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Cyclotron resonance of figure-of-eight orbits in a type-II Weyl semimetal

We study the cyclotron resonance in the electron-hole joint Fermi surface of a type-II Weyl semimetal. In magnetic field, the electron and hole pockets touching at the Weyl node are hybridized to form quantized Landau levels corresponding to semiclassical 8-shaped orbits. We calculate the dynamical conductivities for the electric fields oscillating in $x$ and $y$-directions and find that the resonant frequencies in $x$ and $y$ differ by the factor of two, reflecting to the figure-of-eight electron motion in the real space. The peculiar anisotropy in the cyclotron resonance serves as a unique characteristic of the dumbbell-like Fermi surface.