Properties Of Graphene Antidot Lattices Research Articles

A DFT study on the electronic and magnetic properties of triangular graphene antidot lattices

We explore the effect of antidot size on electronic and magnetic properties of graphene antidot lattices from first-principles calculations. The spin-polarized density of states, band gap, formation energy and the total magnetization of two different equilateral triangular and right triangular antidots with zigzag and mixed zigzag-armchair edges are studied. We find that although the values of band gap, formation energy and the total magnetization of both structures are different, these values may increase when the number of zigzag edges is increased. The armchair edges have no contribution in the total magnetization of right triangular antidots. The induced magnetic moments are mainly localized on the edge atoms with a maximum value at the center of each side of the triangles. We show that a spin-dependent band gap opens up in bilayer graphene as a result of antidot pattern in only one layer of the structure. Such periodic arrays of triangular antidots that cause a spin-dependent band gap around the Fermi energy can be utilized for turning graphene from a diamagnetic semimetal into a magnetic semiconductor.

Is Antidot-Patterned Graphene Aromatic? Unusual Aromatic Properties of Graphene Antidot Lattices and Antidot-Functionalized Nanographenes

On the basis of our recent predictions for a coupled resonance aromaticity pattern of graphene (J. Phys. Chem. C 2015, 119, 16991), we have studied the anticipated breaking or uncoupling of such dual patterns induced by the presence of particular antidots arranged periodically in a graphene or nanographene film, using numerous properly selected microscopic real-space models in the framework of ab initio density functional theory (DFT). We found that the aromaticity pattern of the antidots is literally tuned to the Clar-type primary aromaticity pattern of graphene, generated by repeated motifs of the hexagonal circumcoronene (CIRCO) pattern, in such a way that the centers of the CIRCO motifs coincide with the centers of the antidots. Thus, the aromaticity pattern of the antidot lattice consists of the isolated primary CIRCO pattern of graphene. However, the nature of the aromaticity and the related bonding and banding characteristics are largely dependent on the degree of antidot passivation, a subject tha...

Graphene antidot lattices as potential electrode materials for supercapacitors

Thermodynamic stabilities and electronic properties of graphene antidot lattices with hexagonal holes were examined using density functional theory calculations and several crucial factors related to the applications of supercapacitors were discussed. For the graphene antidot lattices with different hole sizes, the formation energy per edge length is about 0.50∼0.60eV/nm, which is comparable to that of graphene nanoribbon edges. Within a hole density of 10%, the graphene antidot lattices can maintain the excellent electronic properties of perfect graphene due to negligible intervalley scattering. Further increasing the hole density will open a band gap. Taking the potassium chloride (KCl) electrolyte as an example, we further investigated the diffusion behaviors of potassium (K) and chlorine (Cl) atoms through the graphene antidot lattices. It was shown that K and Cl atoms can go through the holes with nearly no barrier at an appropriate hole size of 0.54nm, which gives an optimum pore diameter of ∼0.86nm. Therefore, the excellent graphene-like electronic properties and good penetrability for ions suggest promising applications of graphene antidot lattices in the field of supercapacitors.

Electronic and optical properties of graphene antidot lattices: comparison of Dirac and tight-binding models

The electronic properties of graphene may be changed from semimetallic to semiconducting by introducing perforations (antidots) in a periodic pattern. The properties of such graphene antidot lattices (GALs) have previously been studied using atomistic models, which are very time consuming for large structures. We present a continuum model that uses the Dirac equation (DE) to describe the electronic and optical properties of GALs. The advantages of the Dirac model are that the calculation time does not depend on the size of the structures and that the results are scalable. In addition, an approximation of the band gap using the DE is presented. The Dirac model is compared with nearest-neighbour tight-binding (TB) in order to assess its accuracy. Extended zigzag regions give rise to localized edge states, whereas armchair edges do not. We find that the Dirac model is in quantitative agreement with TB for GALs without edge states, but deviates for antidots with large zigzag regions.

Thermoelectric properties of finite graphene antidot lattices

We present calculations of the electronic and thermal transport properties of graphene antidot lattices with a finite length along the transport direction. The calculations are based on the $\ensuremath{\pi}$-tight-binding model and the Brenner potential. We show that both electronic and thermal transport properties converge fast toward the bulk limit with increasing length of the lattice: only a few repetitions ($\ensuremath{\simeq}$6) of the fundamental unit cell are required to recover the electronic band gap of the infinite lattice as a transport gap for the finite lattice. We investigate how different antidot shapes and sizes affect the thermoelectric properties. The resulting thermoelectric figure of merit, $ZT$, can exceed $0.25$, and it is highly sensitive to the atomic arrangement of the antidot edges. Specifically, hexagonal holes with pure armchair edges lead to an order-of-magnitude larger $ZT$ as compared to pure zigzag edges. We explain this behavior as a consequence of the localization of states, which predominantly occurs for zigzag edges, and of an increased splitting of the electronic minibands, which reduces the power factor ${S}^{2}{G}_{e}$ ($S$ is the Seebeck coefficient and ${G}_{e}$ is the electric conductance).

Polaronic signatures and spectral properties of graphene antidot lattices

We explore the consequences of electron-phonon (e-ph) coupling in graphene antidot lattices (graphene nanomeshes), i.e., triangular superlattices of circular holes (antidots) in a graphene sheet. They display a direct band gap whose magnitude can be controlled via the antidot size and density. The relevant coupling mechanism in these semiconducting counterparts of graphene is the modulation of the nearest-neighbor electronic hopping integrals due to lattice distortions (Peierls-type e-ph coupling). We compute the full momentum dependence of the e-ph vertex functions for a number of representative antidot lattices. Based on the latter, we discuss the origins of the previously found large conduction-band quasiparticle spectral weight due to e-ph coupling. In addition, we study the nonzero-momentum quasiparticle properties with the aid of the self-consistent Born approximation, yielding results that can be compared with future angle-resolved photoemission spectroscopy measurements. Our principal finding is a significant e-ph mass enhancement, an indication of polaronic behavior. This can be ascribed to the peculiar momentum dependence of the e-ph interaction in these narrow-band systems, which favors small phonon momentum scattering. We also discuss implications of our study for recently fabricated large-period graphene antidot lattices.

Quasiparticle properties of graphene antidot lattices

A periodic array of holes (antidot lattice) transforms graphene from a semimetal into a semiconductor with a tunable band gap. The magnitude of the gap is highly sensitive to the size and separation of the holes. In the present work, the properties of graphene antidot lattices are analyzed using atomistic models. Density-functional theory (DFT) and tight-binding parameterization of DFT bands usually underestimate band gaps and generally produce incorrect results for other properties related to excited states. To correct this error we consider quasiparticle (QP) corrections to the band structure of graphene antidot lattices within the tight-binding parameterization of the graphene QP band structure of Gr\uneis et al. [Phys. Rev. B 78, 205425 (2008)]. In addition, the optical response is calculated from the QP band structure. We find that band gaps increase by about 15% in the QP model when the hole is small compared to the unit cell. Finally, QP effects on excitons are addressed using the Wannier model with a spatially varying screening.

Electronic properties of graphene antidot lattices

Graphene antidot lattices constitute a novel class of nano-engineered graphene devices with controllable electronic and optical properties. An antidot lattice consists of a periodic array of holes that causes a band gap to open up around the Fermi level, turning graphene from a semimetal into a semiconductor. We calculate the electronic band structure of graphene antidot lattices using three numerical approaches with different levels of computational complexity, efficiency and accuracy. Fast finite-element solutions of the Dirac equation capture qualitative features of the band structure, while full tight-binding calculations and density functional theory (DFT) are necessary for more reliable predictions of the band structure. We compare the three computational approaches and investigate the role of hydrogen passivation within our DFT scheme.

Optical properties of graphene antidot lattices

Undoped graphene is semimetallic and thus not suitable for many electronic and optoelectronic applications requiring gapped semiconductor materials. However, a periodic array of holes (antidot lattice) renders graphene semiconducting with a controllable band gap. Using atomistic modeling, we demonstrate that this artificial nanomaterial is a dipole-allowed direct-gap semiconductor with a very pronounced optical-absorption edge. Hence, optical infrared spectroscopy should be an ideal probe of the electronic structure. To address realistic experimental situations, we include effects due to disorder and the presence of a substrate in the analysis.