Fig. 1: Two-dimensional (2D) Dirac plasmon-polariton dispersion.
From: Two-dimensional Dirac plasmon-polaritons in graphene, 3D topological insulator and hybrid systems
a Numerical calculation results are displayed, where the plasmon frequency ω and wavevector q are divided by Fermi energy EF and Fermi wavevector kF, respectively. The ωnon-local (ωlocal) is calculated from the non-local (local) graphene polarization. The imaginary part of the plasmon mode (γLandau) is obtained from the non-local graphene polarization, emergent when the ω enters either the interband (inter) or intraband (intra) single-particle-excitation (SPE) region. Note that the γLandau is multiplied by 4 for comparison. The background dielectric constant is κ = 1. b Plasmon modes are displayed with κ = 4. c Plasmon-phonon couplings split the unperturbed plasmon mode (black dashed line) into hybridized modes (colored solid lines). Horizontal dashed lines indicate surface phonon-polariton energies in silicon oxide. The plasmon-phonon coupling constant is αsp = 0.03. d Equivalent results are obtained at αsp = 0.3. e Double-layer graphene structure splits monolayer graphene plasmon (ωsingle-layer) into the optical (ωoptical) and acoustic plasmon mode (ωacoustic). The γLandau in the monolayer graphene (black dashed line) is also split into optical (blue dashed line) and acoustic γLandau (red dashed line). The distance between the double layer is kFd = 1.5. f Equivalent calculations with kFd = 0.3 are shown. g Graphene plasmons at cold (ωcold, η = 0) and hot plasma cases (ωhot, η > 0) are displayed with η = kBTe/EF. The γLandau of ωcold (black dashed line) is lower than γLandau at η = 0.6 (red dashed line) and η = 1.2 (yellow dashed line). h The ω as a function of η are plotted at different q
