Anisotropic plasmons in a two-dimensional electron gas with spin-orbit interaction

Spin-orbit coupling-induced anisotropies of plasmon dynamics are investigated in two-dimensional semiconductor structures. The interplay of the linear Bychkov-Rashba and Dresselhaus spin-orbit interactions drastically affects the plasmon spectrum: the dynamical structure factor exhibits variations over several decades, prohibiting plasmon propagation in specific directions. While this plasmon filtering makes the presence of spin-orbit coupling in plasmon dynamics observable, it also offers a control tool for plasmonic devices. Remarkably, if the strengths of the two interactions are equal, not only the anisotropy but all the traces of the linear spin-orbit coupling in the collective response disappear.

Figure 1

(Color online) Fermi contours in the momentum plane $\left(k_x,k_y\right)$ for a spin-orbit interaction of the form given in Eq. (1): (a) $\alpha \ne \beta$ and (b) $\alpha =\beta$. The arrows indicate the spin direction.

Figure 2

(Color online) (a) The intra- and interchirality EHC in the $\omega -q$ plane for two different momentum orientations, ${\varphi }_{\mathbf{q}}=\pi /4$ and $3\pi /4$. The symbols show the plasmon dispersions (see text). (b) The imaginary part of the dielectric function vs energy for the fixed momentum magnitude $q=0.15k_F$ and for ${\varphi }_{\mathbf{q}}=\pi /2$ and $3\pi /4$, shown as square and round symbols, respectively.

Figure 3

(Color online) The SOI induced energy dispersion of the plasmon vs its propagation direction for $q=0.15k_F$ (the left axis and square symbols). The parts of the spectrum which do not represent plasmon excitations (see text) are shown as triangle symbols. The dashed line plots the imaginary part of the dielectric function (the right axis) for $q=0.15k_F$ and $\Delta \omega \equiv \omega -{\omega }_0=1.2\text{K}$ where ${\omega }_0\approx 0.45E_F$.

Figure 4

(Color online) The dynamical structure factor vs ${\varphi }_{\mathbf{q}}$ for $q=0.15k_F$. The solid and dashed lines correspond, respectively, to the local maximum at $\Delta \omega \approx 0.5\text{K}$ and minimum at $\Delta \omega \approx 1.1\text{K}$ of the plasmon spectrum (cf. Fig. 3) and show the single-peak behavior of $S\left(\vec{q},\omega \right)$. The dashed-dot-dot and dashed-dot lines illustrate the splitting of the structure factor peaks for $\Delta \omega \approx 0.25$ and 1.5 K. The inset shows the asymmetric double-peak structure of the structure factor for $\Delta \omega \approx 0.7\text{K}$.