Controlled growth of a line defect in graphene and implications for gate-tunable valley filtering

Atomically precise tailoring of graphene can enable unusual transport pathways and new nanometer-scale functional devices. Here we describe a recipe for the controlled production of highly regular “5-5-8” line defects in graphene by means of simultaneous electron irradiation and Joule heating by applied electric current. High-resolution transmission electron microscopy reveals individual steps of the growth process. Extending earlier theoretical work suggesting valley-discriminating capabilities of a graphene 5-5-8 line defect, we perform first-principles calculations of transport and find a strong energy dependence of valley polarization of the charge carriers across the defect. These findings inspire us to propose a compact electrostatically gated “valley valve” device, a critical component for valleytronics.

Figure 1

Growth of a 5-5-8 line defect from the edges of graphene under large electrical bias. Schematic drawing of the growth process of a 5-5-8 line defect in graphene. Graphene edges and a large electrical current are found to be the necessary condition for the 5-5-8 line defect to grow. Insets (i) and (ii) show the proposed initial stages of the line defect grown from a 5-6 pair at the edge of graphene (see Fig. 3 for experimental data and detailed growth steps).

Figure 2

Reconstructed exit-wave phase image of a 5-5-8 line defect in graphene. (a) The phase of the electron exit wave from a 5-5-8 line defect in graphene was reconstructed using a focal series of 80 TEM images taken at the defect. (b) Illustration of the atomic structure of the line defect (orange dots) and its termination (red dots).

Figure 3

Self-catalyzing growth of the 5-5-8 line defect. (a)–(c) Time series of images capturing the growth of the line defect. Atomic structure models and their overlays onto the experi-mental data are also shown. The line defect grows by one octagon each time by the ejection of one carbon atom (marked by the blue dots in the illustrations) from the 5-6 termination and the formation of a new bond between the two carbon atoms (marked by the yellow dots) that were the nearest neighbors of the lost carbon atom. The same process annihilates the original 5-6 pair and creates a new 5-6 pair as termination. The structure shown in (b) shows no clear dimerization pattern as a result of structural resonance involving several degenerate configurations (more details are in the main text).

Figure 4

Electronic, transport, and valley-filtering properties of the line defect. (a) First-principles electronic band structure calculated for the model of the line defect along $k_{\left|\right|}$ (momentum along the line defect) at $k_{\perp }=0$ (momentum perpendicular to the defect).The circles indicate the degree of localization of electronic states at the line defect. The shaded area corresponds to the continuum of bulk graphene states projected onto the 1D Brillouin zone of the line defect. (b) Transmission probability through the line defect as a function of charge-carrier momentum $k_{\left|\right|}$ and energy $E$. (c), (d) Valley polarizations calculated for electrons and holes, respectively, as a function of the incident angle of charge carriers at their different energies. The dashed lines correspond to the symmetry-based model of Ref. [7].

Figure 5

Proposed electrically operated graphene valley valve. Schematic drawing of an electrically operated graphene valley valve utilizing a pair of parallel 5-5-8 line defects. Electron charge carriers without net valley polarization are injected at a nonzero angle towards two parallel line defects. The Fermi levels of the two line-defect regions are independently controlled by two local gates so as to generate and detect valley polarization in the left and right line defects, respectively.