Prediction of Two-Dimensional Phase of Boron with Anisotropic Electric Conductivity Zhi-Hao Cui,†,‡ Elisa Jimenez-Izal,†,§ and Anastassia N
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Letter pubs.acs.org/JPCL Prediction of Two-Dimensional Phase of Boron with Anisotropic Electric Conductivity Zhi-Hao Cui,†,‡ Elisa Jimenez-Izal,†,§ and Anastassia N. Alexandrova*,†,∥ † Department of Chemistry and Biochemistry, University of California, Los Angeles, 607 Charles E. Young Drive, Los Angeles, California 90095-1569, United States ‡ College of Chemistry and Molecular Engineering, Peking University, 100871 Beijing, China § Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia International Physics Center (DIPC), P. K. 1072, 20080 Donostia, Euskadi, Spain ∥ California NanoSystems Institute, Los Angeles, California 90095-1569, United States *S Supporting Information ABSTRACT: Two-dimensional (2D) phases of boron are rare and unique. Here we report a new 2D all-boron phase (named the π phase) that can be grown on a W(110) surface. The π phase, composed of four-membered rings and six-membered rings filled with an additional B atom, is predicted to be the most stable on this support. It is characterized by an outstanding stability upon exfoliation off of the W surface, and unusual electronic properties. The chemical bonding analysis reveals the metallic nature of this material, which can be attributed to the multicentered π-bonds. Importantly, the calculated conductivity tensor is anisotropic, showing larger conductivity in the direction of the sheet that is in-line with the conjugated π-bonds, and diminished in the direction where the π-subsystems are connected by single σ-bonds. The π-phase can be viewed as an ultrastable web of aligned conducting boron wires, possibly of interest to applications in electronic devices. n the past decades, the outstanding geometry and electronic deposition (CVD). In these cases, the exoticism of boron I properties of graphene inspired a wide interest in low- structures again implied the complexity of the bonding features. dimensional structures.1,2 However, for elements right next to The substrate obviously dictates the structural and electronic carbon in the Periodic Tablesilicon, boron, and phospho- preferences in these materials, and also the feasibility of their rusthe preparation of elemental two-dimensional (2D) preparation. Accordingly, the possibly rich 2D chemistry of 3−5 phases has been proven to be much more difficult. Among boron might be accessible through templating on different these elements, boron is particularly intriguing and challenging. supporting surfaces. First, the elemental allotropes of boron are dominated by the In this work we focus on the most stable surface of tungsten, 6 well-known and very stable B12 icosahedral clusters. Second, W(110), as a substrate for 2D boron growth. This surface the 2D nature has been found to prevail only in small clusters features good stability and an excellent performance in growth of boron, governed by a mix of covalent and delocalized bonds of carbon nanotubes.18 Most importantly, while Cu and Ag in an undercoordinated situation.7,8 Planarity does not easily fi surfaces have an hexagonal symmetry, W(110) has a translate to extended systems, because of the electron-de cient rectangular symmetry. Therefore, it might be a promising nature of boron, as compared to carbon: like a metal, the support to obtain novel boron monolayers. Indeed, we will metalloid boron tends to go toward 3D bulk. In purely describe here a unique new 2D sheet of boron that can be theoretical works, a large amount of effort went into finding formed on the W(110) substrate and, upon exfoliation, retains stable 2D boron phases, e.g., the α sheet,9,10 β sheet,9,10 and χ 11,12 its structure and stability up to strikingly high temperatures. We sheet, by different approaches, including cluster expansion (CE),13 particle-swarm optimization (PSO),13,14 and based on show that this phase possesses special electronic structure and existing structural characteristics.15 These works mainly focus anisotropic electric conductivity. on the boron monolayer, constraining the global optimization To identify the most stable structure of 2D boron on W(110), we applied the particle-swarm global optimization to two dimensions, and not considering the possibility of 19−21 22,23 growing the boron phase on a substrate to support it. The method combined with DFT-PBE calculations to ff substrate, however, plays a crucial role in experimental explore several di erent chemical compositions, varying the preparation of 2D boron, which is one of the major differences between boron sheets and graphene in the experiment. Only Received: February 3, 2017 very recently have a few types of boron sheets been synthesized Accepted: March 1, 2017 on Cu foils16 and on a Ag(111) surface5,17 by chemical vapor Published: March 1, 2017 © XXXX American Chemical Society 1224 DOI: 10.1021/acs.jpclett.7b00275 J. Phys. Chem. Lett. 2017, 8, 1224−1228 The Journal of Physical Chemistry Letters Letter Figure 1. Cohesive energy is plotted as a function of the number of boron atoms. The representative structures are also labeled on the curve, where W and B atoms are depicted in gray and green, respectively. Figure 2. The π sheet and related structures: (a) top view and (b) side view (with Bader charges) of the π sheet on the substrate, (c) π sheet without χ the substrate, (d) 3 sheet, and (e) the four-membered-ring structure. number of B atoms from 12 to 18 per supercell, within an area All the structures are based on a triangular lattice, where each of 6.34 Å × 8.97 Å. In order to estimate the relative stabilities of boron is three or four-coordinated, a common feature in boron different compositions, we calculate the cohesive energy, monolayers. Due to the symmetry of the W substrate, however, these structures are quite different from the ones reported EEnEtot−− sub B 5,16,17 Ec = previously. Their most distinct feature is that they are n (1) composed of both four-membered and six-membered boron where E is the total energy of the system with the boron sheet rings, where the formation of the four-membered rings can be tot regarded as a compromise in order to match the substrate on the substrate, Esub is the energy of pure W substrate, EB is the energy of a single boron atom and n the number of B structure as much as possible. First, boron atoms tend to form atoms. Note that the specific product obtained in the chemical an epitaxial skeleton, matching the distribution of tungsten vapor deposition depends not only on the cohesive energy E , atoms. As the number of boron atoms increases, boron atoms c 9,15 but also the condition of preparation, which determines the fill the “holes” of the hexagons. Previous studies found that chemical potential of boron. The predicted global minima filling all of the holes is unfavorable, due to the electron- structures for each composition and their corresponding deficient nature of boron. In fact, electron-deficient bonding cohesive energies are shown in Figure 1 (see also the Figure generally has a strong multicenter character, which would tend S2 of the Supporting Information for the detailed structures to favor greater aggregation of atoms and destabilize 2D boron. with unit cell labeled). Our results further confirm this phenomenon by manually 1225 DOI: 10.1021/acs.jpclett.7b00275 J. Phys. Chem. Lett. 2017, 8, 1224−1228 The Journal of Physical Chemistry Letters Letter adding the boron atoms to the holes of the six-membered rings, which is found to be energetically unfavorable. Indeed, although the cohesive energy is still negative for the case where the number of boron atoms is larger than 16, its absolute value decreases significantly, indicating that the structure is unwilling to accept new boron atoms to fill the holes. Therefore, the structure containing 16 B atoms (Figure 2a), is thermodynami- cally more likely to be prepared in practice. To our knowledge, this structure has never been reported, and we will hereafter refer to it as π sheet. Due to the interaction with the substrate, the π phase is slightly buckled (Figure 2b); the Bader charge analysis shows a small charge transfer from the W surface to the boron sheet. π We note that the amount of charge on boron here is relatively Figure 3. Electronic band structures and PDOS of the boron sheet, larger than the case of other 2D boron on Cu(111) (usually where the black lines denote the result by PBE, the red dots denote smaller than 0.1 e per boron atom).24 This is due to the bigger the result by HSE06 and the blue dashed line indicates the Fermi level. ff The Brillouin zone path can be found in Figure S4 of the Supporting electronegativity di erence between B and W, compared to the Information. difference between Cu and B, and reflects a stronger interaction in the present case, leading to a distinctive 2D structure. Next, we analyze the π sheet without the substrate. Alone, this These features inspire us to establish a connection between monolayer is a totally flat 2D material (Figure 2c) and the the delocalized electronic band structure and the chemical bond 25 phonon analysis, with no imaginary frequencies (see Figure so that one can easily understand the electronic structures of S3 of the Supporting Information), confirms its dynamical 2D boron. The chemical bonding is analyzed using the Solid stability. Additionally, ab initio MD simulations are performed State Adaptive Natural Density Partitioning (SSAdNDP) at different temperatures in order to study the thermal stability method.29 This method can be regarded as an extension of of the new boron phase. These calculations suggest that the π the NBO method. It maximally localizes the electron pairs into sheet is stable up to 1800 K and only small buckling vibration, 1-center (lone-pairs), 2-centers (single bonds), and multi- following the normal phonon mode, occurs with temperatures centered bonds (delocalized bonds).