Structure sensitivity of electronic transport across graphene grain boundaries

Graphene grown by large-scale synthesis methods usually contains grain boundaries. They can strongly affect the electronic and mechanical properties of graphene and it is promising to exploit them for the design of electronic components and sensors. Here, we consider semiconducting graphene bicrystals and study how grain boundary structure variations influence electron transport using density functional theory in conjunction with the nonequilibrium Green function method. We find that the size of the transport gap in these bicrystals is not changed by structure variations. Interestingly however, electron transport outside the transport gap is very sensitive to modifications of the grain boundary. We show that these results can be understood within the ballistic transport approximation and by inspecting the electronic density of states resolved in energy-momentum space. Our findings suggest that the electronic response of graphene bicrystals can be controlled not only by grain misorientation but also by manipulation of the grain boundary structure.

Figure 1

(a) GB structure model with the GB oriented along the $y$ -axis. The vector $\mathbf{d}$ represents the repetition unit along the GB and can be represented as a linear combination $(n,m)\left[(n^{\prime },m^{\prime })\right]$ of the unit cell vectors ${\mathbf{a}}_1$ and ${\mathbf{a}}_2({\mathbf{a}}_1^{\prime }$ and ${\mathbf{a}}_2^{\prime })$ of the left (right) grain. (b) Lattice mismatch strain for zz/ac GBs as a function of the GB length in units of $r_{cc}$.

Figure 2

(a) Structure models of $(5,0)\left|\right(3,3)$ GBs A–C and $(7,0)\left|\right(4,4)$ GBs D–${\mathrm{G}}^{\prime }$. GB setup for relaxation (b) and transport calculations (c). Note that the electrode edges are terminated with hydrogen during structural relaxation (see Sec. 2b for details of the relaxation procedure). In the transport calculation the electrodes are substituted by semi-infinite graphene electrodes.

Figure 3

Ballistic transport across GBs in graphene. Total transmission functions of $(5,0)\left|\right(3,3)$ GBs (a) and $(7,0)\left|\right(4,4)$ GBs (b) normalized to the GB length. (c) Electronic DOS resolved in momentum space. (d) Electron transmission resolved in momentum space. (e) Schematic overlap of Dirac cones from an armchair grain domain and a zigzag grain domain. (f) Schematic $k$-resolved transmission constructed from (e). (g) $k$-averaged electronic DOS. (h) $k$-averaged electron transmission. (c)–(h) are calculated for structure A.

Figure 4

(a) $I\left(U\right)$ characteristics of the investigated GBs normalized to the GB length. (b)–(d) Evolution of the DOS and transmission resolved in energy-momentum space at different bias voltages for structure A.

Figure 5

Atom-projected DOS of the $(5,0)\left|\right(3,3)$ GBs. Solid lines show GB atoms as indicated by the structure insets. Dashed lines show bulk atoms.