Electronic States and Local Density of States in Graphene with a Corner Edge Structure (original) (raw)
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Electronic States and Local Density of States Near Graphene Corner Edge
Localisation 2011, 2012
We study that stability of edge localized states in semi-infinite graphene with a corner edge of the angles 60 • , 90 • , 120 • and 150 •. We adopt a nearest-neighbor tight-binding model to calculate the local density of states (LDOS) near each corner edge using Haydock's recursion method. The results of the LDOS indicate that the edge localized states stably exist near the 60 • , 90 • , and 150 • corner, but locally disappear near the 120 • corner. By constructing wave functions for a graphene ribbon with three 120 • corners, we show that the local disappearance of the LDOS is caused by destructive interference of edge states and evanescent waves.
Decay behavior of localized states at reconstructed armchair graphene edges
Physical Review B, 2013
Density functional theory calculations are used to investigate the electronic structures of localized states at reconstructed armchair graphene edges. We consider graphene nanoribbons with two different edge types and obtain the energy band structures and charge densities of the edge states. By examining the imaginary part of the wavevector in the forbidden energy region, we reveal the decay behavior of the wavefunctions in graphene. The complex band structures of graphene in the armchair and zigzag directions are presented in both tight-binding and first-principles frameworks.
Localized States at Zigzag Edges of Bilayer Graphene
Physical Review Letters, 2008
We report the existence of zero energy surface states localized at zigzag edges of bilayer graphene. Working within the tight-binding approximation we derive the analytic solution for the wavefunctions of these peculiar surface states. It is shown that zero energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene; (ii) states with finite amplitude over the two layers, with an enhanced penetration into the bulk. The bulk and surface (edge) electronic structure of bilayer graphene nanoribbons is also studied, both in the absence and in the presence of a bias voltage between planes.
Edge States and Stacking Effects in Nanographene Systems
Journal of Superconductivity and Novel Magnetism, 2011
Bilayer graphene nanoribbon with a zigzag edge is investigated with the tight binding model. Two stacking structures, α and β, are considered. The band splitting is seen in the α structure, while the splitting in the wave number direction is found in the β structure. The local density of states in the β structure tend to avoid sites where inter-layer hopping interactions are present.
Edge states for the n = 0 Laudau level in graphene
Journal of Physics: Conference Series, 2009
In the anomalous quantum Hall effect (QHE), a hallmark of graphene, nature of the edge states in magnetic fields poses an important question, since the edge and bulk should be intimately related in QHE. Here we have theoretically studied the edge states, focusing on the E = 0 edge mode, which is unusual in that the mode is embedded right within the n = 0 bulk Landau level, while usual QHE edge modes reside across adjacent Landau levels. Here we show that the n = 0 Landau level, including the edge mode, has a wave function amplitude accumulated along zigzag edges whose width scales with the magnetic length, lB. This contrasts with the usual QHE where the charge is depleted from the edge. The implications are: (i) The E = 0 edge states in strong magnetic fields have a topological origin in the honeycomb lattice, so that they are outside the continuum ("massless Dirac") model. (ii) The edge-mode contribution decays only algebraically into the bulk, but this is "topologically" compensated by the bulk contribution, resulting in the accumulation over lB. (iii) The real space behavior obtained here should be observable in STM experiments.
Physical Review B, 2008
We have studied zigzag and armchair graphene nano ribbons (GNRs), described by the Hubbard Hamiltonian using quantum many body configuration interaction methods. Due to finite termination, we find that the bipartite nature of the graphene lattice gets destroyed at the edges making the ground state of the zigzag GNRs a high spin state, whereas the ground state of the armchair GNRs remains a singlet. Our calculations of charge and spin densities suggest that, although the electron density prefers to accumulate on the edges, instead of spin polarization, the up and down spins prefer to mix throughout the GNR lattice. While the many body charge gap results in insulating behavior for both kinds of GNRs, the conduction upon application of electric field is still possible through the edge channels because of their high electron density. Analysis of optical states suggest differences in quantum efficiency of luminescence for zigzag and armchair GNRs, which can be probed by simple experiments.
Physical Review B, 2011
Dirac electrons in finite graphene samples with zigzag edges under high magnetic fields (in the regime of Landau-level formation) are investigated with regard to their bulk-type and edge-type character. We employ tight-binding calculations on finite graphene flakes (with various shapes) to determine the sublattice components of the electron density in conjunction with analytic expressions (via the parabolic cylinder functions) of the relativistic-electron spinors that solve the continuous Dirac-Weyl equation for a semi-infinite graphene plane. Away from the sample edge, the higher Landau levels are found to comprise exclusively electrons of bulk-type character (for both sublattices); near the sample edge, these electrons are described by edge-type states similar to those familiar from the theory of the integer quantum Hall effect for nonrelativistic electrons. In contrast, the lowest (zero) Landau level contains relativistic Dirac electrons of a mixed bulk-edge character without an analog in the nonrelativistic case. It is shown that such mixed bulk-edge states maintain also in the case of a square flake with combined zigzag and armchair edges. Implications for the manybody correlated-electron behavior (relating to the fractional quantum Hall effect) in finite graphene samples are discussed.
Localized states at zigzag edges of multilayer graphene and graphite steps
EPL (Europhysics Letters), 2008
We report the existence of zero energy surface states localized at zigzag edges of Nlayer graphene. Working within the tight-binding approximation, and using the simplest nearestneighbor model, we derive the analytic solution for the wavefunctions of these peculiar surface states. It is shown that zero energy edge states in multilayer graphene can be divided into three families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene; (ii) states with finite amplitude over the two last, or the two first layers of the stack, equivalent to surface states in bilayer graphene; (iii) states with finite amplitude over three consecutive layers. Multilayer graphene edge states are shown to be robust to the inclusion of the next nearestneighbor interlayer hopping. We generalize the edge state solution to the case of graphite steps with zigzag edges, and show that edge states measured through scanning tunneling microscopy and spectroscopy of graphite steps belong to family (i) or (ii) mentioned above, depending on the way the top layer is cut.
Lattice density-functional theory on graphene
Physical Review B, 2010
A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.