[Paper Review] Encoding Quantum Mechanics into Pentagonal Geometries for Discovering Novel Two-Dimensional Materials

Lei Liu, Immanuella Kankam+1 more|arXiv (Cornell University)|Aug 10, 2018

Graphene research and applications23 references3 citations

TL;DR

This study proposes a novel framework for discovering two-dimensional (2D) carbon-based materials by encoding quantum mechanical interactions into irregular convex pentagonal geometries using ab initio density functional theory (DFT) calculations. Starting from 14 types of pentagonal tiling patterns, the authors simulate atomic relaxation and identify 13 new 2D carbon nanosheets with diverse electronic properties—ranging from semiconducting to metallic and semi-metallic with Dirac cones—demonstrating that pentagonal symmetry can guide the discovery of functional 2D materials with tunable electronic behavior.

ABSTRACT

Imagine that there is a gapless plane tessellated by irregular, convex pentagons with their side lengths at the sub-nanoscale, and tiny balls are placed at the vertices of each pentagon. If there are no interactions among these balls, one would expect that they stand still at the vertices of the pentagons. But what if these balls symbolize atoms? The electrons and nuclei of the atoms will start to interact following the laws of quantum mechanics. As a result, the atoms will relocate leading to a system of energy minimum. While performing an experiment of manipulating individual atoms and observing the resulting configurations may be challenging, we apply ab initio density functional theory (DFT) calculations to carry out a virtual experiment, where we assign carbon atoms at the vertices of 14 types of convex pentagons and then optimize the positions of these atoms. We obtain a variety of unexpected structures; almost all of them except types 2 and 4 structures{these two structures are equivalent{differ from the initial pentagonal geometries. We compute the band structure of each resulting geometry representing the crystal structure of a two-dimensional (2D) material. We find diverse electrical properties among these 2D materials: metallic, semiconducting, and semi-metallic with a Dirac cone. Our work shows that encoding quantum mechanics into the geometries of irregular, convex pentagons and with the help of DFT calculations open up a novel route for accelerating discovery of new 2D materials.

Motivation & Objective

• To explore whether carbon atoms can self-organize into stable 2D nanosheets when initially placed at the vertices of 14 types of irregular, convex pentagons.
• To investigate how quantum mechanical interactions (electron-electron, electron-ion, ion-ion) alter the initial pentagonal geometries during atomic relaxation.
• To determine the electronic properties of the resulting 2D carbon nanosheets using DFT calculations.
• To identify new 2D materials with exotic electronic behavior, such as Dirac cones or small effective masses, suitable for nanoelectronic applications.

Proposed method

• Ab initio density functional theory (DFT) with the PBE functional is used to perform geometry optimizations of carbon nanosheets derived from 14 types of convex pentagonal tilings.
• The Vienna Ab-initio Simulation Package (VASP) is employed to compute total energies, optimize atomic positions, and calculate electronic band structures.
• Surface supercell models are constructed based on the in-plane lattice vectors of each pentagonal tiling type to simulate periodic 2D materials.
• Band structures are computed along high-symmetry k-point paths to classify materials as metallic, semiconducting, or semi-metallic with Dirac cones.
• Effective masses and Fermi velocities are calculated to evaluate carrier transport properties.
• The study uses a 81×81 k-point grid near the Γ point to analyze band dispersion and confirm the presence or absence of Dirac cones.

Experimental results

Research questions

• RQ1 Can carbon atoms remain at the vertices of irregular convex pentagons after quantum mechanical relaxation, or do they reconfigure into new geometries?
• RQ2 What are the resulting electronic band structures of the 14 carbon nanosheets derived from different pentagonal tiling types?
• RQ3 Do any of the relaxed structures exhibit Dirac cones or semi-metallic behavior similar to graphene?
• RQ4 What is the magnitude of the bandgap in the semiconducting carbon nanosheets, and how does it compare to experimental values?
• RQ5 How do carrier effective masses and Fermi velocities influence the potential for nanoelectronic applications?

Key findings

• Only the carbon nanosheets derived from type 2 and type 4 pentagons retain their initial pentagonal geometry after DFT relaxation, while all other types reconfigure into non-pentagonal structures.
• Five of the 14 carbon nanosheets (types 1, 3, 8, 11, and 12) are semiconducting with bandgaps ranging from 0.14 eV to 0.89 eV at the PBE level.
• The type 3 carbon nanosheet exhibits a direct bandgap at the Γ point, but no Dirac cone is formed, despite initial appearance of cone-like dispersion.
• The type 9 carbon nanosheet (graphene-like) is semi-metallic with a Dirac cone, exhibiting a Fermi velocity of 8.2 × 10⁵ m/s, close to the literature value of ~10⁶ m/s.
• The electron and hole effective masses in the type 3 nanosheet are calculated to be 0.07 m₀, indicating high carrier mobility favorable for electronic transport.
• The type 11 carbon nanosheet shows nearly flat bands near the Fermi level due to isolated C-atom clusters, leading to strong optical absorption and high joint density of states.