically viable phosphorene allotropes with energetic stabilities comparable to black-P and blue-P. The calculated results show that both stair-P and zipper-P are semiconductors with proper band gaps and band edges for photocatalystic applications.

Computational details
The DFT based first-principles calculations as implemented in Vienna ab initio simulation package (VASP) [33] is employed to investigate the structures, stabilities, electronic and optical properties, as well as the photocatalystic properties of stair-P and zipper-P. The projector augmented wave (PAW) potentials is adopted to describe the interactions between nucleus and the valence electrons. The exchange and correlation are approximated by the general gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functionals [34]. A plane-wave basis set with the kinetic energy cutoff of 400 eV is employed to expand the wave functions and the Brillouin zone (BZ) sample meshes is set to be denser enough. Both the lattices and atomic positions of all systems are fully optimized up to the residual force on every atom to be less than 0.01 eV Å −1 before property investigations. To evaluate the dynamic stabilities of these phosphorene allotropes, their vibrational spectrum were simulated though phonopy package [35] with the forces calculated from VASP. We have also considered using HSE06 functionals [36] to evaluate more accurate band gaps and band edges of the systems, for further evaluating if stair-P and zipper-P are proper materials as visible-light photocatalysts for water splitting.
To analyze the relative stability between different allotropes of these elementary 2D phosphous, their averaged energies (E aver meV per atom) relative to black-P are calculated. The results are summarized in table 1 and figure 2, in which the average energy of black-P is set to be zero as reference. Figure 2 contains the averaged energies and work functions of stair-P, zipper-P and some previously proposed singlelayered phosphorene allotropes. We can see that both stair-P and zipper-P possess stabilities better than most of the previously proposed allotropes. Their average energies are of about 0.62 meV/atom and 42.67 meV/atom higher that of black-P. Especially, stair-P possesses remarkable stability as the experimentally synthesized black-P and blue-P, which is expectable to be synthesized in future experiment. We then evaluate the dynamical stabilities of stair-P and zipper-P by calculating the phonon band structures, as shown in figures 3(a) and (b), respectively. We can see that there are no any imaginary frequencies appear in the phonon band structures. Such results confirmed that both stair-P and zipper-P are dynamically stable phases.
The calculated band structures of stair-P and zipper-P based on PBE and HSE06 functionals are shown in figures 4(a) and (b). Their band gaps are summarized in table 1 together with those of black-P, blue-P, red-P and green-P. The PBE-based/ HSE06-based band gaps of black-P, blue-P, red-P and green-P are 0.90/1.58 eV, 1.93/2.76 eV, 1.22/1.97 eV and 1.21/1.96 eV, respectively. This results are consistent well with those reported in previous works [9,[15][16][17]20]. Figure 4(a) shows that the PBE-based/HSE06-based indirect band gap of stair-P is 1.57/2.32 eV, which is slightly smaller than the corresponding direct band gap of 1.58/2.43 eV. That is to say, stair-P can be classified as a quasi-direct band gap semiconductor according to the criteria of E i g < E d g < 0.15 eV + E i g . For zipper-P as show in figure 4(b), it is an indirect band gap semiconductor with band gaps of 1.26 eV and 2.00 eV calculated from PBE and HSE06, respectively. These results indicate that the appearing colors of stair-P and zipper are suitable for harvesting visible sun-light.
Further investigations show that the band gaps of stair-P and zipper-P can be effectively modulated by in-layer strains from different directions. Based on PBE functionals, the modulating effects of uniaxial in-layer strains on the band gaps of stair-P and zipper-P are shown in figures 5(a) and (b), respectively. We can see that the compressive strains along the zigzag direction (σ y ) and the stretching strains along the armchair direction (σ x ) linearly decrease the band gap of stair-P, but not change its quasi-direct band gap feature. The compressive strains along the armchair direction (σ x ) and the stretching strains along the zigzag direction (σ y ) translate stair-P from quasi-direct to indirect band gap semiconductor, with the band gaps increased under small strains and then decreased at larger strains. For zipper-P, both the compressive and stretching strains along the zigzag direction (σ y ) cannot affect the types of band gap. However, they can decrease the band gap from 1.26 eV to 0.2 eV. The compressive strains along armchair direction (σ x ) change zipper-P to be quasidirect band gap semiconductor and correspondingly decrease its band gaps. Stretching strains along armchair direction (σ x ) The space group (SP), optimized layer thickness (LT), averaged energies (E aver ), energy band gaps ( E g PBE and E g HSE06 ) and surface work functions (WF PBE and WF HSE06 ) of black-P, blue-P, red-P, green-P, stair-P and zipper-P.

Systems
Black-P Blue-P Red-P Green-P Stair-P Zipper-P  just slightly affect the band gaps but do not change the types of band gap. We noticed that the band gaps of stair-P and zipper-P are suitable for harvesting visible light. A good material for photo-catalyzed application needs not only the suitable band gaps but also the appropriate band edges compared with the reduction and oxidation potentials. To investigate the potential applications of stair-P and zipper-P in photocatalysis, we need to align the material's band edges potentials with respect to the redox potentials. And, the work function of the photocatalyst material is important for confirming the band edges. Then, we firstly calculated the work function of stair-P, zipper-P, black-P and blue-P. The results of the work function (WF, the Fermi energy level is set as the reference) of these four allotropes are all calculated by DFT-PBE and HSE06 methods, as summarized in table 1. Furthermore, the HSE06-based work functions of stair-P (5.92 eV) and zipper-P (5.81 eV) are close to the standard reduction potential of H + /H 2 (−4.44 eV) and oxidation potential of O 2 /H 2 O (−5.67 eV). These electronic properties are benefit for photocatalytic water splitting. We then turn our attentions to evaluate if their band edges (VBM and CBM) are also proper for photo-catalyzed water splitting. The HSE06-based VBM and CBM for black-P, blue-P, red-P, green-P, stair-P and zipper-P are shown in figure 6(a). The results for black-P and blue-P are good consistent with those reported in the previous work [23,28,29]. For the situation of PH = 0/PH = 7, the CBM of stair-P is 0.5944/0.1814 eV higher than the reduction potential of H + /H 2 and the VBM of stair-P is 0.4917/0.9047 eV lower than the reduction potential of O 2 /H 2 O. These band edges in both acidic and neutral situations are appropriate for sun-light-driven water splitting. For zipper-P, its band edges show that it possesses potential for sun-light associated water splitting in acidic situation. Its   CBM is 0.3283 eV higher than the reduction potential of H + / H 2 and its VBM is 0.4458 eV lower than the reduction potential of O 2 /H 2 O at situation of PH = 0. However, the band edges of zipper-P are not suitable for water splitting at neutral situation of PH = 7. Our results also show that the previously proposed green-P and red-P have potentials for water splitting at neutral situation of PH = 7.
The investigations on optical absorptions of stair-P and zipper-P further confirm their potential applications in sunlight-driven water splitting. As shown in figure 6(b), the optical absorption spectrum of stair-P, zipper-P, black-P, blue-P, red-P and green-P are calculated based on HSE06 functional. We can see that stair-P and zipper-P show better absorbing abilities in the energy range of 2.0 eV to 4.0 eV than black-P and blue-P. These results suggest that stair-P and zipper-P are good visible sun-light absorbers. The results also show that the previously proposed green-P and red-P possess excellent absorbing abilities in the energy range of 2.0 eV to 4.0 eV, which is not reported in previous literatures.

Conclusions
Using first-principles calculations based on density-functional theory, we proposed two new stable phosphorene allotropes (stair-P and zipper-P) to extend phosphorene allotropes family. The structures, stabilities, electronic, optical properties and the potentials for photocatalysis of these two new phosphorene allotropes were systematically investigated. Our results show that both stair-P and zipper-P are dynamically stable phases with remarkable stabilities comparable to the experimentally synthesized black-P and blue-P. Stair-P and zipper-P are all indirect band gap semiconductors with HSE06-based band gaps of 2.32 eV and 2.0 eV, respectively. The proper energy band gaps and band edges, as well as the good sun-light absorbing abilities indicate that both stair-P and zipper-P possess potential for applications in sun-light-driven water splitting, which are also desirable to be synthesized in future experiment in views of their remarkable energetic stabilities and positive dynamical stabilites. Figure 6. The HSE06-based CBM and VBM positions (a) of stair-P, zipper-P, black-P and blue-P respect to the redox potentials for water splitting. The HSE06-based optical absorption spectrum (b) for stair-P, zipper-P, black-P, blue-P, red-P and green-P based.