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Full ranges of both hybrid plasmon-mode dispersions and their damping arestudied systematically by our recently developed mean-field theory in opensystems involving a conducting substrate and a two-dimensional (2D) materialwith a buckled honeycomb lattice, such as silicene, germanene, and a group\rom{4} dichalcogenide as well. In this hybrid system, the single plasmon modefor a free-standing 2D layer is split into one acoustic-like and oneoptical-like mode, leading to a dramatic change in the damping of plasmonmodes. In comparison with gapped graphene, critical features associated withplasmon modes and damping in silicene and molybdenum disulfide are found withvarious spin-orbit and lattice asymmetry energy bandgaps, doping types andlevels, and coupling strengths between 2D materials and the conductingsubstrate. The obtained damping dependence on both spin and valley degrees offreedom is expected to facilitate measuring the open-system dielectric propertyand the spin-orbit coupling strength of individual 2D materials. The uniquelinear dispersion of the acoustic-like plasmon mode introduces additionaldamping from the intraband particle-hole modes which is absent for afree-standing 2D material layer, and the use of molybdenum disulfide with alarge bandgap simultaneously suppresses the strong damping from the interbandparticle-hole modes.

Controlling plasmon modes and damping in buckled two-dimensional material open systems