Structure prediction in low dimensions: concepts, issues and examples

Structure prediction of stable and metastable polymorphs of chemical systems in low dimensions has become an important field, since materials that are patterned on the nano-scale are of increasing importance in modern technological applications. While many techniques for the prediction of crystalline structures in three dimensions or of small clusters of atoms have been developed over the past three decades, dealing with low-dimensional systems-ideal one-dimensional and two-dimensional systems, quasi-one-dimensional and quasi-two-dimensional systems, as well as low-dimensional composite systems-poses its own challenges that need to be addressed when developing a systematic methodology for the determination of low-dimensional polymorphs that are suitable for practical applications. Quite generally, the search algorithms that had been developed for three-dimensional systems need to be adjusted when being applied to low-dimensional systems with their own specific constraints; in particular, the embedding of the (quasi-)one-dimensional/two-dimensional system in three dimensions and the influence of stabilizing substrates need to be taken into account, both on a technical and a conceptual level. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Electronic and transport properties of new carbon nanoribbons with 5-8-5 carbon rings: tuning stability by the edge shape effect

We predicted the existence of five carbon nanoribbons based on POPGraphene, by first-principles calculations. We investigated the role of the shape of the edges in stability, structural, electronic, and transport properties. Density functional theory (DFT) was implemented to relax the unit cell nanoribbons, and DFT combined with non-equilibrium Greens functions was used to obtain the transport properties of molecular devices. Our results strongly suggest that all nanoribbons are stable, and can be feasibly obtained through experiment. Furthermore, the edge termination with pentarings is an important factor in the stability of nanoribbons. The electronic properties show that the three zigzag nanoribbons have a metallic behavior and the two armchair ones are semiconductors, but with a very tiny indirect bandgap of 0.053 eV and 0.050 eV. The transport properties show that the presence of partially filled steep bands crossing deeper into the Fermi level triggers high conductivity in molecular devices and the presence of flat bands decreases the device conductivity. The presence of sub-bandgap regions triggers the rise of negative differential resistance (NDR) regions in the device operation. The molecular device behavior is strongly dependent on the shape of the edges, presenting characteristics of field effect transistors (FETs), lighting emitting diodes (LEDs), or resonant tunneling diodes (RTDs), depending on the edge termination and operation range.

Emerging properties of carbon based 2D material beyond graphene

Graphene turns out to be the pioneering material for setting up boulevard to a new zoo of recently proposed carbon based novel two dimensional (2D) analogues. It is evident that their electronic, optical and other related properties are utterly different from that of graphene because of the distinct intriguing morphology. For instance, the revolutionary emergence of Dirac cones in graphene is particularly hard to find in most of the other 2D materials. As a consequence the crystal symmetries indeed act as a major role for predicting electronic band structure. Since tight binding calculations have become an indispensable tool in electronic band structure calculation, we indicate the implication of such method in graphene's allotropes beyond hexagonal symmetry. It is to be noted that some of these graphene allotropes successfully overcome the inherent drawback of the zero band gap nature of graphene. As a result, these 2D nanomaterials exhibit great potential in a broad spectrum of applications, viz nanoelectronics, nanooptics, gas sensors, gas storages, catalysis, and other specific applications. The miniaturization of high performance graphene allotrope based gas sensors to microscopic or even nanosized range has also been critically discussed. In addition, various optical properties like the dielectric functions, optical conductivity, electron energy loss spectra reveal that these systems can be used in opto-electronic devices. Nonetheless, the honeycomb lattice of graphene is not superconducting. However, it is proposed that the tetragonal form of graphene can be intruded to form new hybrid 2D materials to achieve novel superconducting device at attainable conditions. These dynamic experimental prospects demand further functionalization of these systems to enhance the efficiency and the field of multifunctionality. This topical review aims to highlight the latest advances in carbon based 2D materials beyond graphene from the basic theoretical as well as future application perspectives.

Tripentaphenes: two-dimensional acepentalene-based nanocarbon allotropes

Tripentaphenes are 2D nanocarbon lattices conceptually obtained from the assembly of acepentalene units. In this work, density functional theory is used to investigate their structural, electronic, and vibrational properties. Their bonding configuration is rationalized with a resonance mechanism, which is unique to each of the 2D assemblies. Their formation energies are found to lie within the range of other previously synthesized carbon nanostructures and phonon calculations indicate their dynamical stability. In addition, all studied tripentaphenes are metallic and display different features (e.g., Dirac cone) depending on the details of the atomic structure. The resonance structure also plays an important role in determining the electronic properties as it leads to delocalized electronic states, further highlighting the potential of the structures in nanoelectronics.

A review on role of tetra-rings in graphene systems and their possible applications

Inspired by the success of graphene, various two-dimensional (2D) non-hexagonal graphene allotropes having sp²-bonded tetragonal rings in free-standing (hypothetical) form and on different substrates have been proposed recently. These systems have also been fabricated after modifying the topology of graphene by chemical processes. In this review, we would like to indicate the role of tetra-rings and the local symmetry breaking on the structural, electronic and optical properties of the graphene system. First-principles computations have demonstrated that the tetragonal graphene (TG) allotrope exhibits appreciable thermodynamic stability. The band structure of the TG nanoribbons (TGNRs) strongly depends on the size and edge geometry. This fact has been supported by the transport properties of TGNRs. The optical properties and Raman modes of this graphene allotrope have been well explored for characterisation purposes. Recently, a tight-binding model was used to unravel the metal-to-semiconductor transition under the influence of external magnetic fluxes. Even the introduction of transition metal atoms into this non-hexagonal network can control the magnetic response of the TG sheet. Furthermore, the collective effect of B-N doping and confinement effect on the structural and electronic properties of TG systems has been investigated. We also suggest future directions to be explored to make the synthesis of T graphene and its various derivatives/allotropes viable for the verification of theoretical predictions. It is observed that these doped systems act as a potential candidate for carbon monoxide gas sensing and current rectification devices. Therefore, all these experimental, numerical and analytical studies related to non-hexagonal TG systems are extremely important from a basic science point of view as well as for applications in sensing, optoelectronic and photonic devices.

Theoretical study of electronic transport through P-porphyrin and S-porphyrin nanoribbons

Electronic transport through P-porphyrin and S-porphyrin nanoribbons have been studied by using nonequilibrium Green's function formalism (NEGF) combined with density functional theory (DFT) method. Band structure of both nanoribbons shows metallic behavior and bands near the Fermi level contain π character contributed by p_y orbital. Both nanoribbons exhibit metal-like conduction at extreme low bias. A remarkable negative differential resistance (NDR) effect is observed for both nanoribbons which is further explained with the evolution of transmission peak within energy bias window (EBW), and overlap of energy states of left and right electrodes. The low bias NDR phenomena of our proposed devices could be used in designing NDR devices including frequency multipliers, memory, and fast switches.

First-principles calculation of the electronic and optical properties of a new two-dimensional carbon allotrope: tetra-penta-octagonal graphene

A novel sp² hybridized planar 2D carbon allotrope consisting of tetra, penta and octagonal (TPO) rings is proposed in this work. Its thermodynamic stability is confirmed by molecular dynamics in the canonical ensemble at 600 K and the analysis shows that it can also remain stable at 1000 K. The mechanical stability of this material has been estimated by the Born-Huang criterion. Its in-plane stiffness constants are found to be 85% of that of graphene ensuring its high strength quality. The investigation of the electronic properties reveals that the material is metallic in nature with a Dirac cone at 3.7 eV above its Fermi level at an asymmetric position in the conduction band. The study of its optical property for parallel and perpendicular polarization yields the absence of any plasma frequency. Besides, its absorption is mostly spread within 10-20 eV. Further electrical transport study shows negative differential resistance (NDR) above 3.5 V for one nano device. Nano ribbons made out of a TPO-graphene sheet exhibit metallic character. When the porous sheet of TPO-graphene is exposed to Li and S atoms, it is found that the Li atoms pass through the pores unlike the S atoms owing to the less barrier energy compared to S atoms. Substitutional doping with boron and nitrogen at different sites of TPO-graphene showed splitting of the Dirac feature. Also suitable B and N doping brings about semiconducting properties with tunability in band gap with a maximum band gap of 1.09 eV for an isoelectronic structure. All these theoretical predictions might trigger further new avenues involving this novel TPO graphene.

A new metallic π-conjugated carbon sheet used for the cathode of Li-S batteries

Lithium-sulfur (Li-S) batteries are considered as the most promising next generation high density energy storage devices. However, the commercialization of Li-S batteries is hindered by the shuttle effect of polysulfides, the low electronic conductivity of the sulfur cathode and a large volume expansion during lithiation. Herein, we predict a new two dimensional sp2 hybridized carbon allotrope (PHE-graphene) and prove its thermodynamic and kinetic stability. If it is utilized to encapsulate the cathode of Li-S batteries, not only will the shuttle effect be avoided but also the electronic conductivity of the sulfur cathode will be improved significantly owing to its metallic electronic band structure. The thermal conductivity of PHE-graphene was found to be very high and even comparable with graphene, which is helpful for the heat dissipation of cathodes. In addition, PHE-graphene also exhibited superior mechanical properties including ideal tensile strength and in-plane stiffness.

2D carbon sheets with negative Gaussian curvature assembled from pentagonal carbon nanoflakes

Despite the good progress made in materials fabrication, it remains a big challenge to synthesize 2D sheets by assembling nanoflakes that are usually produced in experiments, and few theoretical studies have explored this topic. Based on the recent experimental synthesis of pentagonal graphene nanoflakes and the novel properties of penta-graphene, we report a series of 2D assembled carbon allotropes (CG568-80, CG568-180 and CG568-320) that have the following unusual properties: different from most other 2D carbon allotropes, the assembled carbon sheets have negative Gaussian curvatures, and exhibit ultra-softness and better chemical reactivity due to the curvature-induced misalignment of π-orbitals as compared with pristine graphene; all three studied carbon sheets are highly stable with binding energies comparable to those of phagraphene and ψ-graphene, and are semiconductors with tunable band gaps, displaying size-dependent carrier mobilities: ∼105 cm2 V-1 s-1 (CG568-80 and CG568-320) and ∼104 cm2 V-1 s-1 (CG568-180). These features indicate that assembling nanoflakes can effectively tune the structural morphology and properties to expand the family of 2D carbon materials for future applications.

Morphology-Controlled Tensile Mechanical Characteristics in Graphene Allotropes

A number of graphene allotropes constructed by sp3, sp2, and sp hybrid orbitals have recently been proposed to provide the broad potential for practical applications. Here, using molecular dynamics simulation, the structural and tensile characteristics of nine distinct graphene allotropes have been investigated to understand their morphology-controlled mechanical properties. Results show that the averaged out-of-plane displacement is independent of nonhexagons while being dominated by the arrangement of carbon polygons on the sheets. Each sheet possesses unique surface morphology and in-plane tensile properties that significantly vary with morphology and anisotropic crystalline orientation. Brittle, semibrittle, or ductile failure is observed, depending on the evolution of their packed polygons in facilitating tension deformation and in dissipating energy. Particularly, pentagraphene exhibits superductility as a consequence of large-scale structural transformations, accommodating stress relaxation beyond initial failure. Two distinct plastic deformation patterns in overstretched pentagraphene are uncovered, depending on the tension directions: one is dominated by structural transition from sp3-carbon-contained penta-(C5) to mixed sp2-carbon polygons and the other is mainly controlled by a stepwise pentagon-to-hexagon transition. These findings provide physical insights into the structural evolvement of two-dimensional graphene allotropes and their effects on the mechanical properties.

New carbon allotropes with metallic conducting properties: a first-principles prediction

Combining density functional theory computation and the global minimum structural search, we have found new α-, β-, and δ-phographene carbon allotropes.

Doped penta-graphene and hydrogenation of its related structures: a structural and electronic DFT-D study

We carried out a dispersion-corrected density functional theory (DFT-D) study of penta-C doped with Si, Ge and Sn atoms and its related hydrogenated penta-C structures (H–penta-C–X).

Theoretical two-atom thick semiconducting carbon sheet

A two-atom-thick carbon sheet, called H-net, consists of distorted squares, hexagons, and octagons with three unequal carbon atoms.