Exploring Two-dimensional Crystals with Atomic Thickness from Molecular Design and Global Structure Search
CAS Key Laboratory of Materials for Energy Conversion, School of Chemistry and Materials Sciences, CAS Center for Excellence in Nanoscience, Hefei National Laboratory of Physical Sciences at the Microscale, Synergetic Innovation of Quantum Information & Quantum Technology, University of Science and Technology of China, Hefei, Anhui 230026, China
1.1 Introduction
The isolation of graphene has attracted enormous attention due to its novel physical and mechanical properties such as high surface ratio, Dirac behavior with ballistic conductance, ultra-high ideal strength and excellent heat transport.1ā6 These properties have inspired a lot of researchers to devote their efforts to searching for graphene allotropes and other two-dimensional (2D) materials.7,8 Experimentally, several kinds of 2D materials have been synthesized by means of physical exfoliation form their three-dimensional (3D) structures or chemical methods like epitaxial growth or chemical vapor deposition, including wide band gap semiconductor-like boron nitride (BN) monolayers, black phosphorene, ferromagnetic VS2etc.9ā11 For other materials, their 3D crystals do not exist in layered structures like BeO, III-N, IV-C, Zn-VI compounds, but as the number of layers along the polarization axis decreases to a certain extent, it will transform into a graphene-like structure. Other growth methods like epitaxial growth, chemical vapor deposition or through the addition process of building blocks like small molecular are also used to fabricate 2D materials such as the topological insulator Bi2Se3, the MoS2 monolayer, the superconducting FeSe monolayer, the Rh monolayer and some covalent organic frameworks.8,12ā16 They have similar properties such as large surface ratio and atomic thickness in the non-periodic direction and have great potential in areas such as information, energy and materials.
However, structural prediction based on first-principle calculation has served as a very useful tool in the field of materials research. Exploring 2D materials with atomic thickness from molecular design and global search has been a hotspot. Naturally, a 2D material should have relatively strong intralayer bonding to retain its 2D form, so layered materials with van der Waals interactions are likely to form stable 2D materials through mechanical exfoliation, growth on specific substrates, chemical solvent separation, or functionalization.17,18 Besides, taking account of the bonding rule and existing geometrical configurations, some novel monolayers with unusual physical and mechanical properties can be designed directly. For instance, we can simply replace some atoms of the already known structures with other atoms or groups, then adjust the bonding length and angle for further calculation. Based on this strategy, 2D structures with tunable band gaps, novel magnetic properties, Dirac cone, superconductivity, or topological insulating have already been developed, which can be used in electronics, spintronics, lithium storage, hydrogen storage, and photocatalytic water splitting etc.19ā21
Based on the bonding characteristics and structural database, we can find a lot of interesting 2D materials, but various 2D sheet structures with close energies have become a challenge for determining their ground state. Furthermore, how to predict the most stable 2D structure just per their elemental composition remains a big problem. The key to solving this dazzling issue is to explore the multi-dimensional potential energy surface (PES) based on the electronic structure calculation. Since the scarcity of calculation resources, more efficient algorithms are necessary to define the optimal structures. In recent years, several global structural search algorithms are widely applied, like the particle swarm optimization algorithm, simulated annealing, genetic algorithms, basin hopping, metadynamic, random sampling, and data mining as well as the machine learning method.22ā24 Among them, two kinds of packages have been widely used to approach the problem of computational crystal structure prediction, referred to as USPEX (Universal Structure Predictor: Evolutionary Xtallography) and CALYPSO (Crystal structure Analysis by Particle Swarm Optimization), respectively.25,26 USPEX is based on the genetic algorithm and possesses the characteristics of genetic information sharing; CALYPSO is based on the particle swarm optimization algorithm and information sharing is one directional, which is good for convergence. Based on these two packages, a lot of 2D materials have been predicted, such as single element allotropes including B/C/Si/Ge/Sn/Pb; some binary compounds like carbides including Be2C, BāC, AlāC, SiāC; silicides including BāC, Cu2Si; nitrides including BāN; CāN; CrN and other compounds SiāP, Bi4F4 and so on.27ā29 The research fields have expanded from the strictly planar structure to non-planar, bilayer, multilayer, substrate-limitation, even structures in possession of specific properties. To investigate the properties of 2D structures, it is necessary to ensure the stability dynamically and kinetically in theory, especially for new structures. So, we perform the phonon-mode analysis and molecular dynamic simulation based on first principle calculations. If there are no imaginary frequencies in the Brillouin zone, and the intrinsic bonding type can sustain with a certain temperature range, we can assume it is stable. Next, further calculations will be carried out to study the electronic and mechanical structure. In this chapter, we encapsulate the research development in the prediction of 2D material including single elemental allotropes like B, C, Si, P and the BāCāN compounds. Their unique physical properties and potential applications are also studied.
1.2 Boron
Boron is one of the most fascinating elements in the Periodic Table due to its chemical and structural complexity. It is an electron deficient atom with three valence electrons distributing in four available orbitals, leading to a more complex bonding mechanism compared with typically sp2 or sp3 hybridization of carbon.30,31 This kind of bonding configuration results in as much as 16 bulk allotropes of boron, composed of icosahedral.
B12 units, small interstitial clusters, and fused supericosahedra.32,33 Meanwhile, boron clusters of medium size have been predicted to be planar and quasi-planar, for example B12ā, B13+, B19ā and B36.34ā36 The above boron molecules have shown carbon-like aromatic and anti-aromatic electronic structures and the recently proposed cage-like B40 clusters further extend the parallels between boron and carbon cluster chemistry.37 Boron has the same short covalent radius and the flexibility to adopt sp2 hybridization as carbon, which would favor the formation of various low-dimensional allotropes, such as boron nanotubes, fullerenes and 2D boron sheets. Nevertheless, a 2D boron sheet meets a large challenge in experimental preparation. The absence of layered boron materials makes it difficult to mechanically exfoliate the corresponding 2D sheet, as successfully realized in other 2D materials. Instead, numerous theoretical studies have examined 2D boron sheets. Here is a brief review of the 2D boron sheets predicted theoretically.
1.2.1 Theoretical Design
1.2.1.1 Ī±-sheet
The st...