Amplification of acoustic waves in armchair graphene nanoribbon in the presence of external electric and magnetic fields

Amplification of acoustic waves in Armchair Graphene Nanoribbon (AGNR) in the presence of an external electric and magnetic fields was studied using the Boltzmann's kinetic equation. The general expression for the amplification $({\Gamma }_{\perp }/{\Gamma }_0)$ was obtained in the region $\mathrm{ql}⪢1$ for the energy dispersion $\epsilon \left(\overrightarrow{p}\right)$ near the Fermi point. For various parameters of the quantized wave vector (β), the graphs of ${\Gamma }_{\perp }/{\Gamma }_0$ against the electric field $\left(\overrightarrow{E_x}\right)$, the acoustic wave-number $\left(\overrightarrow{q}\right)$, the energy gap (E_g) and the dimensionless factor (Ωτ₀) were numerically analyzed. The results showed a linear relation for ${\Gamma }_{\perp }/{\Gamma }_0$ with $\overrightarrow{E_x}$ but non-linear for $\overrightarrow{q}$ and Ωτ₀. The observed amplification can lead to SASER in Armchair Graphene Nanoribbon (AGNR).