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Auxetic and Ferroelastic Borophane: A Novel 2D Material with Negative Possion’s Ratio and Switchable Dirac Transport Channels Liangzhi Kou, Yandong Ma, Chun Tang, Ziqi Sun, Aijun Du, and Changfeng Chen Nano Lett., Just Accepted Manuscript • Publication Date (Web): 17 Nov 2016 Downloaded from http://pubs.acs.org on November 17, 2016
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Auxetic and Ferroelastic Borophane: A Novel 2D Material with Negative Possion’s Ratio and Switchable Dirac Transport Channels Liangzhi Kou1,2,*, Yandong Ma3, Chun Tang4, Ziqi Sun1, Aijun Du1 and Changfeng Chen4 1
School of Chemistry, Physics and Mechanical Engineering Faculty, Queensland University of Technology, Garden Point Campus, QLD 4001, Brisbane, Australia 2
Integrated Materials Design Centre (IMDC), School of Chemical Engineering, University of New South Wales,
Sydney, New South Wales 2052, Australia 3
Department of Physics and Earth Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen,
Germany 4
Department of Physics and Astronomy and High Pressure Science and Engineering Center, University of
Nevada, Las Vegas, Nevada 89154, United States
*
[email protected] Abstract: Recently synthesized atomically thin boron sheets (i.e., borophene) provide a fascinating template for new material property discovery. Here, we report findings of an extraordinary combination of unusual mechanical and electronic properties in hydrogenated borophene, known as borophane, from first-principles calculations. This novel 2D material has been shown to exhibit robust Dirac transport physics. Our study unveils that borophane is auxetic with a surprising negative Poisson’s ratio stemming from its unique puckered triangle hinge structure and the associated hinge dihedral angle variation under a tensile strain in the armchair direction. Our results also identify borophane to be ferroelastic with a stress-driven 90-degree lattice rotation in the boron layer, accompanied by a remarkable orientation switch of the anisotropic Dirac transport channels. These outstanding strainengineered properties make borophane a highly versatile and promising 2D material for innovative applications in microelectromechanical and nanoelectronic devices. Keywords: Borophane, Auxeticity, Ferroelasticity, switchable Dirac transport channels
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Introduction The discovery and exploration of graphene1,
2
has stimulated intensive research in recent
years, leading to the identification and study of a wide range of two-dimensional (2D) materials3-10 that exhibit a rich variety of novel structural, electronic, catalytic, and mechanical properties. Boron allotropes represent a special class of materials that possess versatile bonding capabilities similar to carbon structures. The past decade has seen the rise of various boron nanostructures, such as zero-dimensional boron cage fullerene3, 4, 1D boron nanotubes5, 6, and 3D superhard boron phases7, 8. Conspicuously missing from this list are 2D boron nanostructures, which have long proven difficult to prepare despite theoretical predictions9. The latest experimental advances have finally led to the successful synthesis of 2D boron films10-12. In particular, Mannix et al.12 synthesised borophene, i.e., atomically thin, crystalline 2D boron sheets, on silver surface under ultrahigh vacuum conditions. Such boron sheets, however, tend to degrade in the ambient environments; moreover, calculations show that pristine freestanding borophene exhibits imaginary phonon modes and, therefore, is structurally unstable12. Past studies of similar 2D materials show that volatile atomically thin layers can be stabilized by surface chemical functionalization. Recent work indeed confirms the stability of hydrogenated borophene, known as borophane13, which possesses a prefect Dirac cone in its electronic band structure with ultrahigh Fermi velocity, making it highly desirable for applications in nanoelectronic devices. Besides fabricating borophane by hydrogenation of borophene, which is the approach used for the synthesis of graphene14, an alternative way is to use a bottom-up approach by directly synthesizing borophane via plasma deposition, e.g., by mixing tetrahydrobiopterin (BH4) and H2 inside an ultrahigh vacuum chamber in a high frequency plasma.15 These latest discovery and progress present pressing needs to explore mechanical properties of borophane, especially its structural and property response to applied strain, which may offer crucial insights for elucidating fundamental mechanisms and guiding practical applications. In this Letter, we report findings of an extraordinary combination of unusual mechanical and electronic properties of borophane, which exhibits intrinsic auxeticity, i.e., a negative Poisson’s ratio, and ferroelasticity, i.e., a stress-driven switch of two orientation variants in the crystal lattice. Remarkably, the ferroelastic structural variation leads to an orientation switch of the anisotropic Dirac transport channels in borophane. Our first-principles calculations reveal the bonding configuration changes and structural transformation processes underlying the unusual stress-induced lateral strain response and lattice orientation switch.
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These results offer key insights into the fundamental atomistic mechanisms responsible for the outstanding properties of borophane. The Poisson’s ratio (ν) characterizes the resultant strain in the lateral direction for a material under longitudinal deformation. Most materials contract (expand) laterally when they are stretched (compressed), resulting in a positive Poisson’s ratio. Although negative Poisson’s ratios (NPR) are theoretically permissible, they are usually seen in engineered materials and structures; the only known 2D nanomaterial with an intrinsic NPR is monolayer black phosphorus (phosphorene)16, which has a predicted Poisson’s ratio of -0.027 along the out-of-plane direction. Under ultrahigh strains, phosphorene is also predicted to possess ferroelasticity17, a phenomenon in which a material may exhibit a spontaneous strain. When an external stress is applied to a ferroelastic material, a phase change occurs in the material from one phase to an equally stable one, either of different crystal structure or of different orientation. Ferroelasticity makes a material useful for applications in nonvolatile memory readable/ writeable devices at ambient conditions. Our first-principles study reveals that borophane exhibits a large NPR and a stressdriven lattice orientation rotation accompanied by a switch of the anisotropic Dirac transport channels, making the 2D boron nanosheets the first and so far only material known to possess simultaneously these outstanding properties. The NPR phenomenon in borophane stems from its unique triangular hinges structure, which, under a tensile (compressive) strain along the armchair direction, undergoes a reduction (increase) of lattice constants in the zigzag direction. This in-plane structural response leads to a dihedral angle closing (opening) between the triangular hinge surfaces, producing an increase (decrease) in the layer height, thus the NPR phenomenon. The ferroelasticity in borophane is also rooted in its special bonding structure, where the parallel B-B bonds are significantly weakened by hydrogenation, thus facilitating a bond configuration change into a transition state with a rhombus unit, followed by a spontaneous structural transformation to a new stable state with the switched (90-degree rotated) lattice orientation. Since the Dirac physics in borophane is highly anisotropic22, this ferroelastic structural transformation results in a remarkable orientation switch of the Dirac transport channels. The presence of these outstanding mechanical and electronic properties makes borophane a highly promising 2D material for a variety of applications in nanoscale devices.
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Methods Structural relaxation and electronic band structure calculations were carried out using firstprinciples methods based on the density functional theory (DFT) as implemented in the Vienna Ab Initio Simulation (VASP) package18. The generalized gradient approximation (GGA) in the Perdew−Burke−Ernzerhof (PBE)19, 20 form for the exchange and correlation potential, together with the projector-augmented wave (PAW) method, were adopted. The structural model for monolayer borophane is periodic in the xy plane and separated by at least 10 Å along the z direction to avoid the interactions between adjacent layers. All of the atoms in the unit cell are fully relaxed until the force on each atom is less than 0.01 eV/Å. When the lattice is strained under a specific loading condition, the lattice constants in other directions are fully relaxed. The strain is defined as ߳ = (ܽ − ܽ )/ܽ , while the strain along out-of-theplane direction is defined as ߳௭ = ( ݐ− ݐ )/ݐ , where ܽ and ݐ are the lattice constant and thickness of the freestanding film, a and t are the corresponding values at the strained states. The Brillouin zone integration was sampled by a 10 × 8 × 1 k-grid mesh for a unit cell. A denser k-grid mesh of 12 × 10 × 1 leads to a difference of only several meV in total energy, indicating that our k-grid choice is sufficient for a good convergence. An energy cutoff of 400 eV was chosen for the plane wave basis. The van der Waals interaction is introduced, as described by a semiempirical correction by the Grimme method 19.
Results and discussion The recently synthesized borophene exhibits intrinsic corrugation or wave-shape with a height of 0.9 Å in the out-of-plane direction12, and its surface is chemically active, making it highly susceptible to the influence of the environment. Moreover, the freestanding borophene is structurally unstable with imaginary phonon modes21. It was recently shown21 that surface hydrogenation of borophene offers a viable solution, and the resultant fully hydrogenated 2D boron layer, known as borophane, is stable. In borophane, the corrugation boron bonding configuration is preserved, but the bond lengths are modified by hydrogenation with the calculated lattice constants a=1.93 Å and b=2.81 Å, as indicated in Fig. 1a, which are significantly larger than those in borophene22,28. The smallest construction unit of borophane is a triangle comprising three boron atoms (see Fig. 1a and 1c); however, the three B-B bond lengths are not equivalent. The length of the B-B bond along the zigzag direction (referred to as the inclined B-B bond) is l=1.88 Å, while the value along the armchair direction (referred
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to as the parallel B-B bond) is 1.93 Å. These differences in bond lengths and arrangements in borophane compared to borophene are responsible for the interesting properties that we will discuss below. It should be noted that the parallel B-B bond is significantly weakened after hydrogenation, resulting in a considerable elongation from its value of 1.67 Å in borophene, while the two other bond lengths remain nearly unchanged as compared to those in borophene21. Similar to phosphorene16, borophane also has a hinge-like bonding structure with two surfaces of B123 and B234 connected via the axis of B23 (see Fig. 1c).
Figure 1. (a) Top and (b) side view of borophane lattice structure with the brown and white balls representing boron and hydrogen atoms, respectively. The unit cell is indicated by the green shades, while the armchair and zigzag directions are chosen as the x and y axis, respectively. The typical B-B bond lengths are indicated. (c) The geometrical projection of the hinge unit in borophane is depicted, where the hydrogen atoms are not shown for clarity. (d) Schematic diagram of the dihedral angle variation under an armchair (red dashed lines) or zigzag (blue dashed lines) tensile strain deformation.
Having established the bonding configurations in borophane, we proceed to examine its structural response to uniaxial stress and evaluate the resulting Poisson’s ratios. We present in Fig. 2 the calculated resultant lateral strain in response to a uniaxial strain in the range of ±5% applied along the x or y (i.e., the armchair or zigzag) direction in the boron plane. The results in Fig. 2a show that a uniaxial strain in the x (armchair) direction induces an almost linear strain response in the y (zigzag) or z (out-of-plane) direction near the equilibrium lattice position. Remarkably, the induced in-plane and out-of-plane strain show opposite
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signs i.e. the tensile strain along the armchair direction leads to a contraction in the zigzag direction, but a highly unusual expansion in the out-of-plane (i.e., the layer thickness) direction. Using a linear fitting procedure, we have obtained the Poisson’s ratio along the zigzag direction as 0.204, while the value for the out-of-plane direction is -0.053. This establishes borophane as a new 2D material exhibiting the NPR phenomenon22,23, and the resultant negative out-of-plane strain in borophane is twice as large as that recently predicted for phosphorene. The strain range of ±5% examined here is easily accessible to typical experimental measurements on 2D materials24. It should be noted that the NPR phenomenon is still preserved at larger deformation strains. For example, the thickness values increase by 0.5% 8.8%, 8.47%, and 3.37% at armchair strains of 10%, 20%, 30%, and 40%, respectively.
Figure 2. Resultant strain induced by a uniaxial strain along (a) the x, or armchair, and (b) y, or zigzag direction. The Poisson’s ratio is obtained by a linear fitting procedure.
When stretched uniaxially in the y (zigzag) direction, boronphane exhibits positive Poisson’s ratios along both the in-plane and out-of-plane lateral directions. Results presented in Fig. 2b show that the Poisson’s ratio in the x (armchair) direction is 0.13, which is about half the strain value of 0.204 in the y (zigzag) direction induced by a strain in the x direction (Fig. 2a), indicating a highly anisotropic Poisson’s ratio in borophane. Results in Fig. 2b also show that under a uniaxial strain in the y (zigzag) direction, the Poisson’s ratio is 0.16 in the out-of-plane z direction, which is even larger than the value (0.13) of the in-plane strain response. These results reveal highly anisotropic and qualitatively opposite resultant lateral strains in borophane in response to applied strains in different (armchair or zigzag) directions. We now examine stress-induced changes of bonding configurations in borophane to unveil the atomistic mechanisms underlying the anisotropic strain response and the NPR phenomenon. The triangular structural unit in borophane is shown in Fig. 1c. Under a tensile strain along the armchair direction, the B2-B3 bond length is stretched while the distance
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between B1 and B4 is compressed, producing a positive in-plane Poisson’s ratio. Meanwhile, this uniaxial stress induced deformation leads to a decrease of the dihedral angle between the triangle faces of B123 and B234 (see Fig. 1d), resulting in an increase of the thickness in the out-of-plane direction, thus a negative Poisson’s ratio in this direction. For example, at ϵ௫ = 0.05, the dihedral angle α=120.33◌, ֯ which represents a slight increase compared with the value of 119.53◌֯ in the unstretched freestanding borophane. In contrast, when a tensile strain is applied in the zigzag direction, the B1-B4 bond length increases while the B2-B3 bond length slightly decreases, leading to an increase of the dihedral angle (to 124.14◌֯ at ϵ௬ = 0.05 ), see Fig. 1d; as a result, the thickness of the borophane layer decreases. These contrasting variations of the dihedral angle in borophane under tensile strains along different directions induce Poisson’s ratios with opposite signs along the out-of-plane direction, and the more significant change of the dihedral angle under the strain in the zigzag direction leads to a Poisson’s ratio with a larger magnitude (vz=0.16 as shown in Fig. 2b). It is interesting to compare the similarity and difference of the NPR mechanics between borophane and the previously studied phosphorene16. Both systems possess a hinge structure, which is the key structural feature responsible for the NPR phenomenon. However, the two hinge surfaces in borophane are connected directly (Fig.1c) rather than through a connecting P-P bond as in phosphorene. This difference leads to the more pronounced thickness change under strain and, therefore, the larger negative Poisson’s ratio in borophane. It should be noted that the hinge structure by itself is not a sufficient condition for NPR. A case in point is the pristine unhydrogenated borophene: our calculations show no NPR in borophene whose very short and strong parallel B-B bond (1.67Å versus 1.93Å in borophane after hydrogenation) along the armchair direction deforms only slightly under an applied strain, and this small deformation is not enough to induce a large bond rotation seen in borophane; instead, the strain energy is released through a usual deformation mode of contraction in the lateral direction. The hydrogenation of borophene considerably weakens its B-B bonds along the armchair direction, which become even longer than the originally weaker inclined B-B bonds (Fig. 1). These elongated bonds are more prone to breaking under applied strains, which may induce large structural changes. To explore this possibility, we examine borophane under large deformations. Since 2D materials trend to ripple under compressive strains25, here we focus our study on borophane under tensile strains. We show in Fig. 3 the energy variation under tensile strains up to 50%. Such large strains are feasible in borophane because of the large
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bond rotational deformation facilitated by the hinge structure; this is similar to the situation in phosphorene, which also possesses a hinge structure, where ferroelasticity is predicted24 to occur at large tensile strains close to 40%. When tensile strains are in the zigzag direction, the total energy change exhibits a quadratic increase with rising strain. Under tensile strains in the armchair direction, the energy variation shows the same quadratic increase within the elastic region up to 18% strain; however, beyond the elastic region the energy quickly drops by about 0.15 eV, reaching by a plateau until the strain level of 34%. Further increasing strain brings about a more pronounced reduction in energy, and at 42% tensile strain the energy goes back to the value for the original unstrained borophane. These intriguing energy variations are indicative of structural reconstructions and transitions in borophane.
Figure 3. (a) Strain energy of borophane as a function of uniaxial tensile strain along the armchair and zigzag directions. When stretched along the armchair direction, a structural transition occurs at the critical strain of 18%; the lattice enters a transition state with a plateau in strain energy curve until the strain reaches 34%, where an orientation switch of the lattice occurs. Three structures at 0%, 20% and 42% tensile strains are shown as insets, and their ELF profiles with an isovalue of 0.75 (top view: left; side view: right) are presented in (b-d) to indicate the atomic bonding. To explore the strain induced structural transition, we examine and compare the bonding configurations of the borophane lattice at three selected strain values, 0%, 20%, and
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42%, as shown in the insets of Fig. 3. It is seen that at 20% tensile strain past the elastic region, the B-B bonds aligned in the armchair direction are broken, and the smallest structural unit in borophane is changed from the original boron triangle to a boron rhombus. It is known that the rhombus phase is unstable, it will spontaneously transform into another stable configuration. This is evidenced by the energy variation shown in Fig.3a, where no energy barrier is observed after the critical strain of 18%, and the structure is then transformed to another stable configuration at 42%, as shown in Fig.3. In this region (from 18% to 42%), increasing of strain induces a contraction in the zigzag direction, rendering the nearest boron atoms come close to each other and form new B-B bonds in the zigzag direction, leading to a switch of the lattice orientation at 42% strain, we have calculated the phonon dispersion of this new state (see Fig. s1 in Supporting Information), and no imaginary frequency was observed, demonstrating the dynamical structural stability of borophane after the ferroelastic transition. We further examined the bonding change by calculating the electron localization function (ELF)26 at different strain states. The results in Fig. 3b show that the out-of-plane HB and parallel B-B covalent bonds can be clearly identified in the unstrained borophane. At 20% strain (Fig. 3c), the electron localization along the armchair direction disappears, but the charge localization of the inclined B-B bonds is still preserved, indicating the breaking of the parallel B-B bonds past the critical strain of 18%. At 42% strain (Fig. 3d), the in-plane ELF distribution obviously has a 90-degree rotation compared to the unstrained case (Fig. 3a), reflecting the formation of the new B-B covalent bonds along the rotated direction. We also checked the size effect using a larger 3×3 supercell. The same results were obtained as that shown in Fig. 3 (see Fig. s2 in Supporting Informatyion), indicating that the phenomenon is robust and insensitive to the model size. The energy barrier for the lattice orientation switch is calculated to be 0.1 eV/atom (see Fig. 3), which is smaller than the barrier in phosphorene (0.2 eV/atom), but much larger than those in SnS, SnSe, GeS, and GeSe monolayers (1.3-4.2 meV/atom)17. This result indicates that borophane can achieve ferroelasticity under applied strain but would remain stable and robust against environmental perturbations. Borophane has been shown to possess intrinsic Dirac cone in its electronic band structure along the zigzag direction with the Fermi velocity tuneable by external strain13. Here we show that its ferroelastic lattice orientation rotation leads to a switch of the Dirac transport channels. We present in Fig. 4 the strain evolution of the electronic band structure of borophane. It is seen that in the elastic region the Dirac cone moves along the X-Γ line towards the Γ point with increasing strain. In the transition structure with a rhombus unit cell
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(Fig. 3), as represented by the results at 20% strain, the Dirac cone is broken with the states crossing the Fermi level near the Γ point. At larger strains where the transition toward the rotated orientation variant is nearly complete, the Dirac cone is restored, but now shifted to the Γ-Y line moving toward the Y point with increasing strain. This orientation switch indicates that the novel conducting channel associated with the Dirac cone also switches under large strains. Recent transport calculations21 demonstrate that the electric current along the armchair direction of borophane is twice that along the zigzag direction, namely the conducting channel along the armchair direction is dominant. The strain induced ferroelastic orientation switch in borophane is expected to result in a remarkable directional switch of the anisotropic Dirac transport channels. This feature may prove useful in controlling the electric current flow in the design and application of nanoscale devices.
Figure 4. Evolution of electronic band structure of borophane under a uniaxial tensile strain along the armchair direction. It is worth pointing out that although the imaginary phonon frequency of borophene has been removed by hydrogenation, the resulting structure is not very stable and found to survive up to 240 K from molecular dynamics (MD) simulations. We expect that some boundary constraints may also be needed to further stabilize borophane at room temperature, possibly driven by electron transfer between the 2D layer and substrate, as implied by the experimental observation that a substrate can stabilize the unstable freestanding borophene.12 We also found that reducing the surface hydrogen coverage rate may be an effective way to increase the layer stability as evidenced by the shorter B-B bond length (parallel B-B 1.75Å) and increased structural stability temperature of 260K from MD simulations, see Fig. s3 in Supporting Information. More work is certainly needed to further explore and better understand effective approaches to enhance the stability of the borophane layer for practical applications.
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Conclusions We unveil by first-principles calculations intrinsic auxeticity and ferroelasticity in borophane. Moreover, the ferroelastic lattice rotation produces a stress-driven orientation switch of the anisotropic Dirac transport channels. This makes borophane the only known material to simultaneously possess these extraordinary structural, mechanical, and electronic properties. Both the negative Poisson’s ratio and the orientation variation in borophane stem from its hinge-like bonding structure. The dihedral angular rotation of the triangular unit cell under an armchair or zigzag strain induces an expanding or contracting lateral lattice response, which produces a direction sensitive negative or positive Possion’s ratio, respectively. Meanwhile, the hydrogenation weakened B-B bonds along the armchair direction break under tensile strains and reconstruct to generate a 90-degree lattice rotation, which, in turn, switches the orientation of the anisotropic Dirac transport channel. These outstanding strain-engineered properties render borophane an outstanding 2D nanomaterial with great promise for applications in novel nanodevices.
Acknowledgements Financial support by the ARC Discovery Early Career Researcher Award (DE150101854) is gratefully acknowledged. This research was undertaken with assistances provided at the NCI National Facility systems at Australia National University through the National Computational Merit Allocation Scheme Supported by the Australia Government. CFC was partially supported by the US Department of Energy through the Cooperative Agreement DENA0001982. ZS acknowledges the financial support from Australian Research Council through a DECRA project (DE150100280) and a Discovery project (DP160102627).
Supporting Information Available The phonon frequency spectrum of borophane at armchair strain of 42% is presented. Also shown are the total energy variation and structural evolution of a 3x3 borophane supercell under armchair deformation strains, and structure details of a half passivated borophene. This material is available free of charge via the Internet at http://pubs.acs.org/.
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