In an article recently published in the journal Scientific Reports, researchers explored the similarities between electronic states in two nanostructures, including graphene quantum dots (QDs) and planar metallic QDs.
Graphene vs. metallic quantum dots: the confined states. (a–c) The EPWE calculated electronic structure for (a) the smallest graphene quantum dot (GQD) and (b, c) for the same size 2D metallic quantum dots (H-MQG and C-MQD) of hexagonal and circular shapes, respectively, with their potential landscapes depicted in (d). In the three cases, the electronic structure consists of energy levels and near-Fermi gap defining the frontier highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals. (e-h) Local density of states (LDOS) simulations at the energy of the first four energy levels n = 1–4 for GQD (top), H-MQD (middle), and C-MQD (bottom). The progressive transformation from dome-, donut-, to sombrero-like shape is demonstrated for all QDs. Image Credit: https://www.nature.com/articles/s41598-024-63465-2
Background
Graphene is a two-dimensional (2D) model system with tunable and distinguished electronic properties and potential applications in different fields. Although the free-standing extended graphene's gapless electronic band structure is suitable for applications like plasmonics and transport, the nonexistence of a natural energy gap can limit its integration in different nanoelectronic devices.
The rising interest in the applications and unique physics of graphene and its nanostructures has motivated the exploration of graphene-like artificial materials that have tunable lattice parameters. Recently, molecular and atomic graphene were modeled following simple free-electron scattering by periodic muffin tin potential, resulting in exceptional agreement with density functional theory (DFT).
The approach based on simplified nearly free electrons remains valid for carbon-based organic molecules and graphene nanostructures. Similarly, the electronic structure's discretization in small graphene QDs, like molecular coronene, could be reproduced effectively from confined electrons in atomically corrugated and/or smooth quantum wells, where the spectral intensity probed using the frontier orbitals and angle-resolved photoemission (ARPES) coincides with DFT calculations.
Specifically, graphene's electronic band structure is comparable to that of a 2D homogeneous metal, resulting in shared physical properties between the two. However, a key difference lies in the near-Fermi electrons: graphene features triangular holes and electron pockets around the K-points, along with related intravalley scattering, which are unique to graphene structures.
The Study
In this study, researchers extended the analogy of the π-electronic structures and quantum effects between atomic graphene quantum dots (QDs) and homogeneous planar metallic counterparts of similar shape and size. They employed the electron plane wave expansion (EPWE) method to establish a strong analogy between the electronic properties of lateral 2D metallic QDs and graphene QDs.
Researchers simulated the electronic properties of 2D homogeneous metal, graphene QDs, metallic QDs, and extended graphene by solving the one-electron Schrödinger equation for the corresponding 2D potential landscape.
The reference energy for graphene QDs and graphene was set to position the K-point of extended graphene at the Fermi energy. Additionally, the open-source Pybinding package was used to simulate the local and total density of states for a nanoscale large graphene QD.
Study Findings
Researchers showed that relatively small graphene QDs display electronic structures, quasiparticle standing wave patterns, and confined states analogous to those reported for confining metallic nanostructures like molecular networks, quantum corrals, and vacancy islands.
Specifically, at high binding energies below the M-point gap, graphene QDs exhibited standing wave quasiparticle interference patterns and confined states similar to those observed on coinage metal surfaces for nanoscale confining structures like quantum corrals.
These quantum corral-like and confined states in graphene QDs could be resolved using ARPES in tomography experiments. Similarly, the shape of near-Fermi frontier orbitals in graphene QDs could be effectively reproduced from electron confinement in homogeneous metal QDs of similar shape and size.
Most importantly, the wavefunction morphology of graphene QDs' frontier orbitals present at the M-point gap's energy window was reproduced from confinement inside homogeneous metallic QDs. Additionally, the confined states analogous to those found in metallic quantum stadiums could be realized in more complex nanostructures, such as coupled graphene QDs with reduced separation.
However, for large nanoscale graphene QDs, graphene's distinctive electronic confined states and unusual Friedel oscillations caused by confined/scattered Dirac electrons with intravalley scattering wavevectors found no correspondence in metallic QDs.
In scenarios where intravalley scattering is not relevant, this study enabled the simplification of graphene's underlying physics through comparison with a corresponding 2D homogeneous metal, thus offering an effective modeling technique for various carbon-based nanostructures.
Conclusion
To summarize, this study provided a fundamental understanding of graphene electronic structures and paved the way for efficient novel graphene-based nanostructure modeling.
Although the electronic states near the Fermi energy, such as those facilitated by intravalley scattering, can be applied in optical and transport devices, the high-energy confined states in atomic graphene QDs are not feasible for such applications. However, they can mediate catalytic processes and impact selective chemical bonding through their hybridization with other high-energy electronic bands.
Moreover, the energy of the confined states can be brought nearer to the Fermi energy in artificial molecular graphene QDs, which can be used to modulate materials' electronic properties or induce functionalities through the proximity effect.
Journal Reference
Othman, A. M., A., M., Ibraheem, F., Hassan, M. A., Farouk, M., & M., Z. (2024). Analogous electronic states in graphene and planer metallic quantum dots. Scientific Reports, 14(1), 1-12. https://doi.org/10.1038/s41598-024-63465-2, https://www.nature.com/articles/s41598-024-63465-2
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