Amplification of Acoustic Waves in Graphene Nanoribbon in the Presence of External Electric and Magnetic Field

Amplification of Acoustic Waves in Armchair Graphene Nanoribbon (AGNR) in the presence of an external Electric and Magnetic field was studied using the Boltzmann's kinetic equation. The general expression for the Amplification $(\Gamma_{\perp}/\Gamma_0)$ was obtained in the region $ql >> 1$ for the energy dispersion $\varepsilon(\vec{p})$ near the Fermi point. For various parameters of the quantized wave vector ($\beta$), the analysis of $\Gamma_{\perp}/\Gamma_0$ against the sub-bands index $(p_i)$; width of AGNR; and magnetic strength $(\Omega\tau)$, were numerically analyzed. The results showed a linear relation for $\Gamma_{\perp}/\Gamma_0$ with constant electric field $(\vec{E})$ but non-linear for $\Gamma_{\perp}/\Gamma_0$ with $q$ or $\Omega\tau$. Sound Amplification in AGNR is reported with an increase in Acoustic wave number $(\vec{q}) > 1.5\times 10^{7}cm^{-1}$. This can cause SASER in Armchair Graphene Nanoribbon (AGNR).