Standing spin waves excited optically across an indirect gap in short graphene nanoribbons

We report theoretical investigations that unveil unique electronic excitations in graphene nanoribbons of nanoscale length. The main point is that electronic states in short nanowires are standing particle-in-a-box-like waves, amenable to excitation by electromagnetic radiation. The unusual electronic and magnetic properties of graphene nanoribbons add another feature: terahertz (THz) radiation induces edge standing spin waves with different wavelengths at the two edges and a resonant frequency that can be controlled by an external gate voltage, opening the possibility of THz-spintronic applications.

Figure 1

(Color online) A zigzag graphene nanoribbon in $x\text{−}y$ plane with a transverse dc electric field along the $y$ direction and an electromagnetic wave incident along the $z$ direction (perpendicular to the paper).

Figure 2

(Color online) Spin-resolved band structure of an eight-ZGNR (a) with $E_y^{\text{dc}}=0$ and (b) $E_y^{\text{dc}}=2\text{V}/\text{nm}$ closes the band gap; (c) Change in the spin-resolved band gap of the eight-ZGNR as a function of $E_y^{\text{dc}}$.

Figure 3

(Color online) The wave function of HOMO/LUMO at [(a) and (c)] the top edge and [(b) and (d)] the bottom edge of the (8,99) ZGNR. The curves added in (a)–(d) are guides for the eye.

Figure 4

(Color online) The dynamic charge response of the (8,99) ZGNR with strong substrate screening for (a) $\alpha$ and (b) $\beta$ spins. The same response without any substrate screening for the $\beta$ spin is shown in (c) and is an order-of-magnitude smaller. (d) shows the dynamic charge responses of $\beta$ spin in (b) at the top and bottom edges of the (8,99) ZGNR. The dc electric field is $E_y^{\text{dc}}=1.745\text{V}/\text{nm}$, and the electric component of the EM wave is $E_x^{\text{ac}}=0.01\text{V}/\text{nm}$ at $\omega =16\text{GHz}$ frequency.

Figure 5

(Color online) (a) The $q=2\pi /a-2k_v$ (top edge) and $q=2\pi /a-k_v-k_c$ (bottom edge) components of the Fourier transform of the standing spin waves as a function of the driving frequency with the transverse dc electric field $E_y^{\text{dc}}=1.745\text{V}/\text{nm}$; (b) The resonance frequency as a function of the transverse dc electric field.