Quantum conductance of graphene nanoribbons with edge defects

The conductance of metallic graphene nanoribbons (GNRs) with single defects and weak disorder at their edges is investigated in a tight-binding model. We find that a single edge defect will induce quasilocalized states and consequently cause zero-conductance dips. The center energies and breadths of such dips are strongly dependent on the geometry of GNRs. Armchair GNRs are more sensitive to a vacancy than zigzag GNRs, but are less sensitive to a weak scatter. More importantly, we find that with a weak disorder, zigzag GNRs will change from metallic to semiconducting due to Anderson localization. However, a weak disorder only slightly affects the conductance of armchair GNRs.

Figure 1

(Color online) Geometry of graphene ribbons. (a) A zigzag ribbon $(N=4)$; (b) an armchair ribbon $(N=7)$. A black circle denotes an edge carbon and a gray circle denotes a bulk carbon. A unit cell contains $2N$ atoms. From the top down, atoms in a unit cell are labeled as 1A, 1B, 2A, 2B, …, $N\mathrm{A}$, $N\mathrm{B}$. Atoms close to 1B are 1A and 2A, and so on.

Figure 2

(Color online) (a) Conductance of a zigzag ribbon ($N=8$, $W=17.3\mathrm{\AA }$) without vacancy (thin solid line), and when one atom (1A), a pair of atoms (1A and 1B), and nearest three atoms (1A, 1B, and 1A) at its edge are removed. (b) LDOS of a 1B atom when there is no vacancy (thin solid line) and when there is a vacancy near it, corresponding to (a).

Figure 3

(Color online) (a) Conductance of an armchair ribbon ($N=14$, $W=17.4\mathrm{\AA }$) without vacancy (solid line), with a two-atom vacancy (dashed line), and with a one-atom vacancy (dash dot line) at its edge. (b) LDOS of a 2B atom when there is no vacancy (solid line) and when its nearest (1A and 1B) pair atoms are removed (dashed line). (c) LDOS of a 1B atom when there is no vacancy (solid line) and when its nearest 1A atom is removed (dashed line).

Figure 4

(Color online) The decreasing rate of the average conductance (between $\pm 0.5\mathrm{eV}$) due to a single vacancy at the edge. As the width of a zigzag ribbon increases, its conductance becomes immune from a vacancy at its edge.

Figure 5

(Color online) (a) Conductance of a zigzag ribbon $(N=8)$ for various strengths of defect potential when the ribbon has a weak scatter at its edge. (b) The LDOS of an edge atom for $V=0\mathrm{eV}$ (no defect) and $V=2.0\mathrm{eV}$ at that site. (c) Conductance of a zigzag ribbon $(N=8)$ when there is a weak scatter at its 1B site (not an edge atom). (d) The LDOS of a 1B atom for $V=0\mathrm{eV}$ and $V=2.0\mathrm{eV}$ at that site.

Figure 6

(Color online) (a) Conductance of an armchair ribbon $(N=14)$ for various strengths of defect potential when the ribbon has a weak scatter at its edge. (b) The LDOS of an edge atom for $V=0\mathrm{eV}$ (no defect) and $V=2.0\mathrm{eV}$ at that site.

Figure 7

A one-dimensional model of a system including conducting bands and a quasilocalized state (QLS). The bulk of the system is represented by a quantum wire (QW), which has one conducting band.

Figure 8

(Color online) Conductance versus energy for zigzag ribbons $(N=8,16)$ with disorder distributed at both edges over lengths of 100 and $1000\mathrm{\AA }$. With a weak disorder, zigzag GNRs change from metallic to semiconducting.

Figure 9

(Color online) (a) Conductance versus ribbon length for two zigzag ribbons $(N=8,12)$ with different disorder strengths ($V_d=0.25$, $1.0\mathrm{eV}$). The straight lines are exponential fits to the simulated data with the ribbon length larger than $50\mathrm{\AA }$. (b) Conductance versus disorder strength for zigzag ribbons with disorder distributed at both edges over a length of $100\mathrm{\AA }$.

Figure 10

(Color online) Conductance versus energy for an armchair ribbon $(N=14)$ with disorder distributed at its both edges over a length of $1000\mathrm{\AA }$.

Figure 11

(Color online) (a) Conductance versus ribbon length for two armchair ribbons $(N=8,14)$ with different disorder strengths. (b) Conductance versus disorder strength for armchair ribbons with disorder distributed at both edges over a length of $1000\mathrm{\AA }$.