Defect symmetry influence on electronic transport of zigzag nanoribbons
© Zeng et al; licensee Springer. 2011
Received: 19 August 2010
Accepted: 24 March 2011
Published: 24 March 2011
The electronic transport of zigzag-edged graphene nanoribbon (ZGNR) with local Stone-Wales (SW) defects is systematically investigated by first principles calculations. While both symmetric and asymmetric SW defects give rise to complete electron backscattering region, the well-defined parity of the wave functions in symmetric SW defects configuration is preserved. Its signs are changed for the highest-occupied electronic states, leading to the absence of the first conducting plateau. The wave function of asymmetric SW configuration is very similar to that of the pristine GNR, except for the defective regions. Unexpectedly, calculations predict that the asymmetric SW defects are more favorable to electronic transport than the symmetric defects configuration. These distinct transport behaviors are caused by the different couplings between the conducting subbands influenced by wave function alterations around the charge neutrality point.
As a truly two-dimensional nanostructure, graphene has attracted considerable interest, mainly because of its peculiar electronic and transport properties described by a massless Dirac equation [1, 2]. As such, it is regarded as one of the most promising materials since its discovery [3–5] because charge carriers exhibit giant intrinsic mobility and long mean-free path at room temperature [6, 7], suggesting broad range of applications in nanoelectronics [8–11]. Several experimental [4, 8, 12, 13] and theoretical [2, 14, 15] studies are presently devoted to the electronic, transport, and optical properties  of graphene. By opening an energy gap between valence and conduction bands, narrow graphene nanoribbons (GNR) are predicted to have a major impact on transport properties [17, 18]. Most importantly, GNR-based nano-devices are expected to behave as molecular devices with electronic properties similar to those of carbon nanotubes (CNTs) [19, 20], as for instance, Biel et al.  reported a route to overcome current limitations of graphene-based devices through the fabrication of chemically doped GNR with boron impurities.
The investigation of transport properties of GNRs by various experimental methods such as vacancies generation , topological defects , adsorption , doping , chemical functionalization [26–28], and molecular junctions  have been reported. Meanwhile, defective GNR with chemically reconstructed edge profiles also have been experimentally evidenced  and have recently received much attention [31, 32]. In particular, Stone-Wales (SW) defects, as one type of topological defects, are created by 90° rotation of any C-C bond in the hexagonal network , as shown by Hashimoto et al. . More recently, Meyer et al.  have investigated the formation and annealing of SW defects in graphene membranes and found that the existence of SW defects is energetically more favorable than in CNTs or fullerenes. Therefore, the influences of SW defects on electronic transport of GNRs is crucial for the understanding of the physical properties of this novel material and for its potential applications in nanoelectronics.
In this brief communication, we investigate the influence of SW defects on the electronic transport of zigzag-edged graphene nanoribbons (ZGNRs). It is found that the electronic structures and transport properties of ZGNRs with SW defects can very distinctively depend on the symmetry of SW defects. The transformation energies obtained for symmetric SW defects and asymmetric SW defects are 5.95 and 3.34eV, respectively, and both kinds of defects give rise to quasi-bound impurity states. Our transport calculations predict different conductance behavior between symmetric and asymmetric SW defects; asymmetric SW defects are more favorable for electronic transport, while the conductance is substantially decreased in the symmetric defects configuration. These distinct transport behaviors result from the different coupling between the conducting subbands influenced by the wave function symmetry around the charge neutrality point (CNP).
Model and methods
The optimization calculations are done by using the density functional theory utilized in the framework of SIESTA code [36, 37]. We adopt the standard norm-conserving Toullier-Martins  pseudopotentials orbital to calculate the ion-electron interaction. The numerical double-ζ polarized is used for basis set and the plane cutoff energy is chosen as 200 Ry. The generalized gradient approximation  proposed by Perdew and Burke and Ernzerhof was employed to calculate exchange correction term. All nanostructure geometries were converged until no forces acting on all atoms exceeded 0.01eV/Å.
In this study, we consider symmetric and asymmetric SW defects contained in 6-ZGNRs, where 6 denotes the number of zigzag chains (dimers) across the ribbon width . Taking into account screening effects between electrodes and central molecules, we use 10-unit cell's length as scattering regions, and 2 units as electrodes to perform transport calculation. The electron temperature in the calculation is set to be 300 K.
Results and discussions
In Figure 1, we show the geometry of defective ZGNR after relaxation. After introducing symmetric SW defects, the GNR shrinks along the width axis, by 0.526 Å, and correspondingly, the nearest four H atoms move toward the central region by 0.21 Å. As a result, the bond angles of the edge near the SW defects are reduced from 120 to 116°, as shown in Figure 1c, d. In contrast to the shrinking along the width axis, the SW defects stretch from 4.88 to 5.38 Å along the length axis direction. No distinct change for the H-C bond length at the edge is observed. Thus, the effect of symmetric SW defects on the geometry modification is limited to the defective area, with mirror reflection around their axis. However, the presence of asymmetric SW defects to the geometry modification is far more complex. They twist the whole structure by shifting the left side upward, while the right side is downward shifted. Hence, the mirror symmetry is broken because of the asymmetric SW. The transformation energies for symmetric and asymmetric SW defects are 5.95 and 3.34eV, respectively. These results imply that the asymmetric SW defects are energetically more favorable than the symmetric SW defects.
In summary, we investigate the influence of local structural defects on the electronic transport of ZGNR using first principles calculations. The transformation energies reveal that the asymmetric SW defects is energetically more favorable than the symmetric SW defects. Both defects give rise to complete electron backscattering region that depends on the spatial symmetry of the defects. Our transport calculations predict that the asymmetric SW defects are more favorable for electronic transport in contrast to the substantially decreased in the symmetric defects configuration. We attribute these distinct transport behaviors to the different coupling between the conducting subbands influenced by the wave function modification around the CNP.
charge neutrality point
highest-occupied electronic states
lowest-unoccupied electronic states
zigzag-edged graphene nanoribbon.
The authors gratefully thank Prof. K.-L. Yao and Dr. M. A. Kuroda for their technical assistance with performing ab initio transport properties and the relax calculation in the Mac OS X Turing cluster. This study is financially supported by the Scientific Research Foundation of Yangtze University (Grant No.801080010111) and the Chongqing University of Technology (Grant No.2008EDJ01), and the Natural Science Foundation of China under Grant No.11047176.
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