Helium separation via porous silicene based ultimate membrane

Highly efficient helium purification through a dual-membrane system: insights from molecular dynamics simulations

Almost all helium is resourced from natural gas reservoirs. Hence, it is essential to develop new efficient technologies to recover helium from natural gas. In this work, we propose a novel dual membrane system, consisting of C2N (M1) and graphdiyne (M2) membranes, to separate and purify helium from a ternary gas mixture of He/N2/CH4. In this regard, we performed molecular dynamics (MD) simulations to investigate the separation performance of the proposed system. Here, we explored the effect of applied pressure (up to 2 MPa) and the feed composition on the separation performance. The simulation results revealed that in the designed system, the M1 membrane allows He and N2 to diffuse through and prevents CH4 from crossing even at an applied pressure gradient. Next, the M2 membrane only allows He to transfer through and prevents N2 from crossing even at the applied pressure gradient. As a result, the dual membrane system showed a high He permeance of 2.5 × 106 GPU and ultrahigh He selectivity. In addition, the suggested dual membrane system could separate three components simultaneously at the applied pressure of 2 MPa, which implies the outstanding performance of the system. We also analyzed the density map, the van der Waals interactions, and the potential of the mean force calculations to better understand the permeation of gas species across the designed system.

Highly anisotropic and ultra-diffusive vacancies in α-antimonene

α-Antimonene has recently been successfully fabricated in experiment; hence, it is timely to examine how various types of point defects in α-antimonene can affect its novel electronic properties. Herein, we present a comprehensive investigation of a total of nine possible types of point defects in α-antimonene via first-principles calculations. Particular attention is placed on the structural stability of the point defects and the effects of point defects on the electronic properties of α-antimonene. Compared with its structural analogs, such as phosphorene, graphene, and silicene, we find that most defects in α-antimonene can be more easily generated, and that among the nine types of point defects, the single vacancy SV-(5|9) is likely the most stable one while its presence can be orders of magnitude higher in concentration than that in phosphorene. Moreover, we find that the vacancy exhibits anisotropic and low diffusion barriers, of merely 0.10/0.30 eV in the zigzag/armchair direction. Notably, at room temperature, the migration of SV-(5|9) in the zigzag direction of α-antimonene is estimated to be three orders faster than that along the armchair direction, and also three orders faster than that of phosphorene in the same direction. Overall, the point defects in α-antimonene can significantly affect the electronic properties of the host two-dimensional (2D) semiconductor and thus the light absorption capability. The anisotropic, ultra-diffusive, and charge tunable single vacancies, along with the high oxidation resistance, render the α-antimonene sheet a unique 2D semiconductor (beyond the phosphorene) for developing vacancy-enabled nanoelectronics.

Efficient Helium Separation with Two-Dimensional Metal-Organic Framework Fe/Ni-PTC: A Theoretical Study

Helium (He) is one of the indispensable and rare strategic materials for national defense and high-tech industries. However, daunting challenges have to be overcome for the supply shortage of He resources. Benefitted from the wide pore size distribution, sufficient intrinsic porosity, and high specific surface area, metal–organic framework (MOF) materials are prospective candidates for He purification in the membrane-based separation technology. In this work, through first-principles calculations and molecular dynamics (MD) simulations, we studied the permeability and filtration performance of He by the newly synthesized two-dimensional Fe-PTC MOF and its analogue Ni-PTC MOF. We found that both Fe-PTC and Ni-PTC have superior high performance for He separation. The selectivity of He over N₂ was calculated to be ~10¹⁷ for Fe-PTC and ~10¹⁵ for Ni-PTC, respectively, both higher than most of the previously proposed 2D porous membranes. Meanwhile, high He permeance (10⁻⁴~10⁻³ mol s⁻¹ m⁻² Pa⁻¹) can be obtained for the Fe/Ni-PTC MOF for temperatures ranging from 200 to 500 K. Therefore, the present study offers a highly prospective membrane for He separation, which has great potential in industrial application.

First-Principles Insight into Pd-Doped C3N Monolayer as a Promising Scavenger for NO, NO2 and SO2

The adsorption and sensing behavior of three typical industrial toxic gases NO, NO₂ and SO₂ by the Pd modified C₃N monolayer were studied in this work on the basic first principles theory. Meanwhile, the feasibility of using the Pd doped C₃N monolayer (Pd-C₃N) as a sensor and adsorbent for industrial toxic gases was discussed. First, the binding energies of two doping systems were compared when Pd was doped in the N-vacancy and C-vacancy sites of C₃N to choose the more stable doping structure. The result shows that the doping system is more stable when Pd is doped in the N-vacancy site. Then, on the basis of the more stable doping model, the adsorption process of NO, NO₂ and SO₂ by the Pd-C₃N monolayer was simulated. Observing the three gases adsorption systems, it can be found that the gas molecules are all deformed, the adsorption energy (E_ad) and charge transfer (Q_T) of three adsorption systems are relatively large, especially in the NO₂ adsorption system. This result suggests that the adsorption of the three gases on Pd-C₃N belongs to chemisorption. The above conclusions can be further confirmed by subsequent deformable charge density (DCD) and density of state (DOS) analysis. Besides, through analyzing the band structure, the change in electrical conductivity of Pd-C₃N after gas adsorption was studied, and the sensing mechanism of the resistive Pd-C₃N toxic gas sensor was obtained. The favorable adsorption properties and sensing mechanism indicate that the toxic gas sensor and adsorbent prepared by Pd-C₃N have great application potential. Our work may provide some guidance for the application of a new resistive sensor and gas adsorbent Pd-C₃N in the field of toxic gas monitoring and adsorption.

High-efficiency helium separation through an inorganic graphenylene membrane: a theoretical study

Appropriate interactions between an IGP membrane and He molecules result in efficient helium separation.

Stacking stability of C2N bilayer nanosheet

In recent years, a 2D graphene-like sheet: monolayer C₂N was synthesized via a simple wet-chemical reaction. Here, we studied the stability and electronic properties of bilayer C₂N. According to a previous study, a bilayer may exist in one of three highly symmetric stacking configurations, namely as AA, AB and AB′-stacking. For the AA-stacking, the top layer is directly stacked on the bottom layer. Furthermore, AB- and AB′-stacking can be obtained by shifting the top layer of AA-stacking by a/3-b/3 along zigzag direction and by a/2 along armchair direction, respectively, where a and b are translation vectors of the unit cell. By using first-principles calculations, we calculated the stability of AA, AB and AB′-stacking C₂N and their electronic band structure. We found that the AB-stacking is the most favorable structure and has the highest band gap, which appeared to agree with previous study. Nevertheless, we furthermore examine the energy landscape and translation sliding barriers between stacking layers. From energy profiles, we interestingly found that the most stable positions are shifted from the high symmetry AB-stacking. In electronic band structure details, band characteristic can be modified according to the shift. The interlayer shear mode close to local minimum point was determined to be roughly 2.02 × 10¹² rad/s.

Generating Sub-nanometer Pores in Single-Layer MoS2 by Heavy-Ion Bombardment for Gas Separation: A Theoretical Perspective

Single-layer molybdenum disulfide (MoS₂) filters with nanometer-size pores have attracted great attention recently due to their promising performance for membrane separation. Generating nanopores in MoS₂ controllably, however, is still a challenging task, which greatly limits the real application of MoS₂ filters. In this work, the pore forming process in single-layer MoS₂ by heavy-ion bombardment was investigated in detail using molecular dynamics simulations. We found that pores with sub-nanometer size (0.6-1.2 nm) can be created in the MoS₂ sheet by single-ion bombardment, with a probability as high as 0.8 pores per incident ion. The size and shape of the nanopore can be tuned controllably by adjusting bombardment parameters. Furthermore, the performance of the MoS₂ filter with these sub-nanometer-size pores for separation of He, Ne, H₂, Ar, and Kr gases was evaluated by density functional theory-based first-principles calculations. The MoS₂ filter was found to show much higher selectivity for separating H₂/He and He/Ne than that reported for graphene and other membranes. Such high selectivity was attributed to the interaction between gases and the charged edge of pores in MoS₂. Our results suggest the potential application of ion beam technology in single-layer MoS₂ for membrane separation.

First-Principles Study on Layered C2N-Metal Interfaces

Using first-principles calculations, we perform a comprehensive study of representative metal (Al, Sc, Pd, Ag, Pt, and Au) contacts with monolayer (ML) and bilayer (BL) C₂N, which is a low-cost and easily synthesized two-dimensional metal-free semiconductor. Through analyzing the geometries, electronic structures, and Fermi level pinning effects of C₂N-metal interfaces, we find metals Al and Sc top contact with ML C₂N are Ohmic, which can be ascribed to the strong interactions and large orbital overlaps. Besides, owing to weak van der Waals interactions at interfaces and low work functions of metallic materials, Ohmic contacts can also be realized in ML/BL C₂N-Ag and BL C₂N-Sc systems. Furthermore, it was also predicted that C₂N-Sc and C₂N-Ag systems still maintain Ohmic features along the edge contacts. Given the lower resistance of the Ag electrode, the C₂N-Ag electrode should be a more attractive electrode in practical applications. These predictions not only provide insights into the fundamental properties of the layered C₂N-metal interfaces but also pave way to design high-performance devices using low-cost layered C₂N.

Gas Separation through Bilayer Silica, the Thinnest Possible Silica Membrane

Membrane-based gas separation processes can address key challenges in energy and environment, but for many applications the permeance and selectivity of bulk membranes is insufficient for economical use. Theory and experiment indicate that permeance and selectivity can be increased by using two-dimensional materials with subnanometer pores as membranes. Motivated by experiments showing selective permeation of H₂/CO mixtures through amorphous silica bilayers, here we perform a theoretical study of gas separation through silica bilayers. Using density functional theory calculations, we obtain geometries of crystalline free-standing silica bilayers (comprised of six-membered rings), as well as the seven-, eight-, and nine-membered rings that are observed in glassy silica bilayers, which arise due to Stone-Wales defects and vacancies. We then compute the potential energy barriers for gas passage through these various pore types for He, Ne, Ar, Kr, H₂, N₂, CO, and CO₂ gases, and use the data to assess their capability for selective gas separation. Our calculations indicate that crystalline bilayer silica, which is less than a nanometer thick, can be a high-selectivity and high-permeance membrane material for ³He/⁴He, He/natural gas, and H₂/CO separations.

Porous germanene as a highly efficient gas separation membrane

Using a gas separation membrane as a simple gas separation device has an obvious advantage because of the low energy consumption and pollution-free manufacturing. The first-principles calculations used in this work show that germanene with its divacancy is an excellent material for use as a hydrogen (H₂) and helium (He) separation membrane, and that it displays an even better competitive advantage than porous graphene and porous silicene. Porous germanene with its divacancy is chemically inert to gas molecules, because it lacks additional atoms to protect the edged dangling germanium atoms in defects, and thus shows great advantages for gas separation over previously prepared graphene. The energy barriers to H₂ and He penetrating porous germanene are quite low, and the permeabilities to H₂ and He are high. Furthermore, the selectivities of porous germanene for H₂ and He relative to other gas molecules are high, up to 10³¹ and 10²⁷, respectively, which are superior to those of porous graphene (10²³) and porous silicene (10¹³); thus the separation efficiency of porous germanene is much higher than that of porous graphene and porous silicene. Therefore, germanene is a favorable candidate as a gas separation membrane material. At the same time, the successful synthesis of germanene in the laboratory means that it is possible to use it in real applications.

Nitrogen-Modified Graphdiyne as a Promising Membrane for Helium Separation: First-Principles and Molecular Dynamics Simulations

The He separation performance of the N-modified graphdiyne monolayer (N-GDY) was studied by using both the first-principles density functional theory (DFT) and molecular dynamics (MD) simulations. The high cohesive energy of 7.24 eV/atom confirmed the strong stability of N-GDY for a gas separation membrane. Based on the calculations, the N-GDY membrane was found to exhibit extremely high He permeance (4.8 ×10-3 mol/m2·s·Pa at 100 K) and selectivities of He/H2O, He/Ar, He/N2, He/CO, He/CO2, and He/CH4 (102~1012 at 300 K). Therefore, N-GDY should be a good candidate for He separation from natural gas.

Silicene growth through island migration and coalescence

We perform massively-parallel classical molecular dynamics (MD) simulations to study the long timescale monolayer silicene growth on an Ir (111) surface. We observe an intricate multi-stage growth process driven by atomic and cluster migration on the surface. Initial growth involves formation of sub-nanometer clusters via adatom surface diffusion. Subsequently, these clusters rearrange spontaneously with each additional Si atom, forming clusters containing 4-7 member rings. Growth of each cluster through adatom adhesion is accompanied by the formation of larger islands through cluster migration and coalescence. Coalescence of smaller, more mobile islands into larger clusters is aided by the internal rearrangement of rings within each cluster. This flexibility, both of clusters and their constituent atoms, allows the impinging clusters to reorient after first contact and form a more perfect union. We also report on the effect of temperature and flux on the growth process and the final nanostructure. Our study provides atomistic insights into the early stage growth mechanisms of silicene which can be significant for controlled synthesis of its 2D monolayers.

Adaptively Compressed Exchange Operator for Large-Scale Hybrid Density Functional Calculations with Applications to the Adsorption of Water on Silicene

Density functional theory (DFT) calculations using hybrid exchange-correlation functionals have been shown to provide an accurate description of the electronic structures of nanosystems. However, such calculations are often limited to small system sizes due to the high computational cost associated with the construction and application of the Hartree-Fock (HF) exchange operator. In this paper, we demonstrate that the recently developed adaptively compressed exchange (ACE) operator formulation [J. Chem. Theory Comput. 2016, 12, 2242-2249] can enable hybrid functional DFT calculations for nanosystems with thousands of atoms. The cost of constructing the ACE operator is the same as that of applying the exchange operator to the occupied orbitals once, while the cost of applying the Hamiltonian operator with a hybrid functional (after construction of the ACE operator) is only marginally higher than that associated with applying a Hamiltonian constructed from local and semilocal exchange-correlation functionals. Therefore, this new development significantly lowers the computational barrier for using hybrid functionals in large-scale DFT calculations. We demonstrate that a parallel planewave implementation of this method can be used to compute the ground-state electronic structure of a 1000-atom bulk silicon system in less than 30 wall clock minutes and that this method scales beyond 8000 computational cores for a bulk silicon system containing about 4000 atoms. The efficiency of the present methodology in treating large systems enables us to investigate adsorption properties of water molecules on Ag-supported two-dimensional silicene. Our computational results show that water monomer, dimer, and trimer configurations exhibit distinct adsorption behaviors on silicene. In particular, the presence of additional water molecules in the dimer and trimer configurations induces a transition from physisorption to chemisorption, followed by dissociation on Ag-supported silicene. This is caused by the enhanced effect of hydrogen bonds on charge transfer and proton transfer processes. Such a hydrogen bond autocatalytic effect is expected to have broad applications for silicene as an efficient surface catalyst for oxygen reduction reactions and water dissociation.

Defective germanene as a high-efficiency helium separation membrane: a first-principles study

Development of low energy cost membranes for separating helium from natural gas is highly desired. Using van der Waals-corrected first-principles density functional theory (DFT) calculations, we theoretically investigate the helium separation performance of divacancy-defective germanene. The 555 777 divacancy-defective germanene presents a 0.53 eV energy barrier for helium, which is slightly larger than the energy threshold value of gas molecule penetration of a membrane (0.5 eV). Thus, the 555 777 divacancy-defective germanene is difficult for helium to permeate, except under high temperature or pressure. However, the 585 divacancy-defective germanene presents a surmountable energy barrier (0.27 eV) for helium, and it shows extremely high helium selectivities relative to other studied gas molecules. Especially, the He/Ne selectivity can be as high as 1 × 10⁴ at room temperature. Together with the acceptable permeance for helium, the 585 divacancy-defective germanene can be used for helium separation with remarkably good performance.

Efficient 3He/4He separation in a nanoporous graphenylene membrane

Efficient helium isotope separation by tunneling through a nanoporous graphenylene membrane.

A theoretical review on electronic, magnetic and optical properties of silicene

Inspired by the success of graphene, various two dimensional (2D) structures in free standing (FS) (hypothetical) form and on different substrates have been proposed recently. Silicene, a silicon counterpart of graphene, is predicted to possess massless Dirac fermions and to exhibit an experimentally accessible quantum spin Hall effect. Since the effective spin-orbit interaction is quite significant compared to graphene, buckling in silicene opens a gap of 1.55 meV at the Dirac point. This band gap can be further tailored by applying in plane stress, an external electric field, chemical functionalization and defects. In this topical theoretical review, we would like to explore the electronic, magnetic and optical properties, including Raman spectroscopy of various important derivatives of monolayer and bilayer silicene (BLS) with different adatoms (doping). The magnetic properties can be tailored by chemical functionalization, such as hydrogenation and introducing vacancy into the pristine planar silicene. Apart from some universal features of optical absorption present in all these 2D materials, the study on reflectivity modulation with doping (Al and P) concentration in silicene has indicated the emergence of some strong peaks having the robust characteristic of a doped reflective surface for both polarizations of the electromagnetic (EM) field. Besides this, attempts will be made to understand the electronic properties of silicene from some simple tight-binding Hamiltonian. We also point out the importance of shape dependence and optical anisotropy properties in silicene nanodisks and establish that a zigzag trigonal possesses the maximum magnetic moment. We also suggest future directions to be explored to make the synthesis of silicene and its various derivatives viable for verification of theoretical predictions. Although this is a fairly new route, the results obtained so far from experimental and theoretical studies in understanding silicene have shown enough significant promising features to open a new direction in the silicon industry, silicon based nano-structures in spintronics and in opto-electronic devices.

Point defects in lines in single crystalline phosphorene: directional migration and tunable band gaps

Extended line defects in two-dimensional (2D) materials can play an important role in modulating their electronic properties. During the experimental synthesis of 2D materials, line defects are commonly generated at grain boundaries between domains of different orientations. In this work, twelve types of line-defect structures in single crystalline phosphorene are examined by using first-principles calculations. These line defects are typically formed via migration and aggregation of intrinsic point defects, including the Stone-Wales (SW), single or double vacancy (SV or DV) defects. Our calculated results demonstrate that the migration of point defects in phosphorene is anisotropic, for instance, the lowest migration energy barriers are 1.39 (or 0.40) and 2.58 (or 0.49) eV for SW (or SV) defects in zigzag and armchair directions, respectively. The aggregation of point defects into lines is energetically favorable compared with the separated point defects in phosphorene. In particular, the axis of line defects in phosphorene is direction-selective, depending on the composed point defects. The presence of line defects effectively modulates the electronic properties of phosphorene, rendering the defect-containing phosphorene either metallic or semiconducting with a tunable band gap. Of particular interest is the fact that the SV-based line defect can behave as a metallic wire, suggesting a possibility to fabricate a circuit with subnanometer widths in the semiconducting phosphorene for nanoscale electronic application.

A Honeycomb BeN2 Sheet with a Desirable Direct Band Gap and High Carrier Mobility

Using global particle-swarm optimization method, we report, for the first time, a BeN2 sheet (h-BeN2) with a graphene-like honeycomb lattice but displaying a direct band gap. Symmetry group analysis indicates that the dipole transition is allowed between the conduction band minimum and the valence band maximum. Although the direct band gap of 2.23 eV is close to that (2.14 eV) of MoS2 sheet, the h-BeN2 sheet has additional advantages: the direct band gap feature of the h-BeN2 sheet is quite insensitive to the layer stacking pattern and layer number, in contrast to the well-known direct-to-indirect band gap transition observed in TMDs and h-BN sheets. When rolled up, all the resulting h-BeN2 nanotubes have direct band gaps independent of chirality and diameter. Furthermore, the intrinsic acoustic-phonon-limited carrier mobility of the h-BeN2 sheet can reach ∼10(5) cm(2) V(-1) s(-1) for electron and ∼10(4) cm(2) V(-1) s(-1) for hole, which are higher than that of MoS2 and black phosphorus.

Two-Dimensional Covalent Triazine Framework Membrane for Helium Separation and Hydrogen Purification

Ultrathin membranes with intrinsic pores are highly desirable for gas separation applications, because of their controllable pore sizes and homogeneous pore distribution and their intrinsic capacity for high flux. Two-dimensional (2D) covalent organic frameworks (COFs) with layered structures have periodically distributed uniform pores and can be exfoliated into ultrathin nanosheets. As a representative of 2D COFs, a monolayer triazine-based CTF-0 membrane is proposed in this work for effective separation of helium and purification of hydrogen on the basis of first-principles calculations. With the aid of diffusion barrier calculations, it was found that a monolayer CTF-0 membrane can exhibit exceptionally high He and H2 selectivities over Ne, CO2, Ar, N2, CO, and CH4, and the He and H2 permeances are excellent at appropriate temperatures, superior to those of conventional carbon and silica membranes. These observations demonstrate that a monolayer CTF-0 membrane may be potentially useful for helium separation and hydrogen purification.

Structural and electronic properties of zigzag InP nanoribbons with Stone-Wales type defects

By means of density-functional-theoretic calculations, we investigate the structural and electronic properties of a hexagonal InP sheet and of hydrogen-passivated zigzag InP nanoribbons (ZInPNRs) with Stone-Wales (SW)-type defects. Our results show that the influence of this kind of defect is not limited to the defected region but it leads to the formation of ripples that extend across the systems, in keeping with the results obtained recently for graphene and silicene sheets. The presence of SW defects in ZInPNRs causes an appreciable broadening of the band gap and transforms the indirect-bandgap perfect ZInPNR into a direct-bandgap semiconductor. An external transverse electric field, regardless of its direction, reduces the gap in both the perfect and defective ZInPNRs.

Calculations of helium separation via uniform pores of stanene-based membranes

The development of low energy cost membranes to separate He from noble gas mixtures is highly desired. In this work, we studied He purification using recently experimentally realized, two-dimensional stanene (2D Sn) and decorated 2D Sn (SnH and SnF) honeycomb lattices by density functional theory calculations. To increase the permeability of noble gases through pristine 2D Sn at room temperature (298 K), two practical strategies (i.e., the application of strain and functionalization) are proposed. With their high concentration of large pores, 2D Sn-based membrane materials demonstrate excellent helium purification and can serve as a superior membrane over traditionally used, porous materials. In addition, the separation performance of these 2D Sn-based membrane materials can be significantly tuned by application of strain to optimize the He purification properties by taking both diffusion and selectivity into account. Our results are the first calculations of He separation in a defect-free honeycomb lattice, highlighting new interesting materials for helium separation for future experimental validation.

H-Si bonding-induced unusual electronic properties of silicene: a method to identify hydrogen concentration

Hydrogenated silicenes possess peculiar properties owing to the strong H-Si bonds, as revealed by an investigation using first principles calculations. Various charge distributions, bond lengths, energy bands, and densities of states strongly depend on different hydrogen configurations and concentrations. The competition between strong H-Si bonds and weak sp(3) hybridization dominate the electronic properties. Chair configurations belong to semiconductors, while the top configurations show a nearly dispersionless energy band at the Fermi level. Both the systems display H-related partially flat bands at middle energy and the recovery of low-lying π bands during the reduction of concentration. Their densities of states exhibit prominent peaks at middle energy, and the top systems have a delta-funtion-like peak at E = 0. The intensity of these peaks is gradually weakened as the concentration decreases, providing an effective method to identify the H-concentration in scanning tunneling spectroscopy experiments.

Effects of stacking order, layer number and external electric field on electronic structures of few-layer C2N-h2D

Recently, a new type of two-dimensional layered material, i.e. a nitrogenated holey two-dimensional structure C2N-h2D, has been synthesized using a simple wet-chemical reaction and used to fabricate a field-effect transistor device (Nat. Commun., 2015, 6, 6486). Here we have performed a first-principles study of the electronic properties of few-layer C2N-h2D with different stacking orders and layer numbers. Because of the interlayer coupling mainly in terms of the orbital interaction, band structure of this system, especially splitting of the bands and band gap, depends on its stacking order between the layers, and the band gap exhibits monotonically decreasing behavior as the layer number increases. All the few-layer C2N-h2D materials have characteristics of direct band gap, irrespective of the stacking order and layer number examined in our calculations. And bulk C2N-h2D has an indirect or direct band gap, depending on the stacking order. Besides, when we apply an out-of-plane electric field on few-layer C2N-h2D, its band gap will decrease as the electric field increases due to a giant Stark effect except for the monolayer case, and even a semiconductor-to-metal transition may occur for few-layer C2N-h2D with more layers under an appropriate electric field. Owing to their tunable band gaps in a wide range, the layered C2N-h2D materials will have tremendous opportunities to be applied in nanoscale electronic and optoelectronic devices.

Defects in silicene: vacancy clusters, extended line defects, and Di-adatoms

Defects are almost inevitable during the fabrication process, and their existence strongly affects thermodynamic and (opto)electronic properties of two-dimensional materials. Very recent experiments have provided clear evidence for the presence of larger multi-vacancies in silicene, but their structure, stability, and formation mechanism remain largely unexplored. Here, we present a detailed theoretical study of silicene monolayer containing three types of defects: vacancy clusters, extended line defects (ELDs), and di-adatoms. First-principles calculations, along with ab initio molecular dynamics simulations, revealed the coalescence tendency of small defects and formation of highly stable vacancy clusters. The 5|8|5 ELD – the most favorable extended defect in both graphene and silicene sheets – is found to be easier to form in the latter case due to the mixed sp²/sp³ hybridization of silicon. In addition, hybrid functional calculations that contain part of the Hatree-Fock exchange energy demonstrated that the introduction of single and double silicon adatoms significantly enhances the stability of the system, and provides an effective approach on tuning the magnetic moment and band gap of silicene.

Does the Dirac cone exist in silicene on metal substrates?

Absence of the Dirac cone due to a strong band hybridization is revealed to be a common feature for epitaxial silicene on metal substrates according to our first-principles calculations for silicene on Ir, Cu, Mg, Au, Pt, Al, and Ag substrates. The destroyed Dirac cone of silicene, however, can be effectively restored with linear or parabolic dispersion by intercalating alkali metal atoms between silicene and the metal substrates, offering an opportunity to study the intriguing properties of silicene without further transfer of silicene from the metal substrates.

A first-principles study of gas adsorption on germanene

The adsorption of common gas molecules (N₂, CO, CO₂, H₂O, NH₃, NO, NO₂, and O₂) on germanene is studied with density functional theory.