First-principles approach to monitoring the band gap and magnetic state of a graphene nanoribbon via its vacancies

Using first-principles plane-wave calculations we predict that electronic and magnetic properties of graphene nanoribbons can be modified by the defect-induced itinerant states. Structure optimization gives rise to significant reconstruction of atomic structure, which is in good agreement with transmission electron microscope images. The band gaps of armchair nanoribbons can be modified by hydrogen-saturated holes. The band-gap changes depend on the width of the ribbon as well as on the position of the hole relative to the edges of the ribbon. Defects due to periodically repeating vacancy or divacancies induce metallization as well as magnetization in nonmagnetic semiconducting nanoribbons due to the spin polarization of local defect states. Antiferromagnetic ground state of semiconducting zigzag ribbons can change to ferrimagnetic state upon creation of vacancy defects, which reconstruct and interact with edge states. Even more remarkable is that all these effects of vacancy defects are found to depend on their geometry and position relative to the edges. It is shown that these effects can, in fact, be realized without really creating defects.

Figure 1

(Color online) (a) Energy-band structures of $\text{AGNR}\left(N=34;l=6\right)$ with and (b) without a hole consisting of six carbon vacancies. (c) Charge-density isosurfaces of selected states. Carbon atoms (represented by black circles), which have coordination number lower than three, are terminated by hydrogen atoms (represented by small gray circles).

Figure 2

(Color online) Effect of a periodic hole on the electronic structure of armchair nanoribbon. (a) Positions of a hole in the ribbon are indicated by numerals. The nanoribbon without a hole is specified by “0.” Carbon atoms (black circles), which have coordination number lower than three, are terminated by hydrogen atoms (represented by small gray circles). [(b) and (c)] Variations in band gaps of $\text{AGNR}\left(N,l\right)$ with the position of the hole specified as 6 V. (d) Variation in the band gap with repeat periodicity, $l$. Results for $N<58$ are obtained by first-principles calculations.

Figure 3

(Color online) (a) Metallization of the semiconducting AGNR(22) by the formation of divacancies with a repeat period of $l=5$. (b) Magnetization of the nonmagnetic AGNR(22) by a defect due to the single carbon atom vacancy with the same repeat periodicity. Isosurfaces around the vacancy corresponding to the difference of the total charge density of different spin directions, $\Delta {\rho }_T$, indicate a net magnetic moment. Solid (red) and dashed (red) lines are for spin-up and spin-down bands; solid (black) lines are nonmagnetic bands.

Figure 4

(Color online) Vacancy and divacancy formations in an antiferromagnetic semiconductor ZGNR(14) with a repeat period of $l=8$. Carbon atoms at both edges are terminated by hydrogen atoms represented by small gray circles. Calculated total energy, $E_T$ (in eV/cell), net magnetic moment, $\mu$ (in Bohr magneton ${\mu }_B/\text{cell}$), and band gap between spin-up(down) conduction and valence bands, $E_G^{\uparrow (\downarrow )}$) are shown for each case. Blue and yellow isosurfaces correspond to the difference of spin-up and spin-down states. [(a)–(c)] Single vacancy, [(d) and (e)] two separated single vacancy, and (f) a divacancy.

Figure 5

(Color online) (a) Monitoring of band gaps $E_G$ by applying a local bias voltage $V_{\text{tip}}$ across the ribbon. (b) $E_G$ versus $V_{\text{tip}}$ applied at the center of $\text{AGNR}\left(N;6\right)$ for $N=34$, 36, and 38. (b) $E_G$ versus $V_{\text{tip}}$ of AGNR(34) for different tip positions schematically described at the top. The tip (or electrodes) is situated at one of the positions 1–3. The repeat period is $l=20$.