Weyl fermions induced magnon electrodynamics in a Weyl semimetal

Weyl fermions, which are fermions with definite chiralities, can give rise to anomalous breaking of the symmetry of the physical system that they are a part of. In their $(3+1)$-dimensional realizations in condensed matter systems, i.e., the so-called Weyl semimetals, this anomaly gives rise to topological electromagnetic response of magnetic fluctuations, which takes the form of nonlocal interaction between magnetic fluctuations and electromagnetic fields. We study the physical consequences of this nonlocal interaction, including electric field assisted magnetization dynamics, an extra gapless magnon dispersion, and polariton behaviors that feature “sibling” bands in small magnetic fields.

Figure 1

The polariton spectra as we increase the magnetic field from left to right. (Top) Real parts of the polariton poles, where the solid lines correspond to those with vanishing imaginary part while the dashed lines otherwise. Here, the magnon gap is given by ${\omega }_m=\gamma (M{m}^2+B_3)$ and the bifurcation starts at $q_c\approx 2eg{B}_3/\left[\pi \gamma (Mm+\sqrt{M{B}_3})\right]$, which we estimate to be $\sim {10}^{-5}–{10}^{-4}$ ${\mathrm{A}}^{-1}$. We have also shown the forbidden band for the intermediate value of magnetic field, depicted as the shaded region. (Bottom) Imaginary part for the intermediate band, whose maximum value is given by ${\omega }_h$, with ${\omega }_h\approx \sqrt{2}eg{B}_3/\left[\pi \gamma (Mm+\sqrt{M{B}_3})\right]$.

Figure 2

Landau levels for $M_0=-0.005$ eV, $M_1=0.342$ $\text{eV}{\mathring{\mathrm{A}}}^2,M_2=18.225$ $\text{eV}{\mathring{\mathrm{A}}}^2,L_1=1.3$ $\text{eV}\mathring{\mathrm{A}},L_2=2.82$ $\text{eV}{\mathring{\mathrm{A}}}^2$, and $B=5$ T. $n=0$ Landau levels are depicted in red, while the higher Landau levels are depicted in blue.

Figure 3

The spectral density at small magnetic field for different values of momenta $q/q_c=0.2,0.5,0.75$, and $0.99$ for the blue, purple, yellow, and green lines (from left to right), respectively. Here, $q_c\approx 2eg{B}_3/\left[\pi \gamma (Mm+\sqrt{M{B}_3})\right]$ is the momentum at which the bifurcation into the “sibling” bands starts and ${\omega }_m=\gamma (M{m}^2+B_3)$ is the magnon gap.