Effect of zigzag and armchair edges on the electronic transport in single-layer and bilayer graphene nanoribbons with defects

Abstract

We study electronic transport in monolayer and bilayer graphene with single and many short-range defects focusing on the role of edge termination (zigzag versus armchair). Within the tight-binding approximation, we derive analytical expressions for the transmission amplitude in monolayer graphene nanoribbons with a single short-range defect. The analytical calculations are complemented by exact numerical transport calculations for monolayer and bilayer graphene nanoribbons with a single and many short-range defects and edge disorder. We find that for the case of the zigzag edge termination, both monolayer and bilayer nanoribbons in a single-and few-mode regime remain practically insensitive to defects situated close to the edges. In contrast, the transmission of both armchair monolayer and bilayer nanoribbons is strongly affected by even a small edge defect concentration. This behavior is related to the effective boundary condition at the edges, which, respectively, does not and does couple valleys for zigzag and armchair nanoribbons. In the many-mode regime and for sufficiently high defect concentration, the difference of the transmission between armchair and zigzag nanoribbons diminishes. We also study resonant features (Fano resonances) in monolayer and bilayer nanoribbons in a single-mode regime with a short-range defect. We discuss in detail how an interplay between the defect's position at different sublattices in the ribbons, the defect's distance to the edge, and the structure of the extended states in ribbons with different edge termination influence the width and the energy of Fano resonances.

Electronic transport in graphene nanoribbons with sublattice-asymmetric doping

“…The persistence of the T = 1 plateau in the symmetric case has been observed previously [34]. In general, AGNRs are more sensitive to edge disorders than the bulk substitutional disorder considered here [31,41]. The transport gap for asymmetric doping has a corresponding electronic band gap, clearly visible in the averaged DOS plot in Fig.…”

“…This is important since CVD-grown graphene contains extended edgelike defects in the form of grain boundaries [25][26][27][28], unlike bottom-up approaches which may allow the synthesis of more precise geometries [29]. We are further motivated by the strong dependence of GNR transport on edge geometry and impurity distribution [30][31][32][33][34][35][36][37][38][39][40][41][42][43] and by sublattice dependent features in carbon nanotubes [44,45]. We consider both armchair-(AGNR) and zigzag-(ZGNR) edged ribbons, noting the in-built sublattice asymmetry of ZGNRs due to sites along one edge belonging to one sublattice.…”

Random vacancy effect on the electronic transport of zigzag graphene nanoribbon using recursive Green’s function

“…Middle vacancy, on the other hand, is empty space of a carbon atom located in the inner part of GNR, which usually either appears during synthesis process of a GNR [14,15], or artificially produces by techniques like ion and electron irradiation [16][17][18]. A variety of methods, ranging from simple Green's function (GF) approaches to various density functional theory (DFT) calculations, have been developed over the years that enable us to study edge or middle imperfection influence on the electrical conductance of a GNR [8,15,[19][20][21][22][23].…”

Nodal adsorbate bound states in armchair graphene nanoribbons: Fano resonances and adsorbate recognition in weak disorder

“…The novel Dirac properties of graphene [1,2] has prompted much recent research on the quantum transport of graphene nanoribbons (GNRs), both experimentally [3][4][5][6][7][8][9] and theoretically [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. One of the spectacular manifestations of the Dirac physics is in the metallic armchair GNRs (AGNRs), where a subband intercepts the Dirac point to become gapless [24].…”

“…On the other hand, the motivation to tune the GNR energy gap from a microscopic point of view has led to researches on the effects of individual microscopic objects on the GNR. There have been studies of individual doping atoms [13], lattice defects [14,15], vacancies [17,18,22], and adsorbates [19,23] on the quantum transport of GNRs. These single-scatterer studies have found dip structures in G [13][14][15]17,19,22], whose dip energies are associated with the resonant-state energies due to the scatterer in the GNRs.…”