Chiral magnetic plasmons in anomalous relativistic matter

The chiral plasmon modes of relativistic matter in background magnetic and strain-induced pseudomagnetic fields are studied in detail using the consistent chiral kinetic theory. The results reveal a number of anomalous features of these chiral magnetic and pseudomagnetic plasmons that could be used to identify them in experiment. In a system with nonzero electric (chiral) chemical potential, the background magnetic (pseudomagnetic) fields not only modify the values of the plasmon frequencies in the long-wavelength limit, but also affect the qualitative dependence on the wave vector. Similar modifications can be also induced by the chiral shift parameter in Weyl materials. Interestingly, even in the absence of the chiral shift and external fields, the chiral chemical potential alone leads to a splitting of plasmon energies at linear order in the wave vector.

Figure 1

The relative orientation of all relevant vectors used in the analysis of collective modes in an external magnetic field.

Figure 2

The function $F\left({\mu }_{\lambda }/T\right)$, its Padé approximant, and two of its asymptotes.

Figure 3

The dispersion relation of the longitudinal collective mode given by Eq. (79) as a function of the wave vector at $B_{0,5}=0.5\hslash {\mathrm{\Omega }}_e^2/\left(v_{F}e\right)$ (red solid line) and $B_{0,5}=0$ (blue dashed line).

Figure 4

The dispersion relations of the transverse collective modes given by Eq. (76) at different values of $\mu ,{\mu }_5,B_0,B_{0,5}$, and $b_{\parallel }$. Red solid and green dotted lines correspond to ${\omega }_{\mathrm{tr}}^{+}$. Blue dashed and brown dot-dashed lines correspond to ${\omega }_{\mathrm{tr}}^{-}$. We set $e{b}_0=-{\mu }_5$ and $T=0$.

Figure 5

The dispersion relations of the collective modes given by Eq. (74) for $\mu =\sqrt{3\pi /\left(4\alpha \right)}\hslash {\mathrm{\Omega }}_e,{\mu }_5=0$ (left) and $\mu =0,{\mu }_5=\sqrt{3\pi /\left(4\alpha \right)}\hslash {\mathrm{\Omega }}_e$ (right). Red (cyan) solid line corresponds to ${\omega }_l$, blue (brown) dashed one denotes ${\omega }_{\mathrm{tr}}^{+}$, and green (magenta) dotted one corresponds to ${\omega }_{\mathrm{tr}}^{-}$ at $B_0=0[B_0=0.5\hslash {\mathrm{\Omega }}_e^2/\left(v_{F}e\right)]$ in the left panel and $B_{0,5}=0[B_{0,5}=0.5\hslash {\mathrm{\Omega }}_e^2/\left(v_{F}e\right)]$ in the right panel. We set $b_{\perp }=0.5\hslash {\mathrm{\Omega }}_e/e,e{b}_0=-{\mu }_5$, and $T=0$.

Figure 6

The dispersion relations of the collective modes given by Eq. (C13) at $k_{\parallel }=0$ and $b_{\parallel }=0.5\hslash {\mathrm{\Omega }}_e/e$ for $\mu =\sqrt{3\pi /\left(4\alpha \right)}\hslash {\mathrm{\Omega }}_e,{\mu }_5=0$ (left) and $\mu =0,{\mu }_5=\sqrt{3\pi /\left(4\alpha \right)}\hslash {\mathrm{\Omega }}_e$ (right). Red (cyan) solid line corresponds to ${\omega }_l$, blue (brown) dashed one denotes ${\omega }_{\mathrm{tr}}^{+}$, and green (magenta) dotted one corresponds to ${\omega }_{\mathrm{tr}}^{-}$ at $B_0=0[B_0=0.5\hslash {\mathrm{\Omega }}_e^2/\left(v_{F}e\right)]$ in the left panel and $B_{0,5}=0[B_{0,5}=0.5\hslash {\mathrm{\Omega }}_e^2/\left(v_{F}e\right)]$ in the right panel. We set $e{b}_0=-{\mu }_5$ and $T=0$.

Figure 7

The dispersion relations of the collective modes given by Eq. (C13) at $k_{\parallel }=0$ and ${\mathbf{b}}_{\perp }\ne 0$ for $\mu =\sqrt{3\pi /\left(4\alpha \right)}\hslash {\mathrm{\Omega }}_e,{\mu }_5=0$ (left) and $\mu =0,{\mu }_5=\sqrt{3\pi /\left(4\alpha \right)}\hslash {\mathrm{\Omega }}_e$ (right). Red (cyan) solid line corresponds to ${\omega }_l$, blue (brown) dashed one denotes ${\omega }_{\mathrm{tr}}^{+}$, and green (magenta) dotted one corresponds to ${\omega }_{\mathrm{tr}}^{-}$ at $B_0=0[B_0=0.5\hslash {\mathrm{\Omega }}_e^2/\left(v_{F}e\right)]$ in the left panel and $B_{0,5}=0[B_{0,5}=0.5\hslash {\mathrm{\Omega }}_e^2/\left(v_{F}e\right)]$ in the right panel. We set $b_x=0.5\hslash {\mathrm{\Omega }}_e/e$ (top row), $b_y=0.5\hslash {\mathrm{\Omega }}_e/e$ (bottom row), $e{b}_0=-{\mu }_5$, and $T=0$.