Directional plasmon filtering in a two-dimensional electron gas embedded in high-index crystallographic planes

We study theoretically the plasmon excitations in a two-dimensional electron gas (2DEG) with spin-orbit interactions (SOIs) embedded in a (11n) crystallographic plane. We demonstrate that the energy spectra and dielectric functions between the 2DEGs embedded in different crystallographic planes can be related by a unitary transformation. Using the unitary transformation, we find that the anisotropy of plasmon excitations and the directional plasmon filtering (DPF) can be tuned by changing the strengths of SOIs in the high-index planes. There are two advantageous directions [110] and [nn2] for plasmon propagation. Moreover, the anisotropy and the DPF can be smeared out by tuning the strength ratio α/β between the Rashba SOI and the Dresselhaus SOI.