A Kekulé bond texture in graphene modifies the electronic band structure by folding the Brillouin zone and bringing the two inequivalent Dirac points to the center. This can result, in the opening of a gap (Kek-O) or the locking of the valley degree of freedom with the direction of motion (Kek-Y). We analyze the effects of uniaxial strain on the band structure of Kekulé-distorted graphene for both textures. Using a tight-binding approach, we introduce strain by considering the hopping renormalization and corresponding geometrical modifications of the Brillouin zone. We numerically evaluate the dispersion relation and present analytical expressions for the low-energy limit. Our results indicate the emergence of a Zeeman-like term due to the coupling of the pseudospin with the pseudomagnetic strain potential which separates the valleys by moving them in opposite directions away from the center of the Brillouin zone. For the Kek-O phase, this results in a competition between the Kekulé parameter that opens a gap and the magnitude of strain which closes it. While for the Kek-Y phase, in a superposition of two shifted Dirac cones. As the Dirac cones are much closer in the supperlattice reciprocal space that in pristine graphene, we propose strain as a control parameter for intervalley scattering.

The formation of a superlattice in graphene can serve as a way to modify its electronic bandstructure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekulé bond ordering in graphene deposited on top of a Copper substrate, leading to the breaking of the valley degeneracy while preserving the highly desirable feature of linearity and gapless character of its band dispersion. In this paper we study the effects of a Kekulé distortion in zigzag graphene nanoribbons in both, the subband spectrum and on its electronic transport properties. We extend our study to investigate also the electronic conductance in graphene nanoribbons composed of sequentially ordered ν = ±1 Kek-Y superlattice. We find interesting resonances in the conductance response emerging in the otherwise energy gap regions, which scales with the number of Kek-Y interfaces minus one. Such features resembles the physics of resonant tunneling behavior observed in semiconductors heterostructures. Our findings provide a possible way to measure the strenght of Kekulé parameter in graphene nanoribbons.

Graphene's electronic structure can be fundamentally altered when a substrate-or adatom-induced Kekulé superlattice couples the valley and isospin degrees of freedom. Here, we show that the band structure of Kekulétextured graphene can be re-engineered through layer stacking. We predict a family of Kekulé graphene bilayers that exhibit band structures with up to six valleys, and room-temperature Dirac quasiparticles whose masses can be tuned electrostatically. Fermi velocities half as large as in pristine graphene put this system in the strongly coupled regime, where correlated ground states can be expected.Superlattices naturally emerge in multilayered twodimensional (2D) crystals, either by differences in lattice constants or layer orientation. Heterostructures formed by stacking nearly commensurate van der Waals crystals[1] display moiré patterns, with approximate periodicities tens of times larger than the materials' lattice constants. This long-range periodicity has enabled the observation of Hofstadter's butterfly in graphene on hexagonal boron nitride (hBN) [2,3], and more recently of exciton minibands[4-7] and moiréumklapp optical signatures [4] in hetero-bilayers of transitionmetal dichalcogenides. Moiré patterns also form in twisted graphene bilayers, where the conduction and valence bands flatten at so-called "magic angles" [8], leading to strongly correlated phenomena such as unconventional superconductivity and many-body insulating behavior [9,10].A different type of superlattice, caused by Kekulé distorsions, has also been theorized [11,12] and recently reported in graphene monolayers on copper substrates at room temperature [13]. In the latter case, so-called ghost copper adatoms distributed periodically beneath the graphene plane produce a bond density wave that triples the graphene unit cell over nanometre-sized regions, where charge carriers comprise two different species of valley-pseudospin-locked Dirac fermions [14,15]. One may envision Kekulé-distorted graphene as a new building block for multilayered 2D materials, with new electronic properties that can be engineered by controlling the stacking type. However, whether the substrate effect causing the Kekulé distortion will propagate to higher layers is, to our knowledge, still an open question.In this Letter, we show theoretically that Kekulé-distorted graphene bilayers support up to six flavors of valleydegenerate Dirac quasiparticles, with electrostatically tunable relativistic masses. While these low-energy Dirac bands are directly related to the band topology transition below energies of order 1 meV in bilayer graphene [16], we predict band widths of order 20 meV, preserving multi-valley physics almost at room temperature, and for carrier dopings of up to 10 12 cm −2 . We propose a system where two graphene layers with Kekulé distortions are stacked with AB (Bernal) configuration, graphene Cu substrate cut Kek-Y graphene bilayer < l a t e x i t s h a 1 _ b a s e 6 4 = " Z x B W d a s I 5 v R R p f u P i x r 1 y c K U M X c = " > A A A C ...

The effects of second-neighbor interactions in Kekulé-Y 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 Γ point into the subspace defined by the Kekulé 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 ‘pseudo 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 Kekulé 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 Kekulé patterned graphene, specially at surfaces.