Second-order chiral kinetic theory: Chiral magnetic and pseudomagnetic waves

The consistent chiral kinetic theory accurate to the second order in electromagnetic and pseudoelectromagnetic fields is derived for a relativistic matter with two Weyl fermions. By making use of such a framework, the properties of longitudinal collective excitations, which include both chiral magnetic and chiral pseudomagnetic waves, are studied. It is shown that the proper treatment of dynamical electromagnetism transforms these gapless waves into chiral (pseudo)magnetic plasmons, whose Langmuir (plasma) gap receives corrections quadratic in both magnetic and pseudomagnetic fields.

Figure 1

Left figures: The dispersion relation for the longitudinal mode propagating along the direction of background magnetic and pseudomagnetic fields with the wave vector $\mathbf{k}=k\widehat{\mathbf{z}}$ at $B_{0,5}=0.1B^{*}$ (red solid line) and $B_{0,5}=0$ (blue dashed line). Right figures: The same dependence at $B_0=0.1B^{*}$ (red solid line) and $B_0=0$ (blue dashed line).