Electronic structure of super-honeycomb systems: A peculiar realization of semimetal/semiconductor classes and ferromagnetism

Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain withs - porbitals

The topological properties of the flat band states of a one-electron Hamiltonian that describes a chain of atoms withs - porbitals are explored. This model is mapped onto a Kitaev-Creutz type model, providing a useful framework to understand the topology through a nontrivial winding number and the geometry introduced by theFubini-Study (FS)metric. This metric allows us to distinguish between pure states of systems with the same topology and thus provides a suitable tool for obtaining the fingerprint of flat bands. Moreover, it provides an appealing geometrical picture for describing flat bands as it can be associated with a local conformal transformation over circles in a complex plane. In addition, the presented model allows us to relate the topology with the formation of compact localized states and pseudo-Bogoliubov modes. Also, the properties of the squared Hamiltonian are investigated in order to provide a better understanding of the localization properties and the spectrum. The presented model is equivalent to two coupled SSH chains under a change of basis.

Field induced electron emission from graphene nanostructures

Electric fields play a crucial role in modulating the electronic properties of nanoscale materials. Electron emission, induced by an electric field, is a representative phenomenon. Experimental and theoretical aspects of such electron emission from graphene are briefly reviewed. The emission occurs at the edge of graphene flakes, not at the surface, because the edge highly concentrates the electric field. Emission currents are sensitive to the edge shapes and edge functionalization. This review provides guiding principles for designing high-efficiency field-emission devices by using graphene nanostructures.

Science of 2.5 dimensional materials: paradigm shift of materials science toward future social innovation

The past decades of materials science discoveries are the basis of our present society - from the foundation of semiconductor devices to the recent development of internet of things (IoT) technologies. These materials science developments have depended mainly on control of rigid chemical bonds, such as covalent and ionic bonds, in organic molecules and polymers, inorganic crystals and thin films. The recent discovery of graphene and other two-dimensional (2D) materials offers a novel approach to synthesizing materials by controlling their weak out-of-plane van der Waals (vdW) interactions. Artificial stacks of different types of 2D materials are a novel concept in materials synthesis, with the stacks not limited by rigid chemical bonds nor by lattice constants. This offers plenty of opportunities to explore new physics, chemistry, and engineering. An often-overlooked characteristic of vdW stacks is the well-defined 2D nanospace between the layers, which provides unique physical phenomena and a rich field for synthesis of novel materials. Applying the science of intercalation compounds to 2D materials provides new insights and expectations about the use of the vdW nanospace. We call this nascent field of science '2.5 dimensional (2.5D) materials,' to acknowledge the important extra degree of freedom beyond 2D materials. 2.5D materials not only offer a new field of scientific research, but also contribute to the development of practical applications, and will lead to future social innovation. In this paper, we introduce the new scientific concept of this science of '2.5D materials' and review recent research developments based on this new scientific concept.

Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks

We propose a new principle to realize flatbands which are robust in real materials, based on a network superstructure of one-dimensional segments. This mechanism is naturally realized in the nearly commensurate charge-density wave of 1T-TaS_{2} with the honeycomb network of conducting domain walls, and the resulting flatband can naturally explain the enhanced superconductivity. We also show that corner states, which are a hallmark of the higher-order topological insulators, appear in the network superstructure.

Recent advances of novel ultrathin two-dimensional silicon carbides from a theoretical perspective

Compared to graphene with semimetallic features, two-dimensional (2D) silicon carbide (Si-C) materials constitute another highly promising family for opto-electronic applications owing to their intrinsic electronic gaps. Recent theoretical studies of 2D Si-C materials thoroughly investigated their structure and properties. Herein, we overview these high-throughput approaches aiming to theoretically design 2D Si-C crystals. Graphene-like siligraphene and non-siligraphene are described in terms of morphology, physicochemical properties and potential applications based on the insights provided by simulations. In addition, the current progress of experimental exploration of 2D Si-C materials and underlying challenges are assessed as well.

Body-Centered Tetragonal C16 : A Novel Topological Node-Line Semimetallic Carbon Composed of Tetrarings

The present work not only predicts the existence of 3D topological semimetallic carbon allotropes composed of tetrarings, but also provides a likely crystalline structure for the unknown phase produced in the detonation soot.

Towards three-dimensional Weyl-surface semimetals in graphene networks

Graphene as a two-dimensional topological semimetal has attracted much attention for its outstanding properties. In contrast, three-dimensional (3D) topological semimetals of carbon are still rare. Searching for such materials with salient physics has become a new direction in carbon research. Here, using first-principles calculations and tight-binding modeling, we propose a new class of Weyl semimetals based on three types of 3D graphene networks. In the band structures of these materials, two flat Weyl surfaces appear in the Brillouin zone, which straddle the Fermi level and are robust against external strain. Their unique atomic and electronic structures enable applications in correlated electronics, as well as in energy storage, molecular sieves, and catalysis. When the networks are cut, the resulting slabs and nanowires remain semimetallic with Weyl lines and points at the Fermi surfaces, respectively. Between the Weyl lines, flat surface bands emerge with possible strong magnetism. The robustness of these structures can be traced back to a bulk topological invariant, ensured by the sublattice symmetry, and to the one-dimensional Weyl semimetal behavior of the zigzag carbon chain.

Existence of Dirac cones in the Brillouin zone of diperiodic atomic crystals according to group theory

We have considered non-magnetic materials with weak spin-orbit coupling, that are periodic in two non-collinear directions, and finite in the third, orthogonal direction. In some cases, the combined time-reversal and crystal symmetry of such systems, allows the existence of Dirac cones at certain points in the reciprocal space. We have investigated in a systematic way, all points of the Brillouin zone of all 80 diperiodic groups and have found sufficient conditions for the existence of s  =  1/2 Dirac fermions, with symmetry-provided band touching at the vertex of the Dirac cones. Conversely, complete linear dispersion is forbidden for orbital wave functions belonging to two-dimensional (2D) irreducible representations (irreps) of little groups that do not satisfy certain group theoretical conditions given in this paper. Our results are illustrated by a tight-binding example.

Predicting Two-Dimensional Silicon Carbide Monolayers

Intrinsic semimetallicity of graphene and silicene largely limits their applications in functional devices. Mixing carbon and silicon atoms to form two-dimensional (2D) silicon carbide (SixC1-x) sheets is promising to overcome this issue. Using first-principles calculations combined with the cluster expansion method, we perform a comprehensive study on the thermodynamic stability and electronic properties of 2D SixC1-x monolayers with 0 ≤ x ≤ 1. Upon varying the silicon concentration, the 2D SixC1-x presents two distinct structural phases, a homogeneous phase with well dispersed Si (or C) atoms and an in-plane hybrid phase rich in SiC domains. While the in-plane hybrid structure shows uniform semiconducting properties with widely tunable band gap from 0 to 2.87 eV due to quantum confinement effect imposed by the SiC domains, the homogeneous structures can be semiconducting or remain semimetallic depending on a superlattice vector which dictates whether the sublattice symmetry is topologically broken. Moreover, we reveal a universal rule for describing the electronic properties of the homogeneous SixC1-x structures. These findings suggest that the 2D SixC1-x monolayers may present a new "family" of 2D materials, with a rich variety of properties for applications in electronics and optoelectronics.

Universal rule on chirality-dependent bandgaps in graphene antidot lattices

Graphene with periodically patterned antidots has attracted intense research attention as it represents a facile route to open a bandgap for graphene electronics. However, not all graphene antidot lattices (GALs) can open a bandgap and a guiding rule is missing. Here, through systematic first-principles calculations, it is found that bandgaps in triangular GALs are surprisingly well defined by a chirality vector R = n a1 + ma2 connecting two neighboring antidots, where a1 and a2 are the basis vectors of graphene. The bandgap opens in the GALs with (n-m)mod3 = 0 but remains closed in those with (n-m)mod3 = ±1, reminiscent of the gap-chirality rule in carbon nanotubes. Remarkably, the gap value in GALs allows ample modulation by adjusting the length of chirality vectors, shape and size of the antidots. The gap-chirality relation in GALs stems from the chirality-dependent atomic structures of GALs as revealed by a super-atom model as well as Clar sextet analyses. This chirality-dependent bandgap is further shown to be a generic behavior in any parallelogram GAL and thus serves as an essential stepping stone for experimenters to realize graphene devices by antidot engineering.

Evidence for interlayer coupling and moiré periodic potentials in twisted bilayer graphene

We report a study of the valence band dispersion of twisted bilayer graphene using angle-resolved photoemission spectroscopy and ab initio calculations. We observe two noninteracting cones near the Dirac crossing energy and the emergence of van Hove singularities where the cones overlap for large twist angles (>5°). Besides the expected interaction between the Dirac cones, minigaps appeared at the Brillouin zone boundaries of the moiré superlattice formed by the misorientation of the two graphene layers. We attribute the emergence of these minigaps to a periodic potential induced by the moiré. These anticrossing features point to coupling between the two graphene sheets, mediated by moiré periodic potentials.

Ferromagnetism in hydrogenated graphene nanopore arrays

Theoretically, the so-called zigzag edge of graphenes provides localized electrons due to the presence of flat energy bands near the Fermi level. Spin interaction makes the localized spins strongly polarized, yielding ferromagnetism. However, in most experimental studies, ferromagnetism has been observed in uncontrollable and complicated carbon-based systems. Here, we fabricate graphenes with honeycomblike arrays of hexagonal nanopores, which have a large ensemble of hydrogen-terminated and low-defect pore edges that are prepared by a nonlithographic method (nanoporous alumina templates). We observe large-magnitude ferromagnetism derived from electron spins localizing at the zigzag nanopore edges. This promises to be a realization of graphene magnets and novel spintronic devices.

Electronic structures of porous nanocarbons

We use large scale ab-initio calculations to describe electronic structures of graphene, graphene nanoribbons, and carbon nanotubes periodically perforated with nanopores. We disclose common features of these systems and develop a unified picture that permits us to analytically predict and systematically characterize metal-semiconductor transitions in nanocarbons with superlattices of nanopores of different sizes and types. These novel materials with highly tunable band structures have numerous potential applications in electronics, light detection, and molecular sensing.

Bandgap opening in graphene antidot lattices: the missing half

The electronic structure of graphene antidot lattices (GALs) with zigzag hole edges was studied with first-principles calculations. It was revealed that half of the possible GAL patterns were unintentionally missed in the usual construction models used in earlier studies. With the complete models, the bandgap of the GALs was sensitive to the width W of the wall between the neighboring holes. A nonzero bandgap was opened in hexagonal GALs with even W, while the bandgap remained closed in those with odd W. Similar alternating gap opening/closing with W was also demonstrated in rhombohedral GALs. Moreover, analytical solutions of single-walled GALs were derived based on a tight-binding model to determine the location of the Dirac points and the energy dispersion, which confirmed the unique effect in GALs.

Porous graphene as an atmospheric nanofilter

The fabrication of nanoscale membranes exhibiting high selectivity is an emerging field of research. The possibility to use bottom-up approaches to fabricate a filter with porous graphene and analyze its functionality with first principle calculations is investigated. Here, the porous network is produced by self-assembly of the hexaiodo-substituted macrocycle cyclohexa-m-phenylene (CHP). The resulting porous network exhibits an extremely high selectivity in favor of H(2) and He among other atmospheric gases, such as Ne, O(2), N(2), CO, CO(2), NH(3), and Ar. The presented membrane is superior to traditional filters using polymers or silica and could have great potential for further technological applications such as gas sensors or fuel cells.

Band Structures of Carbon Nanotubes with Nanoscale Periodic Pores Depending on their Circumferences

We theoretically evaluate the electronic band structures in carbon nanotubes with nanoscale periodic pores with a tight-binding approximation of π electrons, and demonstrate that band gaps of the carbon nanotubes with nanoscale periodic pores differ significantly from those of conventional carbon nanotubes. The band gaps of the carbon nanotubes with nanoscale periodic pores depend strongly on the size of pores and inter-pore distances. In some carbon nanotubes with nanoscale periodic pores, band gaps are constant as a function of their circumferences. In other ones, band gaps have the exact periodicity of three as a function of their circumferences. Those behaviors can be explained by taking properties of nanoscale periodic porous graphite into consideration. In some carbon nanotubes with relatively large nanoscale periodic pores, flat bands appear, which may cause singular properties about magnetism in one-dimensional porous carbon nanotubes.

Gate-induced band ferromagnetism in an organic polymer

We propose that a chain of five-membered rings (polyaminotriazole) should be ferromagnetic with an appropriate doping that is envisaged to be feasible with a field-effect transistor structure. The ferromagnetism is confirmed by a spin density functional calculation, which also shows that ferromagnetism survives the Peierls instability. We explain the magnetism in terms of the Mielke and Tasaki flatband ferromagnetism with the Hubbard model. This opens a new possibility of band ferromagnetism in purely organic polymers.