Fig. 2. Comparison of plasmon excitations on the surface of a bulk metal, on a metallic thin film, and in atomically thin metals, which are different in nature.
a Dispersion relation for a surface plasmon and the lower-energy surface plasmon-polariton (SPP) branch on the surface of a three-dimensional metal with a bulk plasmon energy ~20 eV, similar to that of bulk TaS2. Retardation effects of the Coulomb interaction, which give rise to hybrid SPPs modes, are noticeable around the intersect of the light cone with the surface plasmon dispersion (inset). The colored intensity sketch represents the electric potential associated with the surface plasmon. b Same as a, but for a thin metallic film with thickness d = 100 . The two distinct surface plasmon modes (red and blue solid lines), as well as the two lower-energy SPP modes (red and blue dashed lines), correspond to antisymmetric and symmetric relative oscillations of the electron density on the opposite surfaces, with the symmetric mode being lower in energy. c Dispersion relation for monolayer TaS2. The energy of the intrinsic plasmons in the dispersionless region is one order of magnitude smaller than that of the surface plasmons shown in b, and the critical wavevector 1/ρ0 ≈ 0.04 that defines the flat dispersion in monolayer TaS2 is about an order of magnitude smaller than that of a classical, atomically thin metallic film of the same thickness, which is 1/d1L = 0.2 (ρ0 = 25 is the screening length and d1L ~ 5 the thickness of monolayer TaS2). Moreover, when interaction with the light field is considered, the intersection of the light cone with the intrinsic plasmon dispersion in monolayer TaS2 occurs at a wavevector that is orders of magnitude smaller than the critical wavevector shown in Fig. 1b. Thus, the dispersionless plasmons in real quasi-2D materials that is the focus of this work are not the result of hybridizing a plasmon with a photon, i.e., it is not the same as the traditional plasmon polariton (inset).