Surface plasmons in anisotropic 3D gapped topological insulators

Topological insulators (TIs) are materials having conductive surfaces but insulating bulk, which are ideal platforms for plasmonic applications. The most commonly known TIs, such as Bi₂Se₃and Bi₂Te₃, are in fact highly anisotropic. The dielectric constants are largely different parallel and perpendicular to the surface. Here, we have extended the electromagnetic calculations of the surface plasmons in TIs to the anisotropic case. Magnetic field perpendicular to the surface is allowed, which opens a gap among the surface states. We model anisotropic TIs as bulk dielectric materials with different in-plane and out-of-plane permittivities; the surface states caused by the band inversion lead to a two-dimensional conductivity which supports surface plasmons. We have found two rather than one surface modes. Due to such anisotropy, quasi transverse electric (TE) polarized mode may occur near the interband transition threshold. Far below the transition frequency, another mode with both TE and transverse magnetic polarized components dominates, the dispersion relation of which is seriously modified by the Hall conductivity. By taking Bi₂Te₃as an example, we have derived the conductivity tensor with the consideration of the hexagonal warping effect, and solved the above mentioned two surface plasmon modes. In the end, finite element method has been used to calculate the electric field distributions. Our extension of the electromagnetic calculations of surface plasmons including a specific kind of anisotropy might be useful in other surface conductive materials with similar symmetry as well.