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Electrically tunable magnetoplasmons in a monolayer of silicene or germanene

We theoretically study electrically tunable magnetoplasmons in a monolayer of silicene or germanene. We derive the dynamical response function and take into account the effects of strong spin-orbit coupling (SOC) and of an external electric filed $E_z$ perpendicular to the plane of the buckled silicene/germanene. Employing the random-phase approximation we analyze the magnetoplasmon spectrum. The dispersion relation has the same form as in a two-dimensional electron gas with the cyclotron and plasma frequencies modified due to the SOC and the field $E_z$. In the absence of SOC and $E_z$, our results agree well with recent experiments on graphene. The predicted effects could be tested by experiments similar to those on graphene and would be useful for future spintronics and optoelectronic devices.