Guidelines for band gap opening in graphene superlattices with periodic π-vacancy distribution
Abstract
Periodic π-vacancies in graphene superlattices (GSLs) provide a symmetry-based route to band-gap opening in graphene by modifying the π-band dispersion. However, the symmetry conditions that determine whether a vacancy motif can open a band gap remain unclear. Here, we investigate periodic π-vacancy GSLs using a nearest-neighbor tight-binding model with one pz orbital per carbon site to identify the symmetry requirements for gap opening. π-vacancies, representing functionalized, substituted, or missing carbon sites, are modeled as site deletions in the π basis, with all hopping matrix elements to and from the deleted sites set to zero. We focus on π-vacancy motifs with C2 and C3 point-group symmetry. A 3n × 3n GSL, where n=1,2,3,… is the integer scaling factor multiplying the honeycomb primitive-cell vectors, folds K and K' to Γ and can therefore open a band gap. For C3-type vacancies, the Dirac cones remain pinned at high-symmetry points and thus stay at Γ in folded 3n GSLs. In contrast, C2-type vacancies that reduce the global point group of the GSL to D2h by preserving a pair of perpendicular mirror symmetries, σv ⊥ σd, can also constrain the Dirac cones to Γ. When the σv and σd mirror planes are absent, the cones are allowed to shift away from Γ to (± Δq,± Δq) in the 3n superlattice.
Versions
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BibTeX
@misc{dzujah2026guidelines,
title = {{Guidelines for band gap opening in graphene superlattices with periodic π-vacancy distribution}},
author = {Diyan Unmu Dzujah and Hongde Yu and Thomas Heine},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.04900},
eprint = {2605.04900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04900},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Guidelines for band gap opening in graphene superlattices with periodic π-vacancy distribution
AU - Diyan Unmu Dzujah
AU - Hongde Yu
AU - Thomas Heine
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2605.04900
UR - https://arxiv.org/abs/2605.04900
AB - Periodic π-vacancies in graphene superlattices (GSLs) provide a symmetry-based route to band-gap opening in graphene by modifying the π-band dispersion. However, the symmetry conditions that determine whether a vacancy motif can open a band gap remain unclear. Here, we investigate periodic π-vacancy GSLs using a nearest-neighbor tight-binding model with one p_z orbital per carbon site to identify the symmetry requirements for gap opening. π-vacancies, representing functionalized, substituted, or missing carbon sites, are modeled as site deletions in the π basis, with all hopping matrix elements to and from the deleted sites set to zero. We focus on π-vacancy motifs with C_2 and C_3 point-group symmetry. A 3n × 3n GSL, where n=1,2,3,… is the integer scaling factor multiplying the honeycomb primitive-cell vectors, folds K and K' to Γ and can therefore open a band gap. For C_3-type vacancies, the Dirac cones remain pinned at high-symmetry points and thus stay at Γ in folded 3n GSLs. In contrast, C_2-type vacancies that reduce the global point group of the GSL to D_2h by preserving a pair of perpendicular mirror symmetries, σ_v ⊥ σ_d, can also constrain the Dirac cones to Γ. When the σ_v and σ_d mirror planes are absent, the cones are allowed to shift away from Γ to (± Δq,± Δq) in the 3n superlattice.
ER -