Two-dimensional boron: structures, properties and applications

Zhuhua Zhang ab, Evgeni S. Penev b and Boris I. Yakobson *bc
aState Key Laboratory of Mechanics and Control of Mechanical Structures, and Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
bDepartment of Materials Science and NanoEngineering, Rice University, Houston, TX 77005, USA
cDepartment of Chemistry, Rice University, Houston, TX 77005, USA. E-mail:; Tel: +1 713-348-3572

Received 11th April 2017

First published on 31st October 2017

Situated between metals and non-metals in the periodic table, boron is one of the most chemically versatile elements, forming at least sixteen bulk polymorphs composed of interlinked boron polyhedra. In low-dimensionality, boron chemistry remains or becomes even more intriguing since boron clusters with several to tens of atoms favor planar or cage-like structures, which are similar to their carbon counterparts in terms of conformation and electronic structure. The similarity between boron and carbon has raised a question of whether there exists stable two-dimensional (2D) boron, as a conceptual precursor, from which other boron nanostructures may be built. Here, we review the current theoretical and experimental progress in realizing boron atomic layers. Starting by describing a decade-long effort towards understanding the size-dependent structures of boron clusters, we present how theory plays a role in extrapolating boron clusters into 2D form, from a freestanding state to that on substrates, as well as in exploring practical routes for their synthesis that recently culminated in experimental realization. While 2D boron has been revealed to have unusual mechanical, electronic and chemical properties, materializing its potential in practical applications remains largely impeded by lack of routes towards transfer from substrates and controlled synthesis of quality samples.

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Zhuhua Zhang

Prof. Zhuhua Zhang obtained his BE degree in 2004 and completed his PhD research with Prof. Wanlin Guo in 2010, both at Nanjing University of Aeronautics and Astronautics, China. As a postdoctoral fellow, he joined Prof. Yakobson's group in the Department of Materials Science and NanoEngineering at Rice University in May 2012. With the support of the Thousand Talent Program of China, he started a theoretical group at Nanjing University of Aeronautics and Astronautics from May 2017. His current research interests include modulation of structures and properties of low-dimensional materials, nanomechanics as well as computational design of novel nanostructures.

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Evgeni S. Penev

Evgeni S. Penev is an assistant research professor at Rice University. He studied physics at the St. Clement of Ohrid University of Sofia, Bulgaria, and holds a MS degree in solid state physics. He received his PhD degree from the Fritz Haber Institute of the Max Planck Society, Germany, and was awarded the Otto Hahn Medal for outstanding scientific achievement.

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Boris I. Yakobson

Boris I. Yakobson is the Karl F. Hasselmann Chair in Engineering, a professor of materials science and nano-engineering, and a professor of chemistry at Rice University, USA. He received his PhD degree in 1982 from the Russian Academy of Sciences, Russia. Prior to joining Rice in 1999, Yakobson was on the physics faculty at North Carolina State University and a visiting scholar at the Department of Chemistry, Columbia University, in 1990.

1. Introduction

Ignited by the discovery of novel physics in graphene, two-dimensional (2D) materials beyond graphene have gained unprecedented interest across materials research. While graphene-like 2D materials have been reported to be rich and diverse, only a small number of them are monoelemental, such as phosphorene, silicene, germanene and stanene.1 More surprising is the fact that none of these elemental 2D materials possesses structural planarity as in graphene, due to their varying degrees of out-of-plane buckling. The reason is that all these elements have very limited ability in varying their bonding nature, unlike carbon which is able to variably form sp3, sp2 and sp bonding. This fact has kept researchers pondering whether there is an element that could be on par with carbon in bonding variability and thereby form a purely flat 2D material. As the Z − 1 (“left”) neighbor of carbon in the periodic table, boron is similar to carbon in terms of electronic properties and potential applications in, for example, superhard materials2 and biological compounds.3 However, boron is still among the most mysterious elements due to its complicated chemistry, despite the long history of boron research and the fact that very few elements can be simpler than this light atom.4,5

The study of boron can be traced back to two centuries ago,6,7 when boron only existed in various compounds due to its unusual ability to combine with almost all other elements. Pure boron was not documented until Sands' work in 1957,8 which reported bulk γ-B106 with an extremely complex structure. Nowadays, bulk boron is known to have at least sixteen polymorphs, but only a few of them have crystal structures identified,9,10 all featuring interlinked polyhedra. Positioned between metallic beryllium and non-metallic carbon, boron has only three valence electrons: [He]2s22p1. The single 2p electron would favor metallicity, but its orbital radius is close to that of the 2s state,11 making it sufficiently localized to allow for the appearance of non-metallicity. Such a unique electronic structure of boron enables the formation of highly diverse bonding in bulk phases, ranging from strongly covalent two-centre bonds to metallic-like multi-centre bonds. The latter are responsible for the polyhedra, dominant in bulk boron (Fig. 1, top left inset), especially for the B12 icosahedra12 that can accommodate the electronic deficiency of boron.

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Fig. 1 The conceptual-geometrical precursor of the diverse boron structures. Two-dimensional (2D) boron monolayer can be cut-tailored into planar boron clusters, rolled into 1D nanotubes, and wrapped up into 0D boron fullerene. It can even be folded into a B12 cluster, the dominant building block of 3D boron (the inset shows the structure of 3D-bulk α-boron).

The strong bonding capability of boron stimulated an upsurge of research interest in boron nanostructures, which include zero-dimensional (0D) clusters, 1D nanotubes and 2D monolayer sheets (Fig. 1). Both theoretical and experimental studies have shown that small boron clusters, Bn, tend to adopt planar conformations in their ground state, whose electronic structures are markedly similar to those of aromatic or antiaromatic molecules.13–19 As the cluster size increases, cage-like conformations start to compete in energy with the planar ones and become increasingly more favorable when the size exceeds a critical value (n ∼ 28 at charge neutrality).20 One prominent example of boron cages is the experimentally reported fullerene-like B40 cluster, which proves to be the ground state among the 40-atom conformations by global minimum search.21 Actually, the research of boron cages has been boosted more by an earlier prediction of a B80 buckyball,22 which remains a subject of particular interest in theory to date. The B80 buckyball is isoelectronic to a C60 buckyball, and its symmetry23,24 and stability relative to other proposed hollow or filled isomers25–30 have been intensely debated. While the B80 buckyball turns out to be less stable than some isomers, unfolding it31 onto a plane can uniquely lead to the prediction of a stable flat crystal (Fig. 1), called an α-sheet,32,33 particularly appealing as a graphene analogue. The prediction of the α sheet further extended the similarities between boron and carbon chemistry and brought the research of boron into the vigorously explored materials flatland.

Despite the striking similarities between boron and carbon, 2D boron layers are made of a triangular grid with a pattern of hollow hexagons (HHs) (Fig. 1), distinctly different from graphene's honeycomb lattice. The HH pattern is highly variable in distribution and concentration, setting apart numerous lattices within a narrow range of energies near the ground-state line and resulting in polymorphism.34 Searching for energetically favorable boron sheets encounters a daunting combinatorial problem and thus necessitates a large number of costly (energy) computations. The configurational space of 2D boron has been explored using different global minimum search methods, such as the particle swarm optimization,35 advanced cluster expansion methods,34 and evolutionary algorithms.36 Yet, reaching the real global minimum of 2D boron is still subject to the development of more efficient methods that would make structures with larger unit cells feasible. Another salient difference from known 2D materials is that boron is remarkably higher in energy than its bulk forms, unlike graphene and h-BN sheet37 that are naturally layered in 3D form. How to entice the boron atoms to assemble into metastable 2D structures proves to be a challenge, albeit experimental efforts intensified for nearly a decade. To this end, several theoretical studies38,39 have suggested using metal substrates, such as Ag and Cu, to lift the polymorphic energy degeneracy and kinetically guide the growth of boron sheets.

Benefiting from theoretical predictions, two recent experiments have independently realized monolayer boron sheets on Ag(111) substrates,40,41 which are one-atom thick and indeed polymorphic. Previously predicted metallic character32,34 of boron sheets is also confirmed experimentally42 and renders them a desirable complement to semimetallic graphene, insulating h-BN, and semiconducting transition metal dichalcogenides. These milestones highlight the power of theory in leading to synthesis of new materials and uncovering new properties and phenomena.43–45 Also, this progress has promptly raised broad interest in exploring the versatile properties and potential applications of borophenes. However, towards realizing practical applications, the separation of borophenes from substrates and controlled synthesis of quality samples remain challenging, calling for continuing synergy between theory and experiment.

In this review, we present the recent theoretical and experimental progress in low-dimensional boron structures, particularly focusing on borophene. We first discuss boron clusters, both compact 3D-cages and 2D-planar varieties. Then, we provide an extensive account of structural and electronic characteristics of 2D boron in vacuum and on substrates and highlight the role of theory in locating favorable structures of boron sheets in different environments and in guiding experimental synthesis. The experimental advances in synthesizing and characterizing borophenes are then surveyed and possible directions for future study are analyzed. Finally, we summarize the current state of the studies of mechanical, electronic and chemical properties of borophenes as well as their prospective applications in relevant technological fields.

2. Boron clusters

The actively explored boron clusters, Bn, normally refer to those with n varying from 3 to ∼100 atoms. A crucial first step in theoretically studying boron clusters is to identify their global energy minima. Yet, as n increases, each boron cluster would have an exponentially growing number of possible isomers due to a rich variety of B–B bonds. Many research groups have developed global minimum search methods based on different algorithms, including gradient embedded genetic algorithm,46 coalescence kick,47 basin hopping,48 Cartesian walk,49 particle swarm optimization,35 genetic/evolutionary algorithms,50–52 data mining methods,53,54etc. Combining these methods with density functional theory (DFT) calculations, theory could identify the ground state structures of a set of boron clusters, most of which have been detected experimentally. Details of these structural search methods and their respective advantages have been summarized in recent reviews,13,15 thus not further discussed here.

While bulk boron phases favor inter-linked polyhedra, small boron clusters tend to adopt planar structures (Fig. 2a), typically consisting of a periphery and interior boron atoms. All bonds around the periphery are classical two-centre two-electron bonds (two electrons shared by two atoms) while those for the interior atoms are delocalized multi-center two-electron bonds (two electrons shared by three atoms or more). The planar conformation of small boron clusters could be rationalized by the aromaticity or antiaromaticity of the delocalized molecular orbitals, similar to the electronic structures of aromatic molecules. For discussion on the bonding configurations in planar boron clusters, we refer the reader to several comprehensive reviews.13,14 As the cluster size increases, the bonds around the periphery become shorter than those in the interior, squeezing the inner boron atoms slightly out of the plane and resulting in quasi-planar structures, e.g., B7 (ref. 55) and B12.56 With further increasing the cluster size, a 2D → 3D structural crossover occurs at n = 20, at which a double-ring tubular isomer (see insets in Fig. 2) can compete with the planar structure in terms of stability, as confirmed by global minimum search in conjunction with photoelectron spectroscopy (PES) characterization.57 The appearance of tubular boron clusters has stimulated interest as they can be considered as embryos of boron nanotubes. However, the tubular cluster turns out to be high in energy at larger size, at least according to results from state-of-the-art DFT calculations.

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Fig. 2 Structures and stability of boron clusters. (a) Cohesive energies per atom for Bn (n = 7–40) clusters at charge-neutral state, calculated using PBE0 functional. The black stars stand for the (quasi-) planar or double-ring tubular (n = 20) structures while the red circles stand for the cage structures (n = 32, 36 and 40). (b) Size-dependent conformation of favorable boron clusters: from planar or quasi-planar, via cage-like, to core–shell structures.

Even though favorable ring-like clusters have not been further identified, fullerene-like boron cages can be favorable when n ≥ 2858,59 (Fig. 2). Structurally, the fullerene-like cages can reduce the edge energy at the expense of bending energy, which decreases with increasing n. The fact that boron cages at specific sizes can satisfy an electron-counting rule for spherical aromaticity further improves their stability over the planar form. The most remarkable example is the recently reported B40 cage,21 which is significantly more stable than its planar isomers at the charge-neutral state. It is unusual that the B40 cage has no pentagon normally required for a spherical structure. Instead, its surface exhibits four hollow heptagons, which would generate a negative Gaussian curvature in a graphene-like lattice. This peculiar cage structure raises a question as to what is its geometrical precursor.60,61 In contrast, one of its larger siblings, the B80 buckyball,22 has a more regular spherical structure composed of pentagons and hexagons, reminiscent of a C60 fullerene that shares the same icosahedral symmetry. Despite presently remaining hypothetical and the fact that several more stable isomers have been proposed,25–30 the B80 buckyball can be directly unfolded into an energetically favorable boron sheet, referred to as an α-sheet, as will be discussed later. It is worth mentioning that hollow structures of these boron cages can trap metal atoms to form various endohedral metallofullerenes with novel magnetic62,63 and chemical64 properties. Further studies of large boron clusters (n ≥ 80) revealed that they would develop into core–shell structures (often with a B12 icosahedron core, see Fig. 2b),25,27,30 showing a tendency of converging to bulk boron lattices.

Aside from the size, the competition between the stability of planar and cage-like boron structures also depends on their charge state. For example, a planar B40 structure is lower in energy than the B40 cage structure, which otherwise is the ground state at charge-neutrality.21 A similar relation also occurs in other boron clusters charged by one electron, such as B28 (ref. 58) and B29.20 It appears that, for a number of boron clusters, a planar geometry is preferred at the −1 anion state while a cage structure is more favorable at charge-neutrality. The charge-dependent structure of boron clusters opens the possibility for their structural control, as recently shown for 2D boron monolayers.65

With increasing size, both the planar and cage-like boron clusters tend to contain hollow hexagons. The smallest planar cluster featuring such a HH is B27.66 As the size increases further, clusters with HHs become increasingly more stable than the isomers without HHs. The planar B36 cluster17 contains a perfect HH and has the same six-fold symmetry as graphene, which can be viewed as a basic unit for constructing the α-sheet. The planar B40 cluster contains a twinned HH21 (see the inset in Fig. 2a), which also appears often in the boron sheets with high HH concentrations.34 Larger planar clusters should show a richer variety of HH patterns. A similar trend holds for the fullerene-like clusters. The more favorable HHs in larger boron clusters are indeed reminiscent of the vacancy-rich structures of stable 2D boron sheets.32–34

On the experimental side, the current method for synthesizing boron clusters is mainly through laser evaporation of boron targets, such as boron rods, similar to early fullerene making. The vaporized atoms are then cooled to form clusters of various sizes, and the cluster of a certain size can be selected by a mass gate. Identification of cluster structures has been carried out primarily through PES,67 which is compared to PES spectra obtained from DFT calculations. While good agreement between experimental and theoretical PES spectra can be achieved for most of the reported boron clusters, there is still no direct imaging of their atomic structures. The challenge lies in the fact that the produced boron clusters are in the gas phase and prone to aggregation upon decreasing the temperature, making microscope-imaging impossible. Controllable synthesis of boron clusters with selected size and then depositing them onto an inert substrate would be the first step towards obtaining atomic-resolution images.

3. Borophenes

3.1 Freestanding borophene

Since the discovery of graphene,68 many elements and blends have been shown to form 2D materials. Boron nitride,69,70 transition metal dichalcogenides,71,72 phosphorus,73 silicon74,75 and tin76,77 have been actively studied in this realm, yet few of them can compete with boron in terms of chemical similarity to carbon. Hence, intriguing questions arise: can boron form a 2D material as carbon does in the form of graphene? If so, what are the energetically preferred structures of 2D boron? The first tentative 2D boron structure is borrowed from graphene, i.e., a hexagonal sheet with boron atoms arranged in a honeycomb network. The graphitic boron layer naturally exists in a group of transition metal diborides and was predicted to be favorable on the (0001) surfaces of NbB2,78 CrB2 and MoB279 under boron rich conditions. Such a honeycomb boron layer was originally named “boraphene”,78 but it is unstable in the freestanding form since boron lacks one electron to form stable sp2 hybridization.80,81 Inspired by the prevalence of hexagonal boron pyramids in quasi-planar boron clusters,82,83 Boustani argued, by invoking the Aufbau principle, that the most stable 2D boron would be composed of buckled triangular motifs.84 Such a buckled triangular sheet was later found to be the most stable among several hand-designed sheet configurations85 and was once used as a precursor to construct boron nanotubes,86,87 reported once as apparently synthesized, several years earlier.88,89 Advances in the theoretical studies of 2D boron structure were made by Tang et al.32 and Yang et al.,33 who independently proposed the boron α-sheet, derived by unfolding the B80 buckyball onto a plane. The α-sheet is composed of triangular lattice patterned by isolated HHs, with a D6h symmetry. As an electronic equivalent of graphene, the α-sheet is more stable by 37 meV per atom than the buckled triangular sheet. Its high stability is explained by an optimal filling of in-plane electronic orbitals,32 which also accounts for its flat conformation. Subsequently, Tang et al. proposed several boron sheets by arranging the HHs in different patterns and concentrations and found that several of them have cohesive energies as good as that of the α-sheet.90 This result opens a broader question about the possible polymorphism of 2D boron.

Searching for the lowest energy structure becomes a focus of subsequent studies of 2D boron. As there are numerous possibilities for arranging HHs (denoted as [[thin space (1/6-em)]] for the vacant sites) in a triangular grid (B), direct use of DFT methods for calculating every possible structure is unrealistic. To evaluate the structural stability and diversity, Penev and coworkers34 treated the boron sheet as a pseudo-alloy B1−v[[thin space (1/6-em)]]v, where the HH concentration is defined as v = m/N, with m the number of HHs in a supercell of N triangular lattice sites. Then any boron sheet can be described by a vector σ, with components σi = +1 for the hexagon center where a B atom is present and −1 if not. For a particular configuration σ, the total energy E can be expanded in series

E(σ) = J0 + (1 − 2v)J1 + ∑dxJxΠx(σ),(1)
where dx is the number of clusters of type x, which can be pairs, triplets, etc., Jx is the corresponding effective cluster interaction, and Πx(σ) = 〈Πiσi〉 represents the “spin” products for configuration σ averaged over all symmetry-equivalent x-type clusters. This treatment allows for the use of the cluster expansion method91 augmented with accurate DFT calculations to determine the expansion coefficients Jx and then to more easily explore the configurational space of 2D boron. All the calculated symmetry-inequivalent structures are depicted in Fig. 3a, where the 2D boron is shown to be inherently polymorphic, with all stable isomers lying in a narrow range of HH concentrations of 10–15%. In particular, the v1/8 and v5/36 sheets are slightly more stable than the α-sheet (v = 1/9). Later on, employing different global-optimization methods, more theoretical studies92–94 have further extended the search for new isomers. All their results confirmed the polymorphism of 2D boron, even though the ground states may differ slightly from calculations using different functionals.

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Fig. 3 Stability and structures of 2D boron. (a) Total energy per atom of all symmetry-inequivalent B sheets as a function of v. Diamonds show the data expanded using a rhombus primitive cell while squares show those expanded from a rectangular primitive cell as shown in the inset, both with the cluster expansion method. The solid line shows the energy variation of ground states with v. Reprinted with permission from ref. 34. Copyright 2012 American Chemical Society. (b) Black line: the buckling magnitude of favorable B sheets as a function of v. Blue line: the dependence of excessive electrons (see text for definition) per atom in the honeycomb boron lattice (grey in the inset of a) with respect to the number of valence electrons per carbon atom in graphene. (c) Front and side views of atomic structures of the triangular, v1/9, v1/8 and v1/6 sheets.

Based on the structure–stability relationship set forth above, a stabilizing mechanism for the boron sheets can be proposed.95 In a boron sheet, the B atoms at the center of hexagons serve as “donors” while the HHs act as “acceptors”,96 which are mixed to compensate for the electronic deficiency of boron. If three valence electrons of each “donor” boron were fully shared with the hexagonal skeleton (colored in grey, inset of Fig. 3a), an ideal boron sheet should have the skeleton isoelectronic to graphene. This simple mechanism explains why the v1/9 sheet is one of the most favorable structures. Including some secondary factors, such as the vacancy–vacancy interaction (e.g., such an interaction is enhanced in twinned vacancies), could shift the ground state structure to a slightly higher v (∼1/8), which then achieves good agreement with DFT calculations. The boron sheets with v < 1/9 are electron-excessive and exhibit off-plane buckling due to mixing of in-plane and out-of-plane orbitals, whereas those sheets with v > 1/9 are purely flat, as shown in Fig. 3c. The boron sheet with a high v is electron-deficient and tends to draw electrons from its surroundings, so as to stabilize its structure. An extreme example is the hexagonal boron sheet (v = 1/3), which is unstable in a vacuum yet at the global minimum in many bulk metal diborides due to electron transfer from the metal layers.79

3.2 Boron nanostructures on substrates

In contrast to other 2D materials (e.g., graphene, h-BN, and MoS2) that are naturally layers stacked in the ground-state 3D forms, 2D boron is far higher in energy than all its 3D forms (Fig. 4a). For example, the α-sheet is less stable by 400 meV per atom than bulk α-boron. The thermodynamic disadvantage of 2D boron, together with its inherent polymorphism, leads to a significant challenge for its synthesis. Prior to experimental efforts, theoretical studies are instrumental in shedding light on several fundamental questions that hamper the synthesis.
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Fig. 4 2D versus 3D boron on metal substrate. (a) Energy comparison between 2D boron sheets and bulk boron in a vacuum. (b) A 2D boron nucleus has all atoms interacting with the metal while only atoms on one surface of a 3D boron nucleus interact with the metal. (c) Upper: Free energy variation of 2D (line with circle) and 3D (line with diamond) boron clusters on Ag as a function of number of B atoms, N. Bottom: Formation energy of 2D boron clusters and chemical potential of boron as functions of N. (d) Representative atomic structures of favorable 3D and 3D boron clusters on Ag, with N = 12, 20 and ∞.
Nucleation of 2D boron. The first question is what can entice boron atoms to assemble into 2D structures. An idea is that the nucleation barriers for 2D or 3D, controlling the material formation, do not need to always rank in the same order as the energies of final phases. A further control knob can be borrowed from the CVD synthesis of graphene or h-BN, namely using a metal substrate. All n atoms of a 2D-nucleus can benefit from the interaction with the substrates while only ∼n2/3/6 atoms in a 3D-nucleus can be in contact with the substrate (Fig. 4b). In this manner, the substrate can selectively stabilize 2D structures, suppressing the nucleation barrier to be lower than that for the 3D case. Once the 2D route is preferentially chosen, the boron structures can be kinetically protected from converting into 3D form. This scenario is supported by atomistic calculations performed by Liu et al.,39 who indeed found a smaller nucleation barrier for the 2D route than that for the 3D route (Fig. 4c and d). Their results also confirmed that planar clusters are more favorable than the 3D clusters (Fig. 4d), at least for Bn with n ≤ 20 on Ag(111). Based on DFT computations, they suggested two potential routes towards the synthesis of 2D boron: (i) deposition of boron sources on the Au or Ag surface, (ii) saturation of B-terminated MgB2 surfaces in a boron-rich environment. Liu, Gao and Zhao97 also investigated favorable geometries and the interaction mechanism of boron clusters on Cu(111) and found that HHs can easily form during the nucleation of 2D clusters, further supporting the viability of using metal substrates to assist the synthesis of 2D boron.
2D boron on metals. While metal substrates are necessary for the growth of 2D boron, the metal–boron interaction may alter its ground-state structure in view of the high structural sensitivity of borophenes to charge doping.65,96,98 The structures of 2D boron predetermined by metal substrates will serve as a basis for any further study of this material. Thus, another fundamental question is what structures will be favored on metals. While the search for the global minimum of freestanding 2D boron has been performed well, including metal substrates into the search will make the tasks computationally much more taxing. Recently, Zhang et al.38 employed the cluster expansion method, including explicitly the metal substrate, while still treating the boron–metal system as a “binary alloy”34 composed of a triangular boron lattice and HHs, both supported on a metal substrate. This treatment enables a comprehensive first-principles study of 2D boron on metals commonly used in CVD synthesis. The results show that 2D boron is the first material whose favorable structure depends on substrates (Fig. 5a). In particular, Ag, Cu and Ni donate electrons into 2D boron and hence increase the HH concentration, which, along with the potential provided by the substrate, results in the v1/6 sheet as the ground state. This trend agrees with the fact that a graphitic boron layer can be the ground state on (0001) surfaces of metal diborides,78,79 where electronic transfer from the metal layers makes the boron electronically equivalent to carbon. In contrast, electrons are drawn from boron by Au, which shifts the ground state of 2D boron toward a smaller v value and preserves its structural degeneracy as in a vacuum (Fig. 5b and c). Remarkably, the predicted optimal v1/6 sheet on Ag(111) has been confirmed by subsequent experiments,41 as discussed in the next section.
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Fig. 5 Structures of 2D boron on metals. (a) Configurational energy spectra of 2D B in a vacuum, on Au, Ag, Cu and Ni. The insets in each column show three most stable structures, and the number below each inset is energy relative to ground states. (b) Vacancy concentration v of the ground state 2D B as a function of metal work function. The dotted line stands for the results when the boron–metal distance is increased to 5 Å. Isosurface plots (0.005 e Å−3) of charge redistribution between the v1/9 sheet and Au as well as between the v1/6 sheet and Cu. Yellow and blue colors represent the electron accumulation and depletion regions, respectively. Boron and metal atoms are colored in pink and black, respectively. Reprinted with permission from ref. 38. Copyright 2015 Wiley.

3.3 Experimental synthesis of borophenes

Crystalline boron nanostructures. Since the prediction of 2D boron, many experimental attempts have been dedicated to realizing this long-sought material. Early experiments have synthesized boron nanowires,99–105 nanoribbons,106–109 nanobelts110–113 and whiskers,107 yet all these 1D boron nanostructures either are amorphous or inherit lattice structures from bulk boron. The synthesis methods for fabricating these boron nanostructures comprise non-catalytic and catalytic methods: the former include laser ablation, magnetron sputtering, pyrolysis of diborane, etc., while the latter include CVD using metal alloys as catalysts. It is likely that the absence of 2D sheets from these experiments is due to the lack of a catalytic surface for guiding the boron growth to follow the 2D route. Moreover, the fact that precursors are not pure boron sources may also be detrimental to the nucleation of 2D boron. It is worth mentioning that several research groups have reported growth of single-walled88 and multiwalled89 boron nanotubes, but the tube walls seem to be crystalline, not layered as in borophenes discussed in this review. Further details on the synthesis, characterization and device applications of 1D boron nanostructures can be found in the dedicated review.114

Very recently, the first 2D boron nanofilms were reported by Tai et al. using the conventional CVD method.115 In their experiment, a mixture of boron and boron oxide powders was heated, to form diboron dioxide vapor at ∼1400 K, and then deposited onto Cu foils for growth at ∼1300 K. Nevertheless, the obtained centimeter-wide nanofilms were not the monoatomic layers discussed here but were rather ∼0.8 nm thick, indicating that the growth of borophenes required a more delicate process.

2D boron monolayers. Following the theory guidelines38,39 and perhaps their own intuition, Guisinger and coworkers40 have indeed realized monolayer boron sheets on Ag(111) using the molecular beam epitaxy method by direct evaporation of a pure boron source on a clean, single-crystal Ag(111) surface. The boron sheets were characterized to be atomically thin and hundreds of nanometres wide (Fig. 6a and b). Scanning tunneling microscopy (STM) characterization revealed that the monoatomic boron layers not only were really expansive but exhibited different phases depending on the deposition rate. A low deposition rate favors a flat striped phase consisting of a rectangular lattice (Fig. 6c), while increasing the deposition rate increases the coverage of a homogeneous phase appearing as periodically protruded atomic chains (Fig. 6d) in STM images. Moreover, increasing the temperature can transform the flat phase into a new striped phase with periodic nanoscale corrugations. The corrugated stripes are fewer at temperature below 720 K but can reach full coverage as the temperature is increased to ∼1000 K.
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Fig. 6 Experimentally synthesized borophenes on silver. (a and b) Large-scale STM topography images of 2D boron with (a) low (Vsample = 2.0 V, It = 100 pA) and (b) medium coverages (Vsample = 3.5 V, It = 100 pA). Red, white and blue arrows denote regions of homogeneous-phase, striped-phase islands and striped-phase nanoribbons, respectively. (c) STM images of atomic-scale structures for the striped phases (Vsample = 0.1 V, It = 1.0 nA), showing a coexistence of flat and corrugated regions. The inset shows a rectangular lattice with overlaid lattice vectors. (d) STM images for the homogeneous phase (Vsample = 0.1 V, It = 1.0 nA). Reprinted with permission from ref. 40. Copyright 2015 American Association for the Advancement of Science. (e) STM image of 2D boron annealed at 650 K. S1 and S2 indicate two different phases. (f and g) High-resolution STM images of (f) S1 and (g) S2 phases recorded with Vsample = 1.0 V. The black rectangle shows the unit cell of the S1 phase, and solid lines denote stripes with 1.5 nm periodicity. The image in g zooms in the region marked by a black square in e and the inset is an image zoomed from g. Reprinted with permission from ref. 41. Copyright 2016 Nature Publishing Group.

Concurrently, Feng et al.41 performed the synthesis of monolayer boron islands (tens of nanometres wide) on Ag(111) by means of essentially the same method (Fig. 6e). Their results also confirm their inherent polymorphism. The samples grown at ∼570 K show a rectangular lattice with parallel atomic rows in the STM image, referred to as the S1 phase (Fig. 6f), closely resembling the flat striped phase reported by Guisinger et al.40 When the temperature is increased to 680 K, a new S2 phase consisting of parallel chains was formed (Fig. 6g). The S2 phase can also be transformed from the S1 phase upon annealing the sample to 650 K. This phase exhibits parallel atomic rows as well, yet with alternating brighter and darker segments and a shorter inter-row spacing than that in the S1 phase. The segments are organized in a compact “brick wall” pattern, very similar to the homogeneous phase produced by Guisinger et al.40 These connections between the two independent experiments underscore the importance of identifying the atomic models for these boron phases.

Atomic models of synthesized 2D boron. Just months prior to the reported experimental realization of borophenes, Zhang et al.38 predicted by global minimum search that the v1/6 sheet, with parallel HH rows spaced by rows of filled hexagons, is the ground state on Ag(111). It was then rather gratifying that the so-called S1 phase in experiment34 was identified to be the very same atomic structure as the v1/6 sheet (Fig. 7a, top), as supported by simulated STM images (Fig. 7a, bottom) and further corroborated by estimating the density of boron atoms.41 Such an example case of theory guiding the actual synthesis realized within such a short period of time is rare and very encouraging. It is worth mentioning that the triangular sheet (Fig. 7b, top) was proposed as an atomic model for the flat striped phase in ref. 40, on the basis of a simulated STM image, and apparently it captures the key features of experimental images as well (Fig. 7b, bottom). This discrepancy in model-interpretation is in itself interesting, since the so-called S1 and flat striped phases look very similar in the STM image. The two models have been widely adopted for further exploration of intrinsic properties and potential applications of borophenes. Based on current experimental characterization, it remains premature to unambiguously affirm which model is the right one. To stimulate further study, we provide two arguments that better support the v1/6 sheet.
image file: c7cs00261k-f7.tif
Fig. 7 Structural models of 2D boron on silver. (a) Atomic structure of (top) the v1/6 sheet and (bottom) simulated STM image, proposed for the flat striped phase in Fig. 6c and the S1 phase in Fig. 6f. (b) Atomic structure of the triangular sheet and simulated STM image, resembling the STM image for the striped phase as well. (c) Atomic structure of the v1/5 sheet and simulated STM image, proposed for the S2 phase shown in Fig. 6g. Vsample is set to 1.0 V for all the STM simulations in constant current mode. The red and black balls denote boron and Ag atoms, respectively. Images were newly simulated and are consistent with those in ref. 40, 41 and 116.

First, ab initio calculations show that the v1/6 sheet is 41 meV per atom more stable than the triangular sheet on Ag(111)116 and matches the lattice constants of Ag(111) (only ∼1% mismatch) better than the triangular sheet (∼3.1% off). Second, Zhang et al.116 have found that the v1/6 sheet can energetically accommodate and even favor periodic nanoscale undulations on concertedly reconstructed Ag(111), by virtue of its anisotropic high bending flexibility. Such an undulated v1/6 sheet can well explain the corrugated phase transformed from the flat striped phase40 in terms of topography, wavelength, Moiré pattern, and prevalence of vacancy defects.116 In contrast, the triangular sheet has a finite thickness, which makes the energy cost of corrugation across its ridges prohibitively high,117 unless a structural transition from the triangular to the v1/6 sheet occurs before the flat-to-corrugated transformation. Such a structural transition lacks evidence in view of the coherent atomic lattice across the interface between the corrugated and flat regions (Fig. 6c). In spite of these arguments, further experimental characterization and theoretical analyses are encouraged to discriminate between the atomic models for these boron phases. Theoretically, an atomistic understanding of growth kinetics and morphology of borophenes will be particularly helpful.

In addition, Feng et al.41 proposed a v1/5 sheet (labeled χ3) as an atomic model for the S2 phase (Fig. 7c, top). On Ag, the v1/5 sheet is nearly as stable as the v1/6 sheet, with energy difference being within mere 2 meV per atom. Simulated STM images reveal a rhombohedral brick-wall pattern (Fig. 7c, bottom), consistent with experimental images. The stripes with alternate dark and light segments are from the HH rows while the rows of filled hexagons are located between the stripes (Fig. 7c, bottom), in contrast to the case of the v1/6 sheet, in which the rows of filled hexagons correspond to the light stripes in the STM image (Fig. 7a, bottom). The v1/5 model was supported by a subsequent theoretical study45 and may also account for the homogeneous phase reported in ref. 40. Another notable fact is that Mannix et al. found that lowering the temperature favors the growth of their homogeneous phase, in contrast to observations by Feng et al.41 that the S2 phase is preferred at higher temperature. Mannix et al. suggested that the homogeneous phase (v1/5 sheet) is metastable relative to the striped phase (v1/6 sheet), whereas Feng et al.41 concluded that the S2 phase (v1/5 sheet) is more stable than the S1 phase (v1/6 sheet). This contrast suggests that the growth of borophenes should be determined by an intricate interplay of more factors, such as substrate condition and deposition rate, which calls for an intensive experimental study. Using the same experimental conditions as those in ref. 41, Zhong et al. recently reported a new boron phase with hexagonal symmetry on Ag(111), proposed to be the well-known α-sheet.118

3.4 Basic properties of 2D boron

Mechanical properties. Being made up of classical covalent bonds and metallic-like multicenter bonds, borophenes exhibit unique mechanical properties.117,119–124 In general, the covalent bonds endow the sheet with considerable strength while the metallic-like multicenter bonds make the structure potentially fluxional. The in-plane stiffness of the synthesized v1/6 sheet is 218 N m−1 and 205 N m−1 along and across the HH rows,125 respectively, both comparable to graphene's 338 N m−1. As long as the 2D boron contains HHs, the in-plane stiffness shows trivial dependence on v, mainly because the elasticity is dominated by deformation around the HHs.117 Having no HH, the buckled triangular sheet is highly anisotropic, with a stiffness of 398 N m−1 along its ridges34,100 and only 163 N m−1 across the ridges. On the other hand, borophenes are flexible during out-of-plane bending. The bending modulus of the v1/6 sheet is as low as 0.39 eV along the HH rows, about one fourth of graphene's value, and increases to 0.56 eV across the HH rows, showing stronger anisotropy than its in-plane elasticity.117 All other boron sheets with HHs have higher bending moduli but the values remain much smaller than that of graphene. The excellent in-plane stiffness and unusual off-plane flexibility open the possibility of using 2D boron layers as reinforcing elements in advanced composites. Again, the triangular sheet has an exceptionally large bending modulus of 4.9 eV along the ridges due to its off-plane buckling.

Of more interest is the ideal strength of borophenes. It has been shown that the v1/6 sheet has ideal strengths of 14 N m−1 and 15 N m−1 along and across the HH rows, respectively, close to that of 2D MoS2125 and significantly higher than those of phosphorene126,127 and silicene,128 yet the critical strains are in the range of 10–15%,117,122 much lower than that (∼25%) of graphene. Beyond the critical strain, the 2D boron does not undergo structural failure as in the case of other 2D materials, but experiences a structural phase transition. As the tensile strain increases, B atoms become increasingly easy to re-organize, in a manner that expands the sheet area via an increase of HH concentration and thereby relieves the tension. The structural phase transition could toughen the material further, to an extent that it could resist large load even when extremely stretched. Note that the HHs are critically important for the ductile breaking process. Having no HH, the triangular sheet becomes brittle during structural stretching, with the breaking strain estimated to be as low as ∼8% when stretched along the ridges.100,104

Electronic properties. While the organizations of chemical bonds in 2D and 3D forms of boron are similar, all 2D boron polymorphs are metallic,32,34 in contrast to the insulating nature of their 3D forms. Fig. 8a and b present the band structures129 of the v1/6 and v1/5 sheets, respectively, calculated using the local density approximation (LDA). The metallic states are mostly derived from the 2pz state, which is highly delocalized over a large energy window around the Fermi level. In the case of the v1/5 sheet, the metallicity is also in part contributed by the 2px and 2py states, which otherwise form a band gap near the Fermi level in the sheets with v = 10–15%.34 The predicted metallicity was confirmed by recent experimental measurements.40–42 In particular, Feng et al.42 performed a detailed analysis of electronic properties of the S1 phase (v1/6 sheet) on Ag(111) using angle-resolved photoemission spectroscopy (ARPES). Their measurements detected the metallic bands derived from boron (Fig. 8c) and found that its Fermi surface on Ag(111) is composed of one electron pocket (B1), centered at the M point, and a pair of electron pockets (B2 and B2′), in the vicinity of the X point (lower-right panel in Fig. 8c).
image file: c7cs00261k-f8.tif
Fig. 8 Electronic properties of 2D boron sheets. (a and b) LDA band structures of (a) the v1/6 and (b) v1/5 sheets in a vacuum. Black solid lines in (a) are single-orbital (pz) tight-binding bands, using t ≈ 1.4 eV, and ε2pEF ≈ −1.2 eV. Reprinted with permission from ref. 129. Copyright 2012 American Chemical Society. (c) ARPES intensity plots of the borophene in the S1 phase on silver at EEF = −100 meV,42 taken along different lines in the Brillouin zone, labeled by 1–3 in the inset, where the green lines denote the Brillouin zone of Ag(111). B1–B6 mark the bands of 2D boron and sp marks the bulk sp bands of Ag(111). The intensity plot in the inset is taken at the Fermi surface, i.e. EEF = 0 meV. Both EF and εF denote the Fermi level. Reprinted with permission from ref. 42. Copyright 2016 American Physical Society.

A Dirac-cone-like feature can be identified already in the pz-derived bands of the v1/6 sheet, appearing at ∼2 eV above the Fermi level EF along ΓX, as shown in Fig. 8a. Such band topology can be understood within the simplest single-orbital tight-binding model of this sheet, with just two parameters: the B 2pz on-site energy, ε2p, and the hopping integral between pz orbitals on nearest-neighbor B atoms, t > 0. Following ref. 130 for instance, the tight-binding Hamiltonian takes the simple form:

image file: c7cs00261k-t1.tif(2)
where hx = 1 + exp(ikx), hy = exp(iky), and −πkiπ (i = x, y) are the 2D quasi-momentum components. The corresponding band structure is superimposed as black solid lines in Fig. 8a, using t ≈ 1.4 eV (approximately half of that in graphene131), and ε2pEF ≈ −1.2 eV to match the position of the two lowest pz states of the LDA-calculated bands at the Γ point. Note that even this simple model exhibits two (somewhat “deformed”) conical band crossings in the Brillouin zone (Fig. 9), with Dirac points located at ±⅔X. A more elaborate tight-binding treatment is given in ref. 132 and 133. Interestingly, Feng et al. indeed observed Dirac cones in the v1/6 sheet on an Ag(111) substrate in a recent ARPES experiment.133 However, their observed Dirac cones are located ∼0.25 eV below EF, in contrast to the level of ∼2 eV above EF for the cones shown in Fig. 9. Since theoretical calculations revealed that the Ag substrate can shift EF of the v1/6 sheet upward by only ∼0.7 eV, the origin of the observed Dirac cones would require a deeper theoretical analysis. It is possible that the v1/6 sheet possesses more Dirac cones other than those captured in Fig. 9, due to its multiple sublattice sites and a rectangular symmetry. Nevertheless, these ARPES experiments36,115 provide solid evidence for another elemental 2D material with massless Dirac fermions, along with graphene and silicene.

image file: c7cs00261k-f9.tif
Fig. 9 Dirac cones in the tight-binding bands of the v1/6 sheet (see also Fig. 8a). Band surfaces are rendered in the energy window ±t/2 relative to the Dirac-point energy, with positive and negative leaves shown in different colors.

The light weight of boron suggests possibly strong electron–phonon coupling, which, along with the intrinsic metallicity, may give rise to conventional, phonon-mediated superconductivity. First-principles calculations129 indeed supported intrinsic superconducting behavior, with critical temperature Tc estimated in the range of 10–20 K, depending on the HH concentration. The Tc values are higher than the theoretically computed Tc ≈ 8 K134 and experimentally measured ∼6 K135 for Li-decorated graphene. Possible superconductivity is also suggested for thicker boron films.136 This result renders 2D boron an attractive testbed for exploring the true 2D limit of conventional superconductivity. It is worth noting that accurate DFT calculations129 reveal characteristic phonon instabilities in the free-standing polymorphs. On a suitable metal substrate, such supported polymorphs would be naturally stabilized, but stronger adhesion, for instance, may eventually reduce Tc. Such suppression of Tc seems to be suggested in subsequent calculations for the triangular B sheet (Fig. 3c, left) on Ag(111).137 It is plausible, however, that 2D boron is stabilized by an inert protecting layer such as 2D hexagonal h-BN, in which case the superconducting behavior may well be preserved.

Furthermore, borophenes can be used to possibly build thick 2D boron structures with novel electronic properties. Global minimum search based on evolutionary algorithms identified a boron nanofilm with Pmmn symmetry, which has a distorted Dirac cone near the Fermi level.36 Later on, a 2D ionic boron, composed of a layer of vertically arranged B2 dimers sandwiched by two graphene-like boron planes, was reported to have double Dirac cones.138 All these boron nanofilms have a honeycomb lattice as the skeleton and the remaining boron atoms as donors, which make the honeycomb skeleton isoelectronic to graphene, thereby creating the Dirac-like electronic states. In hindsight, this justifies and explains the success of the first cluster-expansion study,34 which essentially assumed a ‘configurationally inactive’ boron honeycomb sublattice in the attempt to explore configurational diversity of 2D boron polymorphs. Using an evolutionary approach, He et al. reported a boron nanofilm on Pb(110) with a graphene-like structure, comprising three inter-bonded atomic layers, which has peculiar double Dirac cones.139 Recently, a boron nanofilm composed of B20 clusters arranged in a hexagonal network was predicted to have antiferromagnetic ordering.140 Structurally being closer to bulk boron, these thicker boron nanofilms are lower in energy than monolayer borophenes, but their existence still lacks experimental support.

Chemical properties. The boron sheets were demonstrated to be quite inert to oxidation,41 which should be ascribed to their high planarity that may stabilize electronic states in a similar way to electronic conjugation in graphene. A certain content of oxygen was detected in borophene samples upon exposing to air under ambient conditions, but the oxidation was found to occur mostly at the edges of boron islands, which are chemically reactive due to active edge states. Instead, the regions with perfect lattice remain almost intact, even when the samples are exposed to high doses of oxygen. Nevertheless, the borophenes cannot compete with other popular 2D materials (e.g., graphene) in terms of chemical stability and can be readily contaminated upon long-time exposure to air, as demonstrated by Guisinger et al.40 This is in line with the previous prediction that boron sheets on metals are reactive enough to serve as a catalyst for the hydrogen evolution reaction.38 Such a chemical property has never been possessed by other 2D materials (at least until the recent discovery of catalytically surface-active metal dichalcogenides141) and could be harnessed for achieving a rich spectrum of functionalities through functionalization with various chemical species, such as hydrogen that could result in 2D boron hydrides with Dirac fermions.120,142–144 Meanwhile, it also highlights the need for developing packing techniques for fabricating air-stable borophene-based devices. For example, the boron sheets could be sealed from air by depositing a capping layer. Guisinger et al.40 have demonstrated that the oxidation of borophenes can be greatly impeded by a silicon/silicon oxide capping layer.

The 2D boron is predicted to have a high capability of accommodating point defects. For a flat v1/6 sheet on Ag(111), the formation energy is estimated to be in the range of 1.8–3 eV for a monovacancy and 2.4–4.2 eV for a divacancy,116 depending on the defect site in the lattice, much lower than ∼7.5 eV145,146 for a monovacancy in graphene. The low formation energies of vacancies are attributed to the unusual atomic reconstruction near the defect that efficiently passivates the dangling bonds thereof. The defect-induced reconstruction is facilitated by the delocalized multicenter bonds and thus offers greater energy relief than those in other strongly covalent 2D materials.

4. Challenges to move forward

While borophenes have been synthesized, moving this new material into physical experimentation or even practical applications is hampered by a number of issues. The urgent issues would be the transfer of borophenes from Ag(111) as well as the controlled synthesis of large-scale, high-quality samples. In this section, we analyze these challenges and discuss possible directions to align future works.

4.1 Transfer of 2D boron

Prior to transfer, it is important to know how strongly borophene adheres to the Ag surface. Earlier estimates39 indicated weak adhesion on the (111) surfaces of Ag and Au. The adhesion energy between the v1/6 sheet and Ag(111) is γ = 0.04 eV Å−2,116 only twice that (0.02 eV Å−2) for graphene to Cu(111).147 However, the chemical reactivity of 2D boron precludes the use of common transfer methods adopted for graphene, especially those involving solutions. Actually, silicene has a much stronger adhesion on Ag than borophenes, but even silicene has been sufficiently cleanly transferred from Ag(111) substrates via an encapsulated delamination method.148 Compared to silicene, borophenes have higher in-plane stiffness and excellent flexibility against bending.117 These facts lead one to propose a transfer method by peeling borophenes off the substrate, in a manner similar to mechanical exfoliation of graphene. The transfer process is schematically illustrated in Fig. 10, including the following key steps: (i) attaching a metal pad at one end of the boron domain, (ii) lifting the pad to progressively peel the 2D boron off the silver, (iii) transferring the detached boron layer onto a target substrate and (iv) removal of the pad. To make sure that the boron layer will not fall off the pad during the transfer, the pad must adhere with boron more strongly than Ag and should be as wide as the boron domain in the direction perpendicular to the movement; in principle, the mechanical configuration can be optimized quantitatively, to reduce experimental trial-error expense. Previous DFT calculations38 indicated that Cu and Ni can serve as the pad. The threshold force for lifting can be estimated as f = = 0.04w eV Å−1, where w is the width of boron islands. This method appears promising for separating borophenes once the process can be carefully controlled, even though further improvement may be warranted.
image file: c7cs00261k-f10.tif
Fig. 10 Schematic illustration of separating borophenes from silver. Key steps: adhesive pad attached, lift from Ag, mechanical transfer of boron onto a target substrate and pad removal.

4.2 Large-scale synthesis of 2D boron

Controlled synthesis of large-scale, quality samples is another prerequisite for realizing any prospective industrial applications of 2D boron. Toward this end, the CVD method remains as the first choice. However, years of attempts using this method resulted in amorphous structures,103,149,150 clumps, or thick films.115 By closely examining their growth conditions and precursors, we provide several recipes that may help the CVD synthesis of borophenes.

The growth temperature is the first critical factor. High temperature may activate the nucleation along the 3D route and yield boron films, whereas low temperature cannot overcome the barrier required for 2D growth and results in amorphous clusters.41 Thus, the growth temperature needs to be carefully controlled, to an extent that it is enough to activate the 2D nucleation but not for 3D nucleation. Second, the precursors should be purified boron. Other elements mixed in the precursors, such as hydrogen and oxygen, may stabilize the 3D-nucleus by passivating dangling bonds on its surfaces and thereby suppress the corresponding nucleation barrier. According to ref. 115, the presence of oxygen in the precursors might be one of the reasons for the yield of boron nanofilms. Third, an atomically flat metal substrate is ideal for producing large-scale boron islands. Rough substrates could favor the nucleation of 3D clusters due to local increase of interaction area, thus not conducive to 2D growth. Other factors, such as deposition rate and vapor pressure, should also be carefully tested.

5. Perspective

5.1 Hybrids with other 2D materials

Electronic devices often require the integration of different materials with electronically distinct properties. The application of borophenes in nanodevices will be greatly promoted by the fabrication of hybridized atomic layers composed of borophenes and other 2D materials. Electronically, borophenes are the first metallic 2D material made of a light element, in contrast to other 2D materials that often have a band gap. Interfacing boron sheets with other semiconducting 2D materials could generate, e.g., 2D metal–semiconductor co-planar junctions.151 It will be useful to see what 2D materials can form an ohmic contact with borophenes and what materials result in what degree of Schottky barrier. The in-plane heterostructures with an ohmic contact would allow the integration of semiconducting channels and electrodes within one material, while those with a Schottky barrier can be used to design atomically thin diodes and transistors. Very recently, Liu and coworkers152 demonstrated spontaneous formation of borophene/organic lateral heterostructures by depositing perylene-3,4,9,10-tetracarboxylic dianhydrides onto submonolayer borophene on Ag(111) substrates. The heterostructures were connected by weak chemical interaction between the borophene and organic molecules, with the interface revealed to be electronically abrupt.131 On the other hand, sandwiching the borophenes between insulating h-BN layers will allow an electrically conductive atomic layer encapsulated by chemically inert, thermally stable, atomically smooth skins. Such a system is expected to well preserve the intrinsic properties of borophenes, ideal for fabricating high performance borophene-based devices.

5.2 Other possible novel properties

Since borophenes are strongly metallic, they should exhibit intrinsic plasmons confined in 2D space to allow novel manipulation of light. In particular, the 2D boron can carry a high conductive electron density, σ, independent of the Fermi level, opening a possibility to extend the plasmon energy (frequency ωpl ∝ √σ) into the near-visible range, in contrast to graphene where plasmons, despite being controllable by gating, are usually at mid-infrared and longer wavelength.153,154 The light–metal interaction in 2D boron may be further enhanced by combining with conventional plasmonics, such as noble metals. In addition, the intrinsically metallic 2D boron will accommodate the 2D electron gas that could give rise to a quantum Hall effect under strong perpendicular magnetic fields. Yet, observing the quantum Hall effect should be facility-demanding, because electronic mobility in such type of 2D metal is relatively low, so that the energy distances between Landau levels are too small to easily discern in experiments.

5.3 Potential applications

The lightweight and excellent mechanical properties of 2D boron can be harnessed in designing advanced composites. For one thing, the 2D boron can resist a large load, comparable to graphene, before failure. For another, the reactivity of 2D boron facilitates covalent bonding to the host-matrix that enables efficient load transfer. Experimental effort along this direction is highly encouraged. The abundance of structural information on 2D boron also prompted studies of their electronic transport properties.155,156 Boron nanotubes, especially those rolled up from the α sheet, are predicted to be electrically more conductive155 than carbon nanotubes. These results suggest the possibility of using boron nanotubes as interconnects and contacts in future nanoscale devices, which circumvents the issue of chirality dependence of electrical conductivity in carbon nanotubes. Recent synthesis of ∼10 nm narrow borophene nanoribbons on Ag(110) substrates opens another dimension of controlling electronics of such interconnects by their width.157 In theory, ultimately thin ribbons would be more stable as a 2-atom-wide metallic ribbon than as a single-atom chain, while stretching should switch it to a chain-like semiconductor.158,159 In addition, the excellent structural flexibility makes metallic borophenes promising for potential applications in the emerging flexible electronics.

Borophenes also appear to be attractive materials for energy storage. Their capacities of hydrogen storage have been compared to those of graphene.160 The binding of molecular hydrogen to the boron sheet is stronger than that to graphene, due to its more reactive basal plane. It has also been found that dispersion of alkali metal (Li, Na, and K) atoms onto the boron sheet markedly increases hydrogen binding energies and storage capacities. Meanwhile, the 2D boron provides a template for creating a stable lattice of strongly bound metal atoms with a large nearest neighbor distance. When coated with Ca and Sc, α-boron sheets are found to be excellent adsorbents for ambient CO2 capture with remarkably high adsorption energies of up to 3.0 eV.161 Other theoretical studies also revealed boron sheets as a promising electrode material with high electrochemical performance for both Li-ion and Na-ion batteries.162–165 However, all these works missed to notice that borophenes may undergo structural phase transition upon adsorption of metal atoms as a result of electronic donation from the adsorbates, which requires further examination.

Since boron can combine with most of other elements, it has been used for designing new compound 2D materials. At present, theoretical works have explored the stability of 2D SixB1−x,166 CxB1−x,167,168 and BP169 monolayers. The 2D silicon borides and boron carbides are all metallic, regardless of the stoichiometry, whereas the 2D boron phosphides are polymorphic and can be metallic or semiconducting depending on whether the boron atoms are dimerized or not. In addition, the 2D boron has been used as the basis in the efforts for uncovering new 2D metal borides through combining with various metals. BeB2,170 TiB2,171 BeB2,172 FeB6173 and FeB2174 monolayers have been demonstrated to possess satisfactorily high stability and intriguing properties. In particular, the TiB2, BeB2, and FeB2 sheets possess Dirac-like electronic dispersion near the Fermi level. Note that the Dirac states in the TiB2 and FeB2 sheets primarily originate from metal atoms forming a triangular network and bear lesser contribution from the layer of honeycomb boron lattices. Furthermore, two-dimensional Dirac materials can be designed by insertion of chemical elements into borophene, as β12-XBeB5 (X = H, F, Cl).175

6. Conclusions and outlook

Despite being the fifth element, boron offers more puzzles in its structural organization than its neighbors in the periodic table. It displays multiple bulk phases, and its nanostructures are even more diverse, ranging from planar and cage-like clusters, 1D nanotubes and nanowires to 2D sheets and nanofilms. In particular, the 2D boron is of special interest as a potentially new material and as a conceptual precursor for boron nanostructures of other dimensionalities. Moreover, the metallic character of 2D boron makes it complementary to graphene, h-BN, and transition metal dichalcogenides that are bound to serve as ultimate building components in future devices. However, borophenes exhibit inherent polymorphism and are less stable than all bulk phases, imposing a challenge for their synthesis. Here, we have reviewed current theoretical progress in proposing atomic structures, predicting physical properties and exploring potential applications of 2D boron as well as experimental discoveries and further advances in synthesizing this long-sought material. We particularly focused on elucidating the pioneering role of theory in the creation of 2D boron: from understanding the structures and bonding, to offering practical routes for synthesis, to accurately identifying the atomic structure that 2D boron should have on several technologically important substrates. Benefiting from theoretical suggestions, recent experiments have successfully realized borophenes on silver using the molecular beam epitaxy method, which not only confirmed their structural polymorphism and metallicity but also uncovered the same atomic model on the same substrate as theory predicted earlier. One can already argue that these developments from a theoretical concept, to search and to realization, offer a showcase-example of materials genome initiative (MGI) whose mission is to discover and deploy advanced materials twice faster, at a fraction of the cost.176 However, many issues remain on the way to using this material, calling for continuous joint efforts from both theorists and experimentalists. First, more intensive theoretical works are anticipated to discover new models of 2D boron in different environments, reveal how the material is grown from an atomistic point of view, and explore novel properties for extending applications. Second, experimental attempts should be dedicated to developing efficient transfer methods for lifting borophenes off substrates and more practical CVD methods that allow controlled growth of large-scale samples. To motivate interest and in an attempt to guide further research, we have discussed possible routes towards addressing these issues experimentally. Finally, based on the properties borophenes have shown, we also discussed their potential applications, such as designing 2D heterostructures, advanced composites and energy storage materials as well as fabricating flexible electronics.

Conflicts of interest

There are no conflicts to declare.


We gratefully acknowledge support by the Department of Energy BES grant DE-SC0012547, and by the Office of Naval Research grant N00014-15-1-2372. Z. Z. also acknowledges the support of NSFC (11772153).

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