Amplification of Hypersound in Graphene with degenerate energy dispersion

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Hypersound amplification/absorption of acoustic phonons in Graphene with degenerate energy dispersion ε(p) near the Fermi level was theoretically studied. For kβT << 1 and ql >> 1, the dependence of the absorption coefficient Γ/Γ₀ on VD Vₛ was studied where the results satisfied the Cerenkov effect. That is when VD Vₛ > 1, an amplification was obtained but for VD Vₛ < 1, an absorption was obtained which could lead to Acoustoelectric Effect (AE) in Graphene. A linear dependence of the Γ/Γ₀ on ωq was observed where the result obtianed qualitatively agreed with an experimentally observed acoustoelectric current in Graphene via the Weinrich relation. It is interesting to note from this study that, frequencies above 10THz can be attained for VD = 1.1ms⁻¹. This study permit the use of Graphene as hypersound phonon laser (SASER).