Pseudomagnetic helicons

The existence of pseudomagnetic helicons is predicted for strained Dirac and Weyl materials. The corresponding collective modes are reminiscent of the usual helicons in metals in strong magnetic fields but can exist even without a magnetic field due to a strain-induced background pseudomagnetic field. The properties of both pseudomagnetic and magnetic helicons are investigated in Weyl matter using the formalism of the consistent chiral kinetic theory. It is argued that the helicon dispersion relations are affected by the electric and chiral chemical potentials, the chiral shift, and the energy separation between the Weyl nodes. The effects of multiple pairs of Weyl nodes are also discussed. A simple setup for experimental detection of pseudomagnetic helicons is proposed.

Figure 1

The illustration of two limiting setups for observing helicons. While the usual helicons can be induced in Weyl or Dirac materials in a background magnetic field (left panel), the pseudomagnetic helicons should exist in Weyl or Dirac materials with torsion/strain-induced pseudomagnetic field (right panel).

Figure 2

The helicon dispersion relation ${\omega }_h={\omega }_{-}$ given by Eq. (38) for $b_{\parallel }=0$ (red solid line), $b_{\parallel }=0.5b^{*}$ (blue dashed line), $b_{\parallel }=b^{*}$ (green dotted line), and $b_{\parallel }=2b^{*}$ (brown dot-dashed line). We set $B_{0,5}={10}^{-2}\text{T},B_0=0,{\mu }_5=5\text{meV}$, and $\mu =0$.

Figure 3

The frequency of the collective mode ${\omega }_h={\omega }_{-}$ defined by Eq. (38). Red solid, blue dashed, green dotted, brown dot-dashed, and black thin solid lines correspond to $T=0,T=10\text{K},T=25\text{K},T=50\text{K}$, and $T=100\text{K}$, respectively. The left panel is plotted for ${\mu }_5=5\text{meV}$ and $\mu =0$, while the right one represents results obtained for $\mu =5\text{meV}$ and ${\mu }_5=0$. We set $b_{\parallel }=0.5b^{*},B_0=0$, and $B_{0,5}={10}^{-2}\text{T}$.

Figure 4

The dispersion relation of the low-energy collective mode ${\omega }_h={\omega }_{-}$ defined by Eq. (38). Red solid, blue dashed, green dotted, brown dot-dashed, and black thin solid lines in the left panel correspond to ${\mu }_5=10\text{meV},{\mu }_5=20\text{meV},{\mu }_5=30\text{meV},{\mu }_5=40\text{meV}$, and ${\mu }_5=50\text{meV}$, respectively. The same values, albeit for the electric chemical potential $\mu$, are used in the right panel. The left panel is plotted for $\mu =0$, while the right one represents results obtained for ${\mu }_5=0$. We set $b_{\parallel }=0.5b^{*},T=0,B_0=0$, and $B_{0,5}={10}^{-2}\text{T}$.

Figure 5

The dispersion relation of the low-energy collective mode ${\omega }_h={\omega }_{-}$ defined by Eq. (38). Red solid, blue dashed, green dotted, brown dot-dashed, and black thin solid lines correspond to $B_{0,5}={10}^{-3}\text{T},B_{0,5}=2.5\times {10}^{-3}\text{T},B_{0,5}=5\times {10}^{-3}\text{T},B_{0,5}=7.5\times {10}^{-3}\text{T}$, and $B_{0,5}={10}^{-2}\text{T}$, respectively. The left panel is plotted for ${\mu }_5=5\text{meV},\mu =0$, while the right one represents results obtained for ${\mu }_5=0,\mu =5\text{meV}$. We set $b_{\parallel }=0.5b^{*},T=0$, and $B_0=0$.

Figure 6

The dependence of the gapless collective mode frequency on the wave vector obtained by solving Eq. (4) with dielectric tensor (54) for $b_x=0.5b_z$ (red solid line), $b_x=b_z$ (blue dashed line), and $b_x=2b_z$ (green dotted line). We set $B_{0,5}={10}^{-2}\text{T},B_0=0,e{b}_0^{\left(1\right)}=e{b}_0^{\left(2\right)}=-{\mu }_5^{\left(1\right)}=-{\mu }_5^{\left(2\right)}=-5\text{meV},b_z=b^{*}$, and $\mu =0$.