Role of Symmetry in the Transport Properties of Graphene Nanoribbons under Bias

The intrinsic transport properties of zigzag graphene nanoribbons (ZGNRs) are investigated using first-principles calculations. It is found that although all ZGNRs have similar metallic band structure, they show distinctly different transport behaviors under bias voltages, depending on whether they are mirror symmetric with respect to the midplane between two edges. Asymmetric ZGNRs behave as conventional conductors with linear current-voltage dependence, while symmetric ZGNRs exhibit unexpected very small currents with the presence of a conductance gap around the Fermi level. This difference is revealed to arise from different coupling between the conducting subbands around the Fermi level, which is dependent on the symmetry of the systems.

Figure 1

(a) An asymmetric 7-ZGNR. (b) A symmetric 8-ZGNR, with the mirror plane ($\sigma$) represented by the solid blue line. The dashed rectangle denotes the unit cell of ZGNRs. (c) $I\mathrm{\text{−}}{V}_{\mathrm{bias}}$ curves of ZGNR junctions (see the inset) with different widths. A bias voltage $V_{\mathrm{bias}}$ is applied to the central region with the length ($l$) of 8 unit cells. (d),(e) Conductance of 7-ZGNR and 8-ZGNR under $V_{\mathrm{bias}}=0.5\mathrm{V}$. The conductance gap $C_{\mathrm{gap}}$ is shown as a function of $V_{\mathrm{bias}}$ in the inset of (e).

Figure 2

(a) [(b)] Band structure around the Fermi level and (c) [(d)] isosurface plots of the $\Gamma$-point wave functions of $\pi$ and ${\pi }^{*}$ subbands for 7-ZGNR [8-ZGNR]. In (c) and (d), dark gray (blue) and light gray (yellow) indicate opposite signs of the wave function.

Figure 3

(a) Schematic configuration of a two-gates ZGNR model, where positive (negative) gate voltage $V_{g+}$ ($V_{g-}$) is applied to the red (blue) region. In our calculations, $l_g$ (the length of gate region) and $l_0$ are taken to be 50 and 20 unit cells, respectively. (b) Schematic band structures of the left lead and two-gate regions ($V_{g+}=-V_{g-}=0.25\mathrm{V}$). The dashed lines represent the Fermi level of the regions. (c) Transmission spectra of 8-ZGNR and 7-ZGNR in the two-gate model with $V_{g+}=-V_{g-}=0.25\mathrm{V}$.

Figure 4

(a) Schematic band diagram of the two-probe system under $V_{\mathrm{bias}}$. (b) The optimized geometry and (c) band structure of 8-ZGNR with two edges terminated by H and OH, respectively. (d) $I\mathrm{\text{−}}{V}_{\mathrm{bias}}$ curves of the fully H-terminated 8-ZGNR (red circles), and the H and OH terminated 8-ZGNR shown in (b) (green triangles). $V_{\mathrm{bias}}$ is applied to the central region with the length of 10 unit cells.