Complex edge effects in zigzag graphene nanoribbons due to hydrogen loading

We have performed density-functional calculations as well as employed a tight-binding theory, to study the effect of passivation of zigzag graphene nanoribbons (ZGNR) by hydrogen. We show that each edge C atom bonded with 2 H atoms open up a gap and destroys magnetism for small widths of the nanoribbon. However, a re-entrant magnetism accompanied by a metallic electronic structure is observed from eight rows and thicker nanoribbons. The electronic structure and magnetic state are quite complex for this type of termination, with $s{p}^3$ bonded edge atoms being nonmagnetic whereas the nearest neighboring atoms are metallic and magnetic. We have also evaluated the phase stability of several thicknesses of ZGNR and demonstrate that $s{p}^3$ bonded edge atoms with 2 H atoms at the edge can be stabilized over 1 H atom terminated edge at high temperatures and pressures.

Figure 1

(Color online) Calculated formation energies (divided by $2L$, where $L$ is the length of the unit cell in angstrom) according to the equations shown in the text for different widths of nanoribbons. Ref.: ${\text{H}}_2$ and Ref.: H indicate the calculated values using the expressions for $E_f^{\left(1\right)}$ and $E_f^{\left(2\right)}$, respectively. The vertical dashed line indicates the onset of saturation of the formation energies.

Figure 2

(Color online) Calculated Gibbs formation energies (divided by $2L$) for $n=3$ and 20 rows thick 2H terminated (main plot) and 1H and 2H terminated (left inset) ZGNR, at 300 K as a function of chemical potential of hydrogen molecule according to the equations shown in the text. The black (dark solid line in print) line is for $n=3$ whereas the red (gray solid line in print) line is for $n=20$. The left vertical line indicates the chemical potential for which Gibbs energy of 2H terminated edge becomes negative whereas the right vertical line shows the transition point above which the Gibbs energy of 2H is lower than 1H terminated ZGNR. The blue (gray in print) horizontal arrow indicates that the 2H terminated ZGNR continues to be stable over the 1H one after the crossing point. The plot in the right inset shows the logarithm of pressure of ${\text{H}}_2$ in units of bar for different temperatures at which Gibbs energy $G_{\overline{\text{H}}}$ becomes negative for a 20 rows-ZGNR.

Figure 3

(Color online) Calculated C-C bond lengths relative to an ideal 2D graphene layer $\left(1.42\text{Å}\right)$ for different bonds from the edge toward the center of ZGNRs, with thickness four, eight, and 20 rows.

Figure 4

(Left) Calculated total DOS’s of 2H edge terminated nanoribbons of various widths. (Right) Total DOS of an eight-row ZGNR for a nonspin polarized calculation with (inset) expanded view of the DOS near the Fermi level.

Figure 5

(Color online) (Left) Calculated spin-polarized DOS projected on C atoms for 2H edge terminated eight-rows nanoribbon. DOSs projected on $\text{C}p$ orbitals of different symmetries are shown. The topmost panel shows the projected DOS of a C atom at the edge whereas the panels downwards are for C atoms toward the center of the nanoribbon. (Right) Spin-polarized band structure for 2H edge terminated eight-rows zigzag nanoribbon. Both spin-up and spin-down bands are shown.

Figure 6

(Color online) Isosurface plot of magnetization density of an eight-rows 2H terminated ZGNR.

Figure 7

(Color online) (Left) A schematic diagram for the model theory. (Right) Spin-polarized band structure for the carbon-terminated structure shown at the left panel. Both spin-up and spin-down bands are shown.