Structure Of Zigzag Graphene Nanoribbons Research Articles

Effect of edge defects on band structure of zigzag graphene nanoribbons

In this article, we report band structure studies of zigzag graphene nanoribbons (ZGNRs) on introducing defects (sp3 hybridized carbon atoms) in different concentrations at edges by varying the ratio of sp3 to sp2 hybridized carbon atoms. On the basis of theoretical analyses, bandgap values of ZGNRs are found to be strongly dependent on the relative arrangement of sp3 to sp2 hybridized carbon atoms at the edges for a defect concentration; so the findings would greatly help in understanding the bandgap of nanoribbons for their electronic applications.

Confinement and fermion doubling problem in Dirac-like Hamiltonians

We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling. Second, a typical lattice discretization of the first-order derivative $k\ensuremath{\rightarrow}\ensuremath{-}i{\ensuremath{\partial}}_{x}$ skips the central point and allow spurious low-energy, highly oscillating solutions known as fermion doublers. While a no-go theorem states that the doublers cannot be eliminated without artificially breaking a symmetry, here we show that the symmetry broken by the Wilson's mass approach is equivalent to the enforcement of hard-wall boundary conditions, thus making the no-go theorem irrelevant when confinement is foreseen. We illustrate our arguments by calculating the following: (i) the band structure and transport properties across thin films of the topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, for which we use ab initio density functional theory calculations to justify the model; and (ii) the band structure of zigzag graphene nanoribbons.

Magneto-electronic properties of zigzag graphene nanoribbons doped with triangular boron nitride segment

In this paper, magneto-electronic properties of zigzag graphene nanoribbons (ZGNR) doped with triangular boron nitride (BN) segments are investigated by using first-principles method based on density functional theory. It is shown that in the nonmagnetic state, the ZGNRs doped with triangular BN segments at different positions are metals. In the ferromagnetic state, with the impurities moving from one edge of the nanoribbon to the other edge, a transition is caused from a spin metal to a spin half-metal, and then to spin semiconductor, and as long as the impurity is not on the edge of the nanoribbon, the doped ZGNR is always spin half-metal. In the antiferromagnetic state, the ZGNR doped in the middle of the nanoribbon is spin metal, while the ZGNR doped on the edge of the nanoribbon has no antiferromagnetic state. The electronic structures of the ZGNRs doped with BN segments at different positions are explained by the difference in charge density. The binding energies of doped ZGNRs are negative, thus the structures of the doped ZGNRs are stable. As the impurity moves from position P1 to position P5, the binding energy decreases gradually. When the impurity is located at position P5, the binding energy of ZGNR is smallest, and the structure of ZGNR is most stable. When the impurity doped in the middle of the nanoribbon, the antiferromagnetic state is the ground state, while the impurity is doped on the edge of the nanoribbon, the ferromagnetic state is the ground state. These obtained results are of significance for developing electronic nanodevices based on graphene.

Engineering the electronic structure of zigzag graphene nanoribbons with periodic line defect

By using first principle calculations we have studied the magnetic, electronic and transport properties of zigzag-graphene nanoribbon (zGNR) with a topological line defect (LD) composed of pentagons and heptagons (5-7). We show that one can engineer the magnetic and electronic properties of the edge passivated zGNR with 5-7 LD through the variation of either the width of the zGNR or the position of the LD. Thus, one can have ferromagnetic behaviour in zGNR by introducing 5-7 LD close to one edge of the ribbon. One can tune the zGNR with 5-7 LD from semi-metallic to semi-metallic semiconductor either by increasing the width of the ribbon or by changing the position of the LD. We have also studied the effect of the doping on the degeneracy of the spin states of 4-4-LD-zGNR. The calculation of transport properties of N-doped 4-4-LD-zGNR reveals that it has high spin filtering efficiencies. The tuning of the spin polarization through the formation of 5-7 LD in zGNR holds a promise for its application in spintronic devices.

INDUCED BANDGAP AND MAGNETIC BEHAVIOR IN ZIGZAG GRAPHENE NANORIBBONS ON HEXAGONAL NITRIDE BORON: EDGE AND SUBSTRATE EFFECTS

The results of DFT research on the band structure of zigzag graphene nanoribbons N-ZGNR/h-BN(0001) with ferro- and antiferromagnetic ordering are presented. It is suitable as a potential base for new materials for spintronics. Equilibrium parameters of the graphene nanoribbon atomic structure and boron nitride top layer are determined as well as the equilibrium bond length between atomic layers of the 8-ZGNR nanoribbon and the substrate h-BN(0001). Change regularities of the valence band electronic structure and of the energy gap induction in series 6-ZGNR→ 8-ZGNR→ 6-ZGNR/h-BN(0001)→ 8-ZGNR/h-BN(0001)→ graphene/h-BN(0001) are studied. Spin state features at Fermi level, as well as the roles of the edge effect and the effect of substrate in the formation of the band gap in 6(8)-ZGNR/h-BN(0001) system are discussed. It is shown that 340 meV energy gap appears in 6(8)-ZGNR/h-BN(0001) systems. The contribution of the graphene nanoribbon edge and substrate in opening this energy gap is differentiated. Local magnetic moments on the carbon atoms in graphene nanoribbons in the suspended state and on the substrate with ferro- and antiferromagnetic ordering are estimated. It is shown that the local magnetic moments on the carbon atoms in zigzag graphene nanoribbons 8-ZGNRs with ferro- and antiferromagnetic ordering give almost identical values. The edge carbon atoms possess the largest local magnetic moments (0,28) relative to other carbon atoms.

Edge and substrate-induced bandgap in zigzag graphene nanoribbons on the hexagonal nitride boron 8-ZGNR/h-BN(0001)

The results of DFT (GGA-PBEsol) and DFT(PBE)-D2 study of the band structure of zigzag graphene nanoribbons on hexagonal nitride boron 8-ZGNR/h-BN(0001) are presented, suitable as potential base for new materials for spintronics. It offers a study of regularities in the changes of the valence band electron structure and the induction of the energy gap in the series 8-ZGNR → 8-ZGNR/h-BN(0001) → graphene/h-BN(0001). The peculiarities of the spin state at the Fermi level, the roles of the edge effect and the effect of substrate in formation of the band gap in 8-ZGNR/h-BN(0001) system are discussed. Our calculations shown that vdW-correction plays an important role in the adsorption of GNR on h-BN and results in reduction of the interplanar distances in equilibrium systems ZGNRs/h-BN(0001). As a result of the structural changes we have obtained new values of the energy gap in the 8-ZGNR-AF and 8-ZGNR-AF/h-BN(0001) systems. The paper demonstrates appearance of 600 meV energy gap in the 8-ZGNR/h-BN(0001) interface. The contributions of nanoribbon edges and the substrate in formation of the gap have been differentiated for the first time. The estimations of local magnetic moments on carbon atoms are made. Shown that in case of ferromagnetic ordering substrate presense causes insignificant splitting of the bands. The splitting reached only (14-28 meV). Since the electronic states of a suspended GNR in point (k=π) are degenerate near the Fermi level, we can assume that the above splitting in 8-ZGNR/h-BN(0001) is only determined by the contribution of the h-BN(0001) substrate.

Tailoring the Electronic Structure of Zigzag Graphene Nanoribbons via Cu Impurities

We employed density functional theory based spin polarised calculations to explore the structural stability and electronic properties of ZGNR using Cu as a terminating element as well as a substitutional dopant at various sites. In both the cases (termination and doping) Cu impurities affect the electronic properties of nanoribbons in a different way. The calculated formation energy indicates that all the structures are energetically feasible except the both edges Cu-doped ribbons. Binding energy analysis confirms that Cu impurities are strongly bound to ZGNR in all considered configurations. Moreover, ribbon edge is regarded as the most feasible site for substitutional Cu atoms in ZGNR. The electronic properties of ZGNR are sensitive to the position of Cu atoms and the ribbon width. It is revealed that ZGNR can be made semiconducting, semi-metallic, half metallic or purely metallic in nature merely by changing the ribbon width or the position of Cu atoms. The predicted half metallicity for one edge Cu-terminated ZGNR is robust against the choice of exchange correlation potential.

Edge-adsorption of potassium adatoms on graphene nanoribbon: A first principle study

Using density-functional theory calculations, we studied the electronic properties of graphene nanoribbons (GNRs) with potassium (K) atoms adsorption on the edges of GNRs. Our simulations showed that the electronic structure of the armchair GNR (AGNR) is changed from semiconductor to metal due to the charge transfer from potassium adatoms to the edge carbon atoms. It was observed in AGNR that the K adatom edge-adsorbed system is always nonmagnetic and the interaction between the K adatom and AGNR is purely ionic. In zigzag GNR (ZGNR), we found that K edge-adsorption will suppress the magnetic moment at the impurity site and its vicinity while keeping well the edge structure of ZGNR. We also found that if selectively introduce K impurities asymmetry in two sides of the ZGNR, a ferromagnetic state can be created, while it is antiferromagnetic in pristine. Our results suggest that the electronic properties of GNR can be effectively modulated by K edge-adsorption, and that the alkali-metal edge-adsorbed GNRs can serve as potential materials in nanoelectronics and spintronics.

Absence of edge states near the 120∘corners of zigzag graphene nanoribbons

Based on first-principles total-energy calculations, we studied the energetics and electronic structure of zigzag graphene nanoribbons with nanometer-scale corners. We found that the formation energy of a short zigzag edge with a 120${}^{\ensuremath{\circ}}$ corner is substantially smaller than that of a straight zigzag edge with an infinite length. We also found that zigzag graphene ribbons with 120${}^{\ensuremath{\circ}}$ corners are semiconductors for which the band-gap decreases with increasing length between adjacent corners. The edge state is absent for zigzag graphene ribbons with short corner-corner distances, while the edge state emerges for zigzag ribbons that have a corner-corner distance greater than 1.5 nm. The remarkable stability of the 120${}^{\ensuremath{\circ}}$ corner of the short zigzag edges is in good agreement with the experimental observation of such corners of graphene edges.

Tuning of the Band Structures of Zigzag Graphene Nanoribbons by an Electric Field and Adsorption of Pyridine and BF3: A DFT Study

The influence of pyridine adsorption and the applied electric field on the band structure and metallicity of zigzag graphene nanoribbons (ZGNRs) was investigated by using density functional theory (DFT) calculations. The semiconducting ZGNRs became half-metallic or remained semiconducting depending on the configuration of N–C covalent bonds between pyridine and the outermost C atom of the ZGNRs. In addition, the band gap of the α- and β-spin states of the ZGNRs could be tuned by noncovalent bonds. This effect was enhanced when BF3 was introduced simultaneously at the opposite edge. The applied external electric field also modulated the band structures of the ZGNRs, making them half-metallic or semiconducting to some extent. These features suggest that the well-arranged adsorption of pyridine and BF3 could be used to tune the band structures of nanoscale electronic devices based on graphene.