Acoustic plasmons in type-I Weyl semimetals

Massless chiral fermions emergent in inversion symmetry-breaking Weyl semimetals (WSMs) reside in the vicinity of multiple low-symmetry nodes and thus acquire strongly anisotropic dispersion. We investigate the longitudinal electromagnetic modes of two-component degenerate Weyl plasma relevant to the realistic band structure of type-I WSM. We show that the actual spectrum of three-dimensional collective density excitations in the TaAs family of WSM is gapless due to emergence of acoustic plasmons corresponding to out-of-phase oscillations of the plasma components. These modes exist around the [001] crystallographic direction and are weakly damped, due to large difference in the Weyl velocities of the $W_1$ and $W_2$ quasiparticles propagating along [001]. We show that acoustic plasmons can manifest themselves as slow beatings of electric potential superimposed on fast plasmonic oscillations upon charge relaxation. The revealed acoustic modes can stimulate purely electronic superconductivity, collisionless plasmon instabilities, and formation of Weyl soundarons.

Figure 1

Implementation of the two-component degenerate plasma in Weyl semimetals: (a) homogeneous plasma formed within the single Weyl node group, and (b) heterogeneous plasma in the multigroup Weyl semimetals (TaAs-like).

Figure 2

Existence conditions and velocities of acoustic plasmons. The relative difference of Weyl velocities $\delta v$ is varied along the horizontal axis, and the relative difference of carrier densities of two types $\delta n$ is varied along the vertical one. The color encodes the velocity of acoustic plasmon $s$ (in units of minimum Weyl velocity). In the middle blue-filled region, acoustic plasmon does not exist. Solid lines correspond to homogeneous plasma (e.g., doped HgTe [22] under strain or chalcopyrite compounds [23]), heterogeneous plasma of TaAs (${\mu }_2/{\mu }_1=5$ [17]), and NbAs (${\mu }_1/{\mu }_2=8.25$ [20, 28]). Dashed part of the TaAs composition line corresponds to the anisotropic WP in (110) and $\left(1\overline{1}0\right)$ planes within the numerically predicted band structure [24, 28].

Figure 3

Contour plot of the dimensionless damping parameter (10) for acoustic plasmon in the region of its existence in WSM with ${\eta }_2/{\eta }_1=2$.

Figure 4

Projection of the band structure of (a) TaAs family WSMs and (b) HgTe family WSMs on the (001) crystallographic plane. Filled ellipses show the cross sections of the approximate Fermi surfaces. Red dashed lines denote mirror symmetry planes perpendicular to (001). Blue lines and dots correspond to symmetry axes.

Figure 5

Anisotropy (red curve) of acoustic plasmon velocity $s\left(\theta \right)$ [in units of $v_{\left(110\right)}^{\left(1\right)}\left(\theta \right)$] in the upper half of the (110) crystallographic plane of TaAs with Weyl velocities taken from Ref. [28]. Directions in which acoustic plasmon can propagate lie inside the $2{\theta }_{\mathrm{crit}}^{\left(110\right)}$ angle formed by the two solid blue lines.

Figure 6

Full RPA energy-loss function for the cases of (a) heterogeneous WP in TaAs supporting the acoustic plasmon mode and (b) homogeneous plasma of HgTe-like WSM (see Fig. 2). Here $\langle \mu \rangle =({\mu }_1+{\mu }_2)/2$ and $\langle v\rangle =(v_1+v_2)/2$.

Figure 7

Relaxation dynamics [(a), (d)] of the self-consistent potential $\delta {\mathcal{V}}_q\left(t\right)$ (20), relaxation spectrum ${\tilde{K}}_2(\omega ,q)$ [(b), (e)] after (21), and full RPA loss function [(c), (f)] at $\langle v\rangle q=0.4\langle \mu \rangle$ in heterogeneous [Fig. 6] and homogeneous [Fig. 6] WP respectively. Vertical dashed black lines correspond to the boundaries $\omega =v_{1,2}q$ of intraband and interband single-particle excitations.