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Flat bands without twists: periodic holey graphene.

Abdiel de Jesús Espinosa-Champo^1,2,3, Gerardo G Naumis²

¹Posgrado de Ciencias Físicas, Universidad Nacional Autónoma de México, Apartado Postal 20-364 01000 Ciudad de México, Mexico.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|April 2, 2024

Summary

Researchers explored holey graphene (HG) and discovered flat electronic bands emerge due to sublattice imbalance. This provides a simpler method for creating flat bands, potentially leading to novel quantum phases.

Keywords:

berry curvature compact localized states flat bands holey graphene α-T3 hamiltonian

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Area of Science:

Condensed Matter Physics
Materials Science
Quantum Chemistry

Background:

Holey graphene (HG) is utilized for synthesizing high-purity crystalline materials.
Understanding the electronic properties of patterned graphene structures is crucial for advanced material design.

Purpose of the Study:

To investigate the electronic properties of holey graphene with periodic lattice holes.
To demonstrate the emergence of flat bands and topological properties in HG.
To present a facile method for generating flat bands and exploring correlated quantum phases.

Main Methods:

Theoretical exploration of electronic properties in HG with periodic lattice holes.
Analysis of band structures, sublattice imbalance, and symmetry breaking (path-exchange and inversion).
Derivation of a low-energy Hamiltonian for the central bands.

Main Results:

Periodic lattice holes in graphene induce sublattice imbalance, leading to the formation of flat electronic bands.
Breaking inversion symmetry opens gaps and induces topological bands with nonzero Berry curvature.
Dirac cones fold into the superlattice Brillouin zone, resulting in gap formation periodicity (n≡0 mod 3).
The system exhibits behavior analogous to effective α-T3 graphene.

Conclusions:

A simple protocol for reliably obtaining flat bands in holey graphene is presented.
This method offers an accessible route to engineer flat bands, which enhance electron-electron correlation effects.
HG provides a promising platform for realizing highly correlated quantum phases, alternative to complex twisted systems.