Plasmon mode as a detection of the chiral anomaly in Weyl semimetals

Weyl semimetals are one kind of three-dimensional gapless semimetal with nontrivial topology in the momentum space. The chiral anomaly in Weyl semimetals manifests as a charge imbalance between the Weyl nodes of opposite chiralities induced by parallel electric and magnetic fields. We investigate the chiral anomaly effect on the plasmon mode in both intrinsic and doped Weyl semimetals within the random phase approximation. We prove that the chiral anomaly gives rise to a different plasmon mode in intrinsic Weyl semimetals. We also find the chiral anomaly leads to some exotic properties in the plasmon dispersion in doped Weyl semimetals. Consequently, the unconventional plasmon mode acts as a signature of the chiral anomaly in Weyl semimetals, by which the spectrum of plasmon provides a proper way to detect the Lifshitz transition.

Figure 1

The distribution of electrons in the two Weyl nodes $\chi =\pm$ induced by the chiral anomaly $\left(\mathbf{E}·\mathbf{B}\ne 0\right)$ in undoped Weyl SMs.

Figure 2

Plasmon modes in undoped 3D Weyl SMs with chiral anomaly, i.e., $\mathbf{E}·\mathbf{B}\ne 0$ are calculated within the RPA. The red dotted-dashed line shows the long wavelength plasmon mode, the blue dashed line corresponds to the approximate solution obtained from Eq. (10), and the green solid line represents the exact solution of Eq. (9). The shaded area indicates the intraband and interband SPE regions [39].

Figure 3

(a) Equilibrium distribution of electrons in the two Weyl nodes without chiral anomaly $\left(\mathbf{E}·\mathbf{B}=0\right)$. (b) Fermi levels of the Weyl nodes shift away from the equilibrium position $\mu$ due to the chiral anomaly $\left(\mathbf{E}·\mathbf{B}\ne 0\right)$. ${\mu }_{\pm }$ are the resulting chirality-dependent chemical potentials.

Figure 4

(a) Energy-loss function for a series of values of $\gamma$ in doped Weyl SMs with the chiral anomaly. (b) Dependence of frequencies of the undamped plasmon mode on the ratio $\gamma$. The LT occurs at the turning point of the plasmon dispersion [39].