Crossover from diffusive to nondiffusive dynamics in the two-dimensional electron gas with Rashba spin-orbit coupling

We present the calculation of the density matrix response function of the two-dimensional electron gas with Rashba spin-orbit interaction, which is applicable in a wide range of parameters covering the diffusive and nondiffusive and dirty and clean limits. A description of the crossover between the different regimes is thus provided as well. On the basis of the derived microscopic expressions we study the propagating charge and spin-polarization modes in the clean, nondiffusive regime, which is accessible in modern experiments.

Figure 1

The structure factors $S^{\left(e\right)}(z,w)∕\nu$ (upper panel) and $S^{\left(o\right)}(z,w)∕\nu$ (lower panel) at $y={10}^{-3}$ and $\Gamma =0.5\times {10}^{-4}$.

Figure 2

Upper panel: The peaks’ heights (weights) $S^{\left(o\right)}[z,w_{\pm }^{\left(o\right)}\left(z\right)]$ (dashed and dotted) and $S^{\left(e\right)}[z,w_{+}^{\left(e\right)}\left(z\right)]$ (solid) normalized by $\nu$. Lower panel: The widths ${\gamma }_{\pm }^{\left(o\right)}\left(z\right)$ and ${\gamma }_{+}^{\left(e\right)}\left(z\right)$ of the corresponding modes normalized by $\Gamma$.

Figure 3

The structure factors $S^{\left(e\right)}(z,w)∕\nu$ (upper panel) and $S^{\left(o\right)}(z,w)∕\nu$ (lower panel) at $y=\Gamma ={10}^{-3}$.

Figure 4

The real (solid) and the imaginary (dashed) parts of ${\tilde{M}}_x^y=(4k_F∕e\nu )M_x^y(y\times \{0.01+0.15j\},w)+18j[j=0,\dots ,4]$ at $y={10}^{-3}$ and $\Gamma =0.5\times {10}^{-5}$.