Braiding of edge states in narrow zigzag graphene nanoribbons: Effects of third-neighbor hopping on transport and magnetic properties

Abstract

We study narrow zigzag graphene nanoribbons (ZGNRs), employing density functional theory (DFT) simulations and the tight-binding (TB) method. The main result of these calculations is the braiding of the conduction and valence bands, generating Dirac cones for non-commensurate wave vectors k. Employing a TB Hamiltonian, we show that the braiding is generated by the thirdneighbor hopping (N3). We calculate the band structure, the density of states and the conductance, new conductance channels are opened, and the conductance at the Fermi energy assumes integer multiples of the quantum conductance unit Go = 2e 2 /h. We also investigate the satisfaction of the Stoner criterion by these ZGNRs. We calculate the magnetic properties of the fundamental state employing LSDA (spin-unrestricted DFT) and we confirm that ZGNRs with N = (2, 3) do not satisfy the Stoner criterion and as such the magnetic order could not be developed at their edges. These results are confirmed by both tight-binding and LSDA calculations. arXiv:1711.10027v2 [cond-mat.mes-hall]

Ground-state properties of the narrowest zigzag graphene nanoribbon from quantum Monte Carlo and comparison with density functional theory

“…This could explain the previous LDA outcome published in Ref. 4, which reports an AFM stabilization energy of a few meV, while in our case the AFM gain is null. The sensitiveness to k-points sampling is clearly due to a Dirac cone formation in the PM band structure, arising from edge states 4 .…”

“…4, which reports an AFM stabilization energy of a few meV, while in our case the AFM gain is null. The sensitiveness to k-points sampling is clearly due to a Dirac cone formation in the PM band structure, arising from edge states 4 . This is particulary evident in the 2-ZGNR, while the Dirac velocities flatten out for larger n-ZGNR, yielding a braided band structure.…”

“…Zigzag graphene nanoribbons (ZGNRs) have attracted a great deal of interest in the last decades as ones of the most promising graphene derivatives for technological applications, in particular for their potential use in spintronic devices. Indeed, density functional theory (DFT) calculations showed that these systems are spin gapped, with the occurrence of spin-polarized zigzag edges 1 that become antiferromagnetically (AFM) ordered [2][3][4][5] . It has been suggested that an in-plane electric field perpendicular to the graphene nanoribbon could lead to a half-metal 6 , where only one spin carries electric current.…”

Metallic bands in chevron-type polyacenes

“…1(D), the 3-ZGNR exhibits valence and conduction band braiding with two degenerate Dirac-points; a commensurate one at the BZ boundary and other incommensurate degeneracy at k k $ 1.1 A À1 , in agreement with DFT and third NN-TB calculations. 29 This metallic band structure is preserved for chevron polymer of higher N, but with a single commensurate degeneracy at BZ boundary. The effect of different N values only shows up as relatively atter dispersion (i.e., smaller Fermi velocity v F ) for polymers with longer arms, yet the degeneracy point is unaltered.…”

Prediction of a Kinetic Pathway for Fabricating the Narrowest Zigzag Graphene Nanoribbons on Cu(111)

“…These two shortcomings can both be avoided by invoking the narrowest zigzag graphene nanoribbon (nZGNR) which is made up of linearly fused benzene rings. First, zigzag graphene nanoribbons (ZGNRs) possess nonzero bandgaps tuned by the width, with the nZGNR showing the largest bandgap. − Second, the nZGNR has spin-polarized electronic states along the two edges, , as widely studied for broader ZGNRs. , These quasi-one-dimensional systems have higher spin wave stiffness than traditional magnetic materials and thus possess relatively long spin correlation lengths . Given that the coupling strength between the spins along the two opposite edges increases when the width of the ZGNRs decreases, the nZGNR will have the strongest interedge interactions. , Moreover, the nZGNR has the largest magnetoresistance among the ZGNR family .…”