Electronic spectrum of Kekule patterned graphene considering second neighbor-interactions

TL;DR

This paper investigates how second-neighbor interactions influence the electronic properties of Kekule patterned graphene, revealing band mass effects, energy shifts, and edge state hybridization, especially in nanoribbons, highlighting their significance in realistic surface models.

Contribution

It introduces a low-energy effective Hamiltonian incorporating second-neighbor interactions in Kekule patterned graphene, validated against full tight-binding calculations, and explores effects in nanoribbons.

Findings

Second-neighbor interactions induce band mass and energy shifts.

Degeneracy at the Dirac point is lifted by second neighbors.

Edge states become dispersive and hybridized in nanoribbons.

Abstract

The effects of second-neighbor interactions in Kekule patterned graphene electronic properties are studied starting from a tight-binding Hamiltonian. Thereafter, a low-energy effective Hamiltonian is obtained by projecting the high energy bands at the Gamma point into the subspace defined by the Kekule wave vector. The spectrum of the low energy Hamiltonian is in excellent agreement with the one obtained from a numerical diagonalization of the full tight-binding Hamiltonian. The main effect of the second-neighbour interaction is that a set of bands gains an effective mass and a shift in energy, thus lifting the degeneracy of the conduction bands at the Dirac point. This band structure is akin to a spin-one Dirac cone, a result expected for honeycomb lattices with a distinction between one third of the atoms in one sublattice. Finally, we present a study of Kekule patterned graphene nanoribbons. This shows that the previous effects are enhanced as the width decreases. Moreover, edge states become dispersive, as expected due to second neighbors interaction, but here the Kek-Y bond texture results in an hybridization of both edge states. The present study shows the importance of second neighbors in realistic models of Kekule patterned graphene, specially at surfaces.