Abstract
We investigate the Dirac cone in α-graphdiyne, which is a predicted flat one-atom-thick allotrope of carbon using first-principles calculations. α-graphdiyne is derived from graphene where two acetylenic linkages (-C ≡C-) are inserted into the single bonds (-C-C-). Thus, α-graphdiyne possesses a larger lattice constant which subsequently affects its electronic properties. Band structures show that α-graphdiyne exhibits similar Dirac points and cone to graphene. Further, the tight-binding method is used to exploit the linear dispersion in the vicinity of Dirac points. Thanks to the larger lattice constant, α-graphdiyne yields a lower Fermi velocity, which might make itself an ideal material to serve the anomalous integer quantum Hall effect.
Highlights
Band theory was first used to study the band structure of graphene over half a century ago [1], and it demonstrated that graphene is a semimetal with unusual linearly dispersing electronic excitations called Dirac electron
We introduce a tight-binding model to mimic the hopping energy between the hexagonal vertices, which realizes the linear dispersion of bands near the Dirac points, allowing the Dirac cone to be studied explicitly
The vacuum space is at least 15 Å, which is large enough to avoid the interaction between periodical images; 15×15×1 and 25×25×1 are used for the k-grid of geometry optimization and self-consistent calculation, respectively
Summary
Band theory was first used to study the band structure of graphene over half a century ago [1], and it demonstrated that graphene is a semimetal with unusual linearly dispersing electronic excitations called Dirac electron. Such linear dispersion is similar to photons which cannot be described by the Schrödinger equation. We introduce a tight-binding model to mimic the hopping energy between the hexagonal vertices, which realizes the linear dispersion of bands near the Dirac points, allowing the Dirac cone to be studied explicitly
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