Original citation: Zhenqing, Li, He, Chaoyu, Ouyang, Tao, Zhang, Chunxiao, Tang, Chao, Roemer, Rudolf A. and Zhong, Jianxin (2018) New allotropes of phosphorene with remarkable stability and intrinsic piezoelectricity. Physical Review Applied, 9 . 044032. doi:10.1103/PhysRevApplied.9.044032 Permanent WRAP URL: http://wrap.warwick.ac.uk/101768 Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available. Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher statement: © 2018 American Physical Society Published version: https://doi.org/10.1103/PhysRevApplied.9.044032 A note on versions: The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher’s version. Please see the ‘permanent WRAP url’ above for details on accessing the published version and note that access may require a subscription. For more information, please contact the WRAP Team at: [email protected] warwick.ac.uk/lib-publications New allotropes of phosphorene with remarkable stability and intrinsic piezoelectricity Zhenqing Li,1, 2 Chaoyu He,1, 2, ∗ Tao Ouyang,1, 2 Chunxiao Zhang,1, 2 Chao Tang,1, 2, y Rudolf A. Roemer,¨ 3, 2, z and Jianxin Zhong1, 2, x 1Hunan Key Laboratory for Micro-Nano Energy Materials and Devices, Xiangtan University, Hunan 411105, P. R. China; 2School of Physics and Optoelectronics, Xiangtan University, Xiangtan 411105, China. 3Department of Physics, University of Warwick, Coventry, CV4 8UW, UK. (Dated: March 17, 2018) We construct a new class of two-dimensional (2D) phosphorus allotropes via assembling the previously pro- posed ultrathin metastable phosphorus nanotube into planar structures in different stacking orientations. Based on first-principle methods, the structures, stabilities and fundamental electronic properties of these new 2D phos- phorus allotropes are systematically investigated. Our results show that these 2D van der Waals phosphorene allotropes possess remarkable stabilities due to the strong inter-tube van der Waals interactions, which cause an energy release of about 30-70 meV/atom depending on their stacking details. Most of them are confirmed ener- getically more favorable than the experimentally viable α-P and β-P. Three of them, showing relatively higher probability to be synthesized in the future, are further confirmed to be dynamically stable semiconductors with strain-tunable band gaps and intrinsic piezoelectricity, which may have potential applications in nano-sized sensors, piezotronics, and energy harvesting in portable electronic nano-devices. PACS numbers: 73.20.At, 61.46.-w, 73.22.-f, 73.61.Cw INTRODUCTION The experimental discovery of piezoelectricity in two- dimensional (2D) materials, such as the hexagonal MoS2 [1– (a) 3] and carbon nitride (C3N4) [4], leads nano-scale piezo- 4 2.1 electricity becomes a very hot topic in recent years [5–8]. 3 1.8 Large numbers of 2D material have been reported as poten- 2 1.5 tial piezoelectric materials with remarkable piezoelectric co- 1 1.2 Eg-HSE=2.99 eV ffi (eV) Egap e cients comparable to traditional three-dimensional (3D) Eg-PBE=2.08 eV 0 Eneregy (eV) Eneregy piezoelectric materials. For example, the metal dichalco- 0.9 -1 0.6 genides (MX2,M=Cr, Mo, W, Nb, Ta; X=S, Se, Te) [3, 7, 9– -10 -8 -6 -4 -2 0 2 4 6 8 10 -2 (b) = = (c) 13], the hexagonal group III-V (MX, M B, Al, Ga, In, X N, Strain (%) P, As, Sb) [7, 12, 14, 15], the group II oxides [7, 16], and the group-IV monochalcogenides (GeS, GeSe, SnS and SnSe) FIG. 1. Schematic crystalline views of um-PNT from different direc- [5, 6, 17–20]. These new discoveries significantly expanded tions (a), where blue balls and purpule balls illustrate the pentagonal configurations of phosphorus atoms in two different arrangements, the application fields of these 2D materials to nano-sized sen- the calculated electron band structures of um-PNT (b), where the sors, piezotronics and energy harvesting in portable electronic black solid lines are calculated from normal density functional theory nano-devices[21, 22]. and the red dash lines are calculated from hybrid functional method Black phosphorene (α-P) [23, 24] is a new 2D materials ex- (HSE06), and the strain dependence of band gaps in um-PNT (c). perimentally synthesized in the same year of the experimen- tal discovery of 2D piezoelectricity [1]. It is considered as a formidable competitor to graphene and other two-dimensional B1, B2 and B3) with pentagons, the multi-atomically-thin lay- (2D) materials for applications in future nano-electronics due er of Hittorfene [37], as well as the porous phosphorene al- to its significant band gap [25, 26] and high carrier mobili- lotropes were previously proposed [38, 39] through the topo- ty [23, 25]. Blue phosphorene (β-P), another 2D phosphorus logical modeling method. However, none of these 2D phos- allotrope, was firstly proposed by Zhu et al. based on first- phorus allotropes were reported as piezoelectric materials due principles calculations [27] in 2014 and recently synthesized to their centrosymmetric crystalline structures. Recently, a by Zhang et al. through epitaxial growth method [28]. The non-centrosymmetric one-dimensional phosphorus nanotube progress in synthesis of 2D phosphorus materials [29–31] has was theoretically predicted [40], which is expected to be po- stimulated significant interests in exploring new 2D phospho- tential piezoelectric material. Very interesting, its correspond- rus materials [32–41] and related heterostructures [42–44]. ing allotropes (helical coil phosphorus) have been experimen- Many new 2D allotropes of phosphorus have been proposed. tally synthesized [41] in a carbon nanotube reactor. For example, the atomically-thin layers of γ-P [32], δ-P [32], Phosphorene allotropes with lone pairs on the surface sim- θ0-P [33] and red phosphorene [34], the diatomically-thin lay- ilar to SnS and SnSe [5, 6] are expected to be excellent 2D ers η-P [35], θ-P [35] and their transformations [36] (G1, G2, piezoelectric materials[1, 2, 7, 12, 45]. However, the exper- 2 Translation Rotation 180 0 0.25 0.5 150 -5.06 x 120 -5.07 black phosphorene 90 60 -5.08 30 0 0 -5.09 Energy(eV/atom) -5.10 y 0 30 60 90 120 150 180 0 0.25 0.5 Rotation angle (degrees) (a) Rotation (b) (c) PNT(0,0.5) PNT(30,0.5) PNT(180,0.25) FIG. 2. Sketch map of the translation and self-rotation for assembling 1D um-PNT (the atoms of the yellow one are free to adjust their positions and the atoms positions of the purple one are fixed in its initial operation, but all atoms are free to move in the process of optimization.) into 2D phosphorus allotropes PNT(θ; τ) (a). The calculated average energy for the 21 new 2D van der Waals phosphorene allotropes PNT(θ; τ) with different rotation angle θ and translation τ, where black circles, blue stars, and red triangles correspond to τ = 0; 0:25, and 0:5, respectively (b). The crystalline views of the most stable three ones, PNT(0,0.5), PNT(30,0.5) and PNT(180,0.25) (c). imentally viable α-P and β-P, as well as most of the previ- METHODS ously proposed 2D allotropes of phosphorus, are centrosym- metric and consequently non-polar, which indicates that they Our calculations were carried out by using the density func- are non-piezoelectric. Inspired by the discovery of the non- tional theory (DFT) within generalized gradient approxima- centrosymmetric phosphorus nanotube and its synthesizing, tions (GGA)[46] as implemented in the Vienna ab initio sim- we theoretically predicted a new class of 2D van der Waal- ulation package (VASP)[47, 48]. The interactions between s crystals of phosphorus via planer stacking of the previous- nucleus and the 3s23p3 valence electrons of phosphorus atom- ly proposed ultrathin metastable phosphorus nanotube (um- s were described by the projector augmented wave (PAW) PNT, P1[40]). Three of them are confirmed to be dynamical- method[49, 50]. A plane-wave basis with a cutoff energy of ly stable allotropes and energetically more favorable than the 500 eV was used to expand the wave functions. The Brillouin α β experimentally viable -P and -P. Especially, two of them zone integration was obtained by a 5 × 8 × 1 k-point grid. We with non-centrosymmetric stacking manners are confirmed to have used the Monkhorst-Pack k-mesh scheme with 7×11×1 be good piezoelectric materials, which have potential applica- to check the accuracy and found the same results. The struc- tions in nano-sized sensors, piezotronics, and energy harvest- tures of all phosphorene allotropes were fully optimized up to ing in portable electronic nano-devices. the residual force on every atom less than 0:001 eV/Å before investigating any material properties. The optimized exchange van der Waals functional (optB86b-vdW) [51, 52] was also applied to take into account van der Waals interactions in the systems. We know that there 3 15 have some debates about the vdW [53, 54].