Abstract
New crystal structures of fully hydrogenated borophene (borophane) have been predicted by first principles calculation. Comparing with the chairlike borophane (Cboropane) that has been reported in literature, we obtained four new borophane conformers with much lower totalenergy. The most stable one, washboardlike borophane (Wborophane), has energy about 113.41 meV/atom lower than Cborophane. In order to explain the relative stability of different borophane conformers, the atom configuration, density of states, charge transfer, charge density distribution and defect formation energy of BH dimer have been calculated. The results show that the charge transfer from B atoms to H atoms is crucial for the stability of borophane. In different borophane conformers, the bonding characteristics between B and H atoms are similar, but the BB bonds in Wborophane are much stronger than that in Cborophane or other structures. In addition, we examined the dynamical stability of borophane conformers by phonon dispersions and found that the four new conformers are all dynamically stable. Finally the mechanical properties of borophane conformers along an arbitrary direction have been discussed. Wborophane possesses unique electronic structure (Dirac cone), good stability and superior mechanical properties. Wborophane has broad perspective for nano electronic device.
Introduction
Twodimensional (2D) boron sheet (borophene) was synthesized on a silver substrate under ultrahighvacuum^{1} and has attracted much attention^{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19}. Difference from graphene which is an isotropic material, borophene shows high anisotropy due to the different arrangements of B atoms along the a and b direction. It has been shown that the mechanical properties of borophene are highly anisotropic^{8}. Furthermore, the electronic and transport properties are also strongly dependent on the direction^{20}. The superconducting transition temperature T _{c} of borophene is about 19 K, which can be increased to 27.4 K by applying a tensile strain, or 34.8 K by hole doping^{9}, similar with previous study on strained MgB_{2} ^{21}. The lattice thermal conductivity of borophene is unexpectedly low on account of the strong phononphonon scattering^{22}. In addition, borophene shows vast potentials as an anode material for Li, Na and Mg ion batteries due to high theoretical specific capacities and outstanding ion transport properties^{18, 23,24,25,26}.
Borophene is unstable against longwavelength transversal waves^{27} due to the small imaginary frequency along the ΓX direction in the phonon dispersion. It has been reported that full hydrogenation can stabilize borophene. After full hydrogenation, no imaginary frequencies were found along the highsymmetry directions of the Brillouin zone. The fully hydrogenated borophene has a directiondependent Dirac cone, and the Dirac fermions possess an ultrahigh Fermi velocity (3.0 × 10^{6} m/s)^{27}. This, combined with the excellent mechanical performance, makes fully hydrogenated borophene attractive for applications in nanoelectronics devices. Hydrogenation is an important approach to modify the physical and chemical properties of 2D materials. Different hydrogenation patterns and coverage on the same 2D material can lead to different physical and chemical properties^{28,29,30}, including the band structure^{31,32,33,34}, optical properties^{35}, magnetic properties^{36} and mechanical properties^{37}. Furthermore, under the same hydrogenation coverage, the mechanical properties are also strongly dependent on the atomic configuration^{38}. It is important to explore stable configurations of borophane. To date, conformers of borophane other than Cborophane have not been reported, and would be the focus of the present study.
In this work, the structural stability, band structures, charge density distribution and mechanical properties of borophanes with different configurations have been studied by first principles calculations. We obtained four new conformers with much lower totalenergy than that of Cborophane. Furthermore, we established the relative stability of different borophane conformers. By analyzing the atom configurations and the totalenergies of borophane conformers, we found the configuration in which B atoms are staggered by zigzag mode along the a direction, and staggered by up and down wrinkle mode along the b direction is the most stable one. Furthermore, we explain the stability of borophane conformers by analyzing density of states, charge transfer, charge density distribution and defect formation energy of BH dimer. The results show that the charge transfer from B atoms to H atoms is crucial for the stability of borophane. The charge density distribution and defect formation energy of BH dimer show that the BB bonds in Wborophane are stronger than that in Cborophane. Moreover, we examined the dynamical stability of borophane conformers by calculating the phonon dispersions. Finally the electronic structures and the mechanical properties of the Cborophane and the four new conformers have been discussed.
Computational details
All calculations are performed using the QuantumEspresso package^{39}. Ultrasoft pseudopotentials^{40} are used for all atoms and the exchangecorrelation approximation is evaluated through the PerdewBurkeErnzerh (PBE)^{41} functional. The kineticenergy cutoff of planewaves is set to be 50 Ry. The atomic positions and lattice constants are fully relaxed, until the forces on all atoms are less than 0.01 eV/Å. A large vacuum region (20 Å) is included along z direction to eliminate the interlayer interactions.
The four nonzero elastic constants of a 2D material are c _{11}, c _{22}, c _{12} and c _{66}. The Young’s modulus along the a and b directions can be written as^{42}
respectively, the Poisson’s ratio along the a and b directions can be given as
respectively, while the shear modulus can be expressed as
Results and Discussion
Crystal structures and stability
In order to study the influence of H adsorption on the atomic and electronic structure of borophene, we calculated the borophene with a single H atom adsorption in the 6 × 2 × 1 supercell. Four different adsorption sites have been taken into consideration. Our results show that the most stable adsorption site is the top site of B atom. Significant shifts of B atoms have been observed when the H atom is adsorbed on the top site. The local atomic structure schematic of borophene with one, two and three H atoms adsorption have been shown in Fig. 1. The shifts of B atoms and the average adsorption energy of H atoms are listed in Table 1. As shown in Fig. 1(a), in the single H atom adsorption, the shift of the B atom (B3) bonded with the H atom is about 0.32 Å along Z direction. For the two first neighbor B atoms (B2 and B4) of the B atom bonded with the H atom, the shifts along the negative Z direction are both about 0.3 Å. However, for the second and third neighbor B atoms of B3, the shifts along z direction are only 0.04 and 0.03 Å, indicating that H atom induced atomic distortion is mainly imposed to the first neighbor B atom of the B atom bonded with H atom. For two H atoms adsorbed borophene, two configurations have been shown. As shown in Fig. 1(b), two H atoms adsorbed on two neighbor B atoms. Adsorption of H atom on B2 atom will lead the shift of B3 atom along negative Z direction. However, adsorption of H atom on B3 atom will make B3 atom move along positive Z direction. For B3 atom, the atomic shifts induced by the two adsorbed H atoms are not along the same direction. However, in H2B (Fig. 1(c), for B3 atom, the atomic distortion induced by the two adsorbed H atoms are consistently, leading to that the average adsorption energy of H atom in H2B configuration is 0.38 eV/H higher than that in H2A. For three H atoms adsorption, in H3A, three H atoms are adsorbed on the three neighbor B atoms, while, in H3B, three H atoms are adsorbed on the three next neighbor B atoms. Similarly, the configuration H3B is much more stable than H3A. More specifically, the average adsorption energy of H atoms in H3B configuration is 0.65 eV/H higher than that in H3A. In addition, by analyzing the partial density of states of H and B atoms in H3A and H3B (as shown in Fig. 2), we found that the orbital hybridization between H (s) and B (p _{ z }) in H3B is much stronger than that in H3A.
Then we studied the atomic, electronic structures and stability of fully hydrogenated borophene. The crystal structures of seven borophane conformers are displayed in Fig. 3. For convenience of description, we named the seven conformers as PlaneSquaretype borophane (PSborophane), PlaneTriangletype borophane (PTborophane), Chairlike borophane, Boatlike borophane (Bborophane), TwistChairBoattype borophane (TCBborophane), Triangletype borophane (Tborophane) and Washboardlike borophane, respectively. The unit cells are marked by the black dashed rectangles. The optimized lattice constants, BH bond lengths, buckling heights and the totalenergy difference relative to Cborophane are listed in Table 2. In the seven borophane conformers, each B atom is hydrogenated with an H atom, namely, the ratio of B:H is 1:1. The Cborophane configuration has been reported, previously^{20, 27, 43}. As shown in Fig. 3(e) and (f), CBorophane has a buckled configuration and the buckling height is 0.80 Å, which is smaller than that of borophene (0.91 Å)^{8}. In Cborophane, Hydrogen atoms alternate on both sides of the borophene sheet. B atoms are aligned along the a direction and staggered by up and down wrinkle mode along the b direction. For comparison, two planner conformers (PS and PTborophane) that all hydrogen atoms bond with B atoms at the same side have been taken into consideration. In PSborophane, each B atom bonds with four neighboring B atoms. In other six conformers, each B atom bonds with six neighboring B atoms. In PSborophane, all B atoms are aligned along the a and b direction. In PTborophane, B atoms are aligned along the a direction, however, staggered by zigzag mode along the b direction. The totalenergy difference relative to that of Cborophane and the schematic drawings of different conformers are shown in Fig. 4. PS and PTborophane have totalenergy difference 685.93 and 425.67 meV/atom higher than Cborophane, respectively, indicating that the buckled configuration is more stable than the planner configurations.
C, B, TCB, T and Wborophane are all buckled configurations. In Bborophane, for convenience of description, we regard the four neighboring B atoms that constitute a parallelogram and the four H atoms that bond with the four B atoms at the same side as a small unit, as shown in Fig. 4(e). The small units are aligned along the a direction, however, staggered by up and down wrinkle mode along the b direction. Bborophane has energy 7.94 meV/atom lower than Cborophane. In TCBborophane, pairs of hydrogen atoms alternate on both sides along the a and b direction. Similarly, we regard the two neighboring B atoms that bond with two H atoms at the same side and the two H atoms as a small unit, as shown in Fig. 4(f). The small units are staggered by zigzag mode along the a direction, and staggered by up and down wrinkle mode along the b direction. TCBborophane has energy 73.85 meV/atom lower than Cborophane. In Tborophane, ternate hydrogen atoms alternate on both sides along the a and b direction. We regard the three neighboring B atoms that constitute a triangle and the three H atoms that bond with the three B atoms at the same side as a small unit, as shown in Fig. 4(g). The small units are staggered by up and down wrinkle mode along the a and b direction. Tborophane has energy 110.66 meV/atom lower than Cborophane. In Wborophane, B atoms are staggered by zigzag mode along the a direction, and staggered by up and down wrinkle mode along the b direction. Wborophane has energy difference about 113.41 meV/atom lower than Cborophane. Compared with Cborophane (wrinkle along b direction), Wborophane has buckled configuration along both a and b direction, leading to superior mechanical properties along a direction. Specifically, the ultimate tensile strain along a direction of Wborophane is 0.17, which is larger than that of Cborophane (0.12). In order to further affirm the relative stability of different borophane conformers, different exchangecorrelation functionals with local density approximation (LDA) and general gradient approximation (GGA, such as typical PBE, and PW91) have been used to check the trend of the totalenergy differences. PBE and PW91 are both belong to GGA exchangecorrelation functional, therefore, the energy difference (ΔE) obtained by PBE and PW91 are highly consistent. The overestimation of the cohesive energy at the LDA level has been reported^{44}, resulting in the distinct difference of ΔE at the LDA and GGA level. On the whole, the trends of energy differences obtained by the three exchangecorrelation functionals are consistent. This further indicates that the stability of the new borophene conformers is independent or less dependent on the form of exchangecorrelation functionals. It is interesting that the energy difference between T and Wborophane is only 2.75 meV/atom under the stressfree states. Under ≥0.05 biaxial tensile stains, the totalenergy of Tborophane change to be lower than that of Wborophane, indicating that there exists a structural phase transition between T and Wborophane under increasing biaxial tensile strains.
In order to examining the dynamical stability of borophane conformers, we calculated the phonon dispersions. Phonon dispersion is an important parameter to estimate the dynamical stability of crystal structure. Imaginary frequencies along any highsymmetry direction of the Brillouin zone are indications of dynamic instability of the crystal structure. The calculated phonon dispersions of B, TCB, T and Wborophane are shown in Fig. 5. For the four new borophane conformers, no imaginary frequencies were found along the highsymmetry directions of the Brillouin zone, indicating that the four new borophane conformers are all dynamically stable.
Electronic structures
In order to further explain the excellent stabilities of Wborophane, we analyzed the electronic structures of different borophane conformers to obtain a deep insight of the bonding characteristics and stabilization mechanism. A simple and clear picture of electronic bonding in boron sheet has been reported^{45}. A structure that optimally fills inplane bonding states (s, p _{ x } and p _{ y }) should be most preferable^{45}. In borophene, inplane sp ^{2} antibonding states are partly occupied. Hence, borophene is unstable and prone to donate electrons^{46}. In hydrogenated borophene, there exist a charge transfer from B atoms to H atoms, leading to that the inplane bonding states are completely filled and the antibonding states are empty; moreover, the outofplane bonding states are also fully filled. Finally, the Fermi level is exactly located at the valley bottom of the total density of states. Consequently, full hydrogenated borophene is stable. The band structures and density of states of B, TCB, T and Wborophane are displayed in Fig. 6. The four new borophane conformers all possess a Dirac cone. The band structure of Cborophane shows clearly a Dirac cone along the ΓX direction^{27, 43}. Similarly, the band structure of Bborophane shows a Dirac cone along the ΓX direction. However, for TCB, T and Wborophane, the Dirac cones are along the ΓY direction. Furthermore, in order to analyze the electronic bonding of Wborophane, we calculated the partial density of states (PDOS) of H and B atoms, as shown in Fig. 7. By analyzing the energy rang and peak position, we found that there exists a strong orbital hybridization between s orbit of H atoms and p _{ z } orbit of B atoms. Furthermore, from the partial density of states near the Fermi level, we can found that the Dirac electron is mainly contributed by the p _{ x } and p _{ y } electron of B atoms for Wborophane. A similar phenomenon has been observed in Cborophane^{27}.
In order to confirm the aforementioned charge transfer, we calculated the deformation charge density of C, B, TCB, T and Wborophane. The deformation charge density is defined as the difference between the total charge density (\(\rho (\mathop{r}\limits^{\longrightarrow})\)) in the solid and the superposition of independent atomic charge densities (\({\sum }_{i}{\rho }_{atom}(\mathop{r}\limits^{\longrightarrow}\mathop{{r}_{i}}\limits^{\longrightarrow})\) placed at the atomic sites of the same solid, the equation can be written as
The yellow areas represent electron accumulation (\({\rm{\Delta }}\rho (\mathop{r}\limits^{\longrightarrow}) > 0\)), and the blue areas represent electron depletion (\({\rm{\Delta }}\rho (\mathop{r}\limits^{\longrightarrow}) < 0\)). As shown in Fig. 8, a charge transfer from B atoms to H atoms is clearly shown. By comparing the electronegativity of boron and hydrogen, we can find that the electronegativity of hydrogen (2.2) is larger than that of boron (2.04). Therefore, the charge transfer from B atoms to H atoms is reasonable. Similarly, a charge transfer from silicon (1.9) to hydrogen (2.2) atom has been found in hydrogenated silicene^{47}. However, the electronegativity of carbon (2.55) is larger than that of hydrogen (2.2), on the contrary, a charge transfer from H atoms to C atoms has been observed in graphane^{32}.
Furthermore, we investigated the bonding characteristics in C and Wborophane by analyzing the charge density distributions and defect formation energy of a BH dimer. The inplane bonds (BB bonds) are stronger that outofplane πbonds (BH bonds). In PT, C, B, TCB, T and Wborophane, the BH bond lengths are almost the same, indicating that the bonding characteristics between B and H atoms are uniform. Similar phenomenon has been reported in different conformers of hydrogenated silicene^{47}. Hence, it is imperative to analyze the bonding characteristics between B and B atoms in borophane conformers. The 2D charge density contours of C and Wborophane are shown in Fig. 9. We have selected two typical planes in C and Wborophane. Plane1 is perpendicular to z coordinate axis and contains a BB bond. Three nearest neighboring B atoms that constitute a triangle determine plane2. Comparing the charge density distribution of C with Wborophane, we can find that more electrons gathered along the BB bond direction in Wborophane than that in Cborophane, indicating that the BB bonds in Wborophane are stronger than that in Cborophane. In order to quantitative describe the bonding strength of BB bonds, we calculated the defect formation energy of a BH dimer in C and Wborophane. The defect formation energy E _{ form } can be expressed as
where E _{ def }/E _{ per } is the total energy of the supercell with/without the BH dimer defect, and N _{ def }/N _{ per } denote the atom numbers of the supercell with/without the BH dimer defect. As shown in Fig. 10, when the defect concentration η = 1/24, the defect formation energy of a BH dimer is only 0.40 eV for Cborophane, however, that value change to 0.95 eV for Wborophane. The defect formation energy of BH dimer in Wborophane is much higher than that in Cborophane, indicating that the BB bonds in Wborophane are much stronger than that in Cborophane. It is agree well with the results of charge density distributions.
Mechanical properties
In addition, we calculated the elastic constants, Young’s modulus, shear modulus, and Poisson’s ratios of B, TCB, T and Wborophane. As listed in Table 3, the Young’s modulus of Cborophane along the a and b direction are 172.24 and 110.59 N/m^{43}. For C and Bborophane, the Young’s modulus along the a direction is much larger than that along the b direction. By analyzing the atomic structure of C and Bborophane, we found that B atoms are aligned along the a direction, however, staggered by up and down wrinkle mode along the b direction. Under uniaxial tensile stains along the a direction, the BB bonds along the a direction were elongated, significantly. However, the uniaxial tensile strains along the b direction can be released due to the buckled configuration. For C and Bborophane, the ratio (Y_{ a }/Y_{ b }) of Young’s modulus along the a and b direction are 1.56 and 2.37, respectively. However, the ratio is reduced to 1.13 for Wborophane. Similarly, we found that all B atoms in Wborophane are staggered along the a and b direction, therefore, the uniaxial strains along the a and b direction can be released. In addition, we also calculated the mechanical properties of B, TCB, T and Wborophane along an arbitrary direction. The results are shown in Fig. 11. For isotropic materials, the Young’s modulus and shear modulus are independent of the direction. The polar diagrams of Young’s modulus and shear modulus are perfect circles. The larger degree of deviation from a perfect circle, the stronger anisotropy the materials possess. The Young’s modulus and shear modulus of Cborophane are strongly dependent on the direction^{43}. However, for Wborophane, the Young’s modulus and shear modulus tend to more isotropic.
Conclusions
In summary, with first principles calculations we have studied the structure stability, electronic structures and mechanical properties of borophane with different configurations. Comparing with Cboropane, we obtained four new conformers with much lower totalenergy. By analyzing the atomic arrangements and the total energies in different conformers, we found that the configuration that B atoms are staggered by zigzag mode along the a direction and staggered by up and down wrinkle mode along the b direction is the most stale one. The most stable one, Wborophane, has energy difference about 113.41 meV/atom lower than Cborophane. The charge transfer from B atoms to H atoms is crucial for the stability of borophane. Furthermore, the results of charge density distribution show that more electrons gathered along the BB bond direction in Wborophane than that in Cborophane, moreover, the defect formation energy of BH dimer in Wborophane is much higher than that in Cborophane, both indicating that the BB bonds in Wborophane are stronger than that in Cborophane. By calculating the phonon dispersions of the four new borophane conformers, we found no imaginary frequencies along the highsymmetry directions of the Brillouin zone, indicating that the four new conformers are all dynamically stable. The band structures of the four new conformers all show a Dirac cone along ΓY or ΓX direction. Furthermore, from the partial density of states near the Fermi level, we can found that the Dirac electron is mainly contributed by the p _{ x } and p _{ y } electron of B atoms. The unique electronic structure results in high carrier mobility, making borophane a promising material for nano electronic device. Finally the mechanical properties of borophane conformers along an arbitrary direction have been discussed. The results show that the Young’s modulus and shear modulus of Cborophane are highly anisotropic. However, for Wborophane, the Young’s modulus and shear modulus tend to more isotropic.
References
 1.
Mannix, A. J. et al. Synthesis of borophenes: Anisotropic, twodimensional boron polymorphs. Science 350, 1513–1516 (2015).
 2.
Penev, E. S., Kutana, A. & Yakobson, B. I. Can TwoDimensional Boron Superconduct? Nano Lett. 16, 2522–2526 (2016).
 3.
Xu, S. G., Zhao, Y. J., Liao, J. H., Yang, X. B. & Xu, H. The nucleation and growth of borophene on the Ag (111) surface. Nano Res. 9, 2616–2622 (2016).
 4.
LopezBezanilla, A. & Littlewood, P. B. Electronic properties of 8−Pmmn borophene. Phys. Rev. B 93, 241405(R) (2016).
 5.
Peng, B. et al. Electronic, optical, and thermodynamic properties of borophene from firstprinciple calculations. J. Mater. Chem. C 4, 3592–3598 (2016).
 6.
Wang, V. & Geng, W.T. Lattice Defects and the Mechanical Anisotropy of Borophene. ArXiv eprints 1607, http://arxiv.org/abs/1607.00642 (2016).
 7.
Carrete, J. et al. Physically founded phonon dispersions of fewlayer materials and the case of borophene. Mater. Res. Lett. 4, 204–211 (2016).
 8.
Wang, H. F. et al. Strain effects on borophene: ideal strength, negative Possion’s ratio and phonon instability. New J. Phys. 18, 073016 (2016).
 9.
Xiao, R. C. et al. Enhanced superconductivity by strain and carrierdoping in borophene: A first principles prediction. Appl. Phys. Lett. 109, 122604 (2016).
 10.
Gao, M., Li, Q. Z., Yan, X. W. & Wang, J. Prediction of phononmediated superconductivity in borophene. Phys. Rev. B 95, 024505 (2017).
 11.
Liu, Y. X. et al. Stable and metallic borophene nanoribbons from firstprinciples calculations. J. Mater. Chem. C 4, 6380–6385 (2016).
 12.
Yang, X. B., Ding, Y. & Ni, J. Ab initio prediction of stable boron sheets and boron nanotubes: Structure, stability, and electronic properties. Phys. Rev. B 77, 041402(R) (2008).
 13.
Pang, Z. Q., Qian, X., Yang, R. G. & Wei, Y. J. Superstretchable borophene and its stability under straining. ArXiv eprints 1602, http://arxiv.org/abs/1602.05370 (2016).
 14.
Zabolotskiy, A. D. & Lozovik, Y. E. Straininduced pseudomagnetic field in Dirac semimetal borophene. Phys. Rev. B 94, 165403 (2016).
 15.
Yuan, J. H., Zhang, L. W. & Liew, K. M. Effect of grafted amine groups on inplane tensile properties and high temperature structural stability of borophene nanoribbons. RSC Adv. 5, 74399–74407 (2015).
 16.
Meng, F., Chen, X. & He, J. Electronic and Magnetic Properties of Borophene Nanoribbons. ArXiv eprints 1601, http://arxiv.org/abs/1601.05338 (2016).
 17.
Liu, H., Gao, J. & Zhao, J. From boron cluster to twodimensional boron sheet on Cu(111) surface: growth mechanism and hole formation. Sci. Rep. 3, 3238 (2013).
 18.
Zhang, X. M. et al. Borophene as an extremely high capacity electrode material for Liion and Naion batteries. Nanoscale 8, 15340–15347 (2016).
 19.
Shu, H., Li, F., Liang, P. & Chen, X. Unveiling the atomic structure and electronic properties of atomically thin boron sheets on an Ag(111) surface. Nanoscale 8, 16284–16291 (2016).
 20.
Padilha, J. E., Miwa, R. H. & Fazzio, A. Directional dependence of the electronic and transport properties of 2D borophene and borophane. Phys. Chem. Chem. Phys. 18, 25491–25496 (2016).
 21.
Zheng, J. C. & Zhu, Y. M. Searching for a higher superconducting transition temperature in strainedMgB2. Phys. Rev. B 73, 024509 (2006).
 22.
Sun, H., Li, Q. & Wan, X. G. Firstprinciples study of thermal properties of borophene. Phys. Chem. Chem. Phys. 18, 14927–32 (2016).
 23.
Jiang, H. R., Lu, Z. H., Wu, M. C., Ciucci, F. & Zhao, T. S. Borophene: A promising anode material offering high specific capacity and high rate capability for lithiumion batteries. Nano Energy 23, 97–104 (2016).
 24.
Shi, L., Zhao, T. S., Xu, A. & Xu, J. B. Ab initio prediction of borophene as an extraordinary anode material exhibiting ultrafast directional sodium diffusion for sodiumbased batteries. Sci. Bull. 61, 1138–1144 (2016).
 25.
Zhang, Y., Wu, Z. F., Gao, P. F., Zhang, S. L. & Wen, Y. H. Could Borophene Be Used as a Promising Anode Material for HighPerformance Lithium Ion Battery? ACS Appl. Mater. Inter. 8, 22175–81 (2016).
 26.
Mortazavi, B., Dianat, A., Rahaman, O., Cuniberti, G. & Rabczuk, T. Borophene as an anode material for Ca, Mg, Na or Li ion storage: A firstprinciple study. J. Power Sources 329, 456–461 (2016).
 27.
Xu, L. C., Du, A. J. & Kou, L. Z. Borophane: Stable Twodimensional Anisotropic Dirac Material with Ultrahigh Fermi Velocity. Phys. Chem. Chem. Phys. 18, 27284–27289 (2016).
 28.
He, H. Y. & Pan, B. C. The hydrogenationdependent thermal expansion properties of hydrogenated graphene. Eur. Phys. J. B 87, 1–6 (2014).
 29.
Liu, G. et al. The stability of freestanding germanane in oxygen: Firstprinciples investigation. Europhys. Lett. 110, 17007 (2015).
 30.
Liu, G. et al. Multiple Dirac Points and HydrogenationInduced Magnetism of Germanene Layer on Al (111) Surface. J. Phys. Chem. Lett. 6, 4936–42 (2015).
 31.
Pujari, B. S., Gusarov, S., Brett, M. & Kovalenko, A. Singlesidehydrogenated graphene: Density functional theory predictions. Phys. Rev. B 84, 041402(R) (2011).
 32.
Sofo, J. O., Chaudhari, A. S. & Barber, G. D. Graphane: A twodimensional hydrocarbon. Phys. Rev. B 75, 153401 (2007).
 33.
Zhou, J., Wang, Q., Sun, Q. & Jena, P. Electronic and magnetic properties of a BN sheet decorated with hydrogen and fluorine. Phys. Rev. B 81, 085442 (2010).
 34.
Lü, T. Y., Liao, X. X., Wang, H. Q. & Zheng, J. C. Tuning the indirect–direct band gap transition of SiC, GeC and SnC monolayer in a graphenelike honeycomb structure by strain engineering: a quasiparticle GW study. J. Mater. Chem. 22, 10062–10068 (2012).
 35.
Putz, S., Gmitra, M. & Fabian, J. Optical conductivity of hydrogenated graphene from first principles. Phys. Rev. B 89, 035437 (2014).
 36.
Boukhvalov, D. W., Katsnelson, M. I. & Lichtenstein, A. I. Hydrogen on graphene: Electronic structure, total energy, structural distortions and magnetism from firstprinciples calculations. Phys. Rev. B 77, 035427 (2008).
 37.
Bhattacharya, A., Bhattacharya, S. & Das, G. P. Straininduced bandgap deformation of H/F passivated graphene andhBN sheet. Phys. Rev. B 84, 075454 (2011).
 38.
Cadelano, E., Palla, P. L., Giordano, S. & Colombo, L. Elastic properties of hydrogenated graphene. Phys. Rev. B 82, 235414 (2010).
 39.
Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and opensource software project for quantum simulations of materials. J. Phys. Condens. Matter. 21, 395502 (2009).
 40.
Vanderbilt, D. Soft selfconsistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892 (1990).
 41.
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
 42.
Andrew, R. C., Mapasha, R. E., Ukpong, A. M. & Chetty, N. Mechanical properties of graphene and boronitrene. Phys. Rev. B 85, 125428 (2012).
 43.
Wang, Z. Q., Lü, T. Y., Wang, H. Q., Feng, Y. P. & Zheng, J. C. High anisotropy of fully hydrogenated borophene. Phys. Chem. Chem. Phys. 18, 31424–31430 (2016).
 44.
Olsen, R. A., Kroes, G. J. & Baerends, E. J. Atomic and molecular hydrogen interacting with Pt(111). J. Chem. Phys. 111, 11155–11163 (1999).
 45.
Tang, H. & IsmailBeigi, S. Novel precursors for boron nanotubes: the competition of twocenter and threecenter bonding in boron sheets. Phys. Rev. Lett. 99, 115501 (2007).
 46.
Xu, L. C., Du, A. J. & Kou, L. Z. Hydrogenated borophene as a stable twodimensional Dirac material with an ultrahigh Fermi velocity. Phys. Chem. Chem. Phys. 18, 27284–27289 (2016).
 47.
Zhang, P., Li, X. D., Hu, C. H., Wu, S. Q. & Zhu, Z. Z. Firstprinciples studies of the hydrogenation effects in silicene sheets. Phys. Lett. A 376, 1230–1233 (2012).
Acknowledgements
This work is supported by the Fundamental Research Funds for Central Universities (Grant Nos 20720160020, 2013121010), the Natural Science Foundation of Fujian Province, China (Grant No. 2015J01029), Special Program for Applied Research on Super Computation of the NSFCGuangdong Joint Fund (the second phase), the National Natural Science Foundation of China (nos 11335006, 51661135011). T.Y.L. acknowledges the National University of Singapore for hosting his visit during which part of the work reported here was carried out.
Author information
Affiliations
Contributions
Z.W. performed the calculation and drafted the manuscript. H.Q.W. and T.Y.L. did the data analysis and revised the manuscript. Y.P.F. participated in the discussions and revised the manuscript. J.C.Z. proposed and led the project and revised the manuscript.
Corresponding author
Ethics declarations
Competing Interests
The authors declare that they have no competing interests.
Additional information
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Wang, Z., Lü, TY., Wang, HQ. et al. New crystal structure prediction of fully hydrogenated borophene by first principles calculations. Sci Rep 7, 609 (2017). https://doi.org/10.1038/s4159801700667x
Received:
Accepted:
Published:
Further reading

Band engineering of borophene superlattice based on zigzag nanoribbons: A DFT study
Modern Physics Letters B (2020)

Firstprinciples study of χ3borophene for chargemodulated switchable CO2 capture
Physical Chemistry Chemical Physics (2020)

Unraveling the effect of the defect and adsorbate on the magnetic properties of χ 3 borophene nanoribbons: an insilico study
Physica Scripta (2020)

2D Boron Sheets: Structure, Growth, and Electronic and Thermal Transport Properties
Advanced Functional Materials (2020)

N 2 electrochemical reduction on two dimensional transition metal monoborides: A density functional theory study
International Journal of Quantum Chemistry (2020)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.