Half-metallicity in graphene nanoribbons with topological line defects

First-principles calculations have been performed to investigate the electronic properties of graphene nanoribbons with topological line defects composed of octagons and fused pentagons. We find that the edge-passivated zigzag graphene nanoribbons (ZGNRs) with the line defects along the edge show half-metallicity as the line defect is close to one edge. The electronic properties of the ZGNRs with line defects can be tuned by changing the ribbon width and the position of the line defect. When the position of the line defect changes, there are transitions from an antiferromagnetic semiconductor to an antiferromagnetic half-metal, and then to a ferromagnetic metal, suggesting the potential applications of the system in spintronic devices.

Figure 1

The relaxed structure of 7-3-LD-ZGNR. The circles represent carbon atoms and the rhombuses represent hydrogen atoms. The carbon atoms in the line defect are represented by the filled gray circles. The sublattice A and B of the left and right ribbons are represented by the empty circles and filled black circles, respectively. The structure is periodic along the line defect with a lattice constant denoted as $d$. The atoms in the middle of the fused pentagons are labeled as DM${}_1$ and DM${}_2$. The atoms in the line defect connected to the left ribbon are labeled as DA${}_1$ and DA${}_2$. The atoms in the line defect connected to DA atoms are labeled as DB${}_1$ and DB${}_2$. The four atoms connected to the the right ribbon are labeled as DA${}_1^{\prime }$, DB${}_1^{\prime }$, DA${}_2^{\prime }$, and DB${}_2^{\prime }$.

Figure 2

The energy difference E${}_{\mathrm{FM}}$ $-$ E${}_{\mathrm{AFM}}$ per unit cell for N${}_1$-1-LD-ZGNRs between the FM and AFM configurations as a function of N${}_1$. The dashed line represents the zero energy difference.

Figure 3

Contour plots for the spin density ${\rho }_{\mathrm{up}}-{\rho }_{\mathrm{down}}$ of 5-1-LD-ZGNR in the (a) AFM and (b) FM states. The thicker lines indicate the spin-up density with ${\rho }_{\mathrm{up}}-{\rho }_{\mathrm{down}}>0$. The range of isovalues is $[0.01,0.40]$ Å${}^{-2}$ in both (a) and (b). The thinner lines represent the spin-down density with ${\rho }_{\mathrm{up}}-{\rho }_{\mathrm{down}}<0$. The range of isovalues is $[-0.32,-0.01]$ Å${}^{-2}$ in (a) and $[-0.1,-0.01]$ Å${}^{-2}$ in (b). (c) The difference between the absolute values of the spin density of the AFM state and the FM state ${\left|\rho \right|}_{\mathrm{AFM}}-{\left|\rho \right|}_{\mathrm{FM}}$ with $\left|\rho \right|=|{\rho }_{\mathrm{up}}-{\rho }_{\mathrm{down}}|$ integrated within the plane perpendicular to the armchair direction. $x$ is the coordinate along the width of the nanoribbon with the left edge atoms located at $x=0$.

Figure 4

Contour plots for the spin density ${\rho }_{\mathrm{up}}-{\rho }_{\mathrm{down}}$ of 13-1-LD-ZGNR in the (a) AFM and (b) FM states. The thicker lines indicate the spin-up density with ${\rho }_{\mathrm{up}}-{\rho }_{\mathrm{down}}>0$. The range of isovalues is $[0.01,0.43]$ Å${}^{-2}$ in both (a) and (b). The thinner lines represent the spin-down density with ${\rho }_{\mathrm{up}}-{\rho }_{\mathrm{down}}<0$. The range of isovalues is $[-0.31,-0.01]$ Å${}^{-2}$ in (a) and $[-0.1,-0.01]$ Å${}^{-2}$ in (b). (c) ${\left|\rho \right|}_{\mathrm{AFM}}-{\left|\rho \right|}_{\mathrm{FM}}$ as a function of $x$.

Figure 5

(a), (b), and (c) The spin resolved band structures of LD-ZGNRs for $N_1=$ 5, 7, and 9 with $N_1+N_2=10$. The thinner and thicker lines denote bands of spin-up and spin-down, respectively. (d) The band gap of the spin-down state ${\Delta }_{\mathrm{down}}$ and the eigenvalue difference ${\Delta }_{\mathrm{up}}$ between the lowest conduction band and the highest valence band of the spin-up state as a function of $N_1$.

Figure 6

(a), (b), and (c) The spin resolved band structures of LD-ZGNRs for $N_1=$ 3, 5, and 7 with $N_2=1$. (d) ${\Delta }_{\mathrm{up}}$, ${\Delta }_{\mathrm{down}}$ and the eigenvalue difference ${\Delta }_X$ between the spin-up and spin-down valence states at the $X$ point as a function of $N_1$.

Figure 7

The spatial distribution of the valence eigenfunction at the $X$point for (a) 3-1-LD-ZGNR and (b) 7-1-LD-ZGNR. The isosurface is 0.015 Å${}^{-3}$.