Figure 1

The chiral Fermi contours in the presence of BR and D SOI in the $(k_x,k_y)$ electron momentum plane. Arrows indicate the direction of the spin. A bosonic excitation of electron-hole pairs of zero energy, which is mediated by carrier scattering with the initial, $\vec{k}$, and final, $\overrightarrow{k^{\prime }}=\vec{k}+\vec{q}$, momenta, is shown by the open and bold dots. Depending on the orientation of the bosonic momentum, $\vec{q}$, there exists a minimum value $q_c$ such that for $q<q_c$ it is no longer possible to form zero-energy excitations on the Fermi surface, mediated by electronic transitions between states of different ($\mu =\pm 1$) chirality subbands. Due to the spectrum anisotropy, the form factor of overlapping spinors, in general, remains finite for scattering with $q=q_c$. The thick dash-dotted line is the interchirality subband diameter, connecting maximally distant points on the different chirality subbands along the direction of $\vec{q}$. The ratio of BR and D SOI strengths and their absolute values are given by the parameters $\theta =\pi /5$ and $\rho =0.2k_F$.Reuse & Permissions

Figure 2

The static polarizability vs the orientation ${\varphi }_{\mathbf{q}}$ of the bosonic momentum $\vec{q}$. Different curves are calculated for the values of parameter $\theta$ shown in the inset and for fixed momentum magnitude, corresponding to $x=1$. Here, $\rho =0.1k_F$.Reuse & Permissions

Figure 3

(left) The relaxation propagator $K\left(\vec{q}\right)$ as a function of the bosonic momentum $q$ for three different orientations ${\varphi }_{\mathbf{q}}=\pi /8$, $\pi /6$, and $2\pi /9$ corresponding, respectively, to the dotted, dashed, and solid curves. The positions of the singularity are shown by the large ticks, respectively, at the momentum values of $q_c/2k_F=q_1/2k_F=0.124$, $q_2/2k_F=0.173$, and $q_3/2k_F=0.254$. (mid) The absolute value of the bosonic momentum $q$ as a function of the electron momentum direction ${\varphi }_{\mathbf{k}}$ for the orientations of the wave vector $\vec{q}$ corresponding to the (left) figure. For each curve, the minimum value of $q$, shown by the grid lines at $q_c=q_1$, $q_2$, and $q_3$, gives the position of the singularity of $K\left(\vec{q}\right)$. (right) The positions of singularities of the relaxation propagator $K(\vec{q},\omega )$ in the ($\omega ,q$) plane. The solid curves starting from the origin show the singularities at the boundaries of the intrachirality subband electron-hole continuum. The format of other curves in the (right) figure and the curves in the (mid) figure corresponds to the same values of ${\varphi }_{\mathbf{q}}$ in the (left) figure. The SOI parameters used here are the same as in Fig. 1.Reuse & Permissions

Figure 4

Density plot of the charge density relaxation propagator $K\left(\vec{q}\right)$ as functions of the parameter $\theta$ and of the bosonic momentum $q/2k_F$. The total SOI strength $\rho =0.2$ and the orientation of the momentum ${\varphi }_{\mathbf{q}}=\pi /6$. The color output plot range is from 5.3 (blue) to 20.5 (red).Reuse & Permissions