Magneto-optical conductivity of Weyl semimetals with quadratic term in momentum

Weyl semimetal is a three-dimensional Dirac material whose low energy dispersion is linear in momentum. Adding a quadratic (Schrödinger) term to the Weyl node breaks the original particle-hole symmetry and also breaks the mirror symmetry between the positive and negative Landau levels in present of magnetic field. This asymmetry splits the absorption line of the longitudinal magneto-optical conductivity into a two peaks structure. It also results in an oscillation pattern in the absorption part of the Hall conductivity. The two split peaks in Reσxx (or the positive and negative oscillation in Imσxy) just correspond to the absorptions of left-handed (σ−) and right-handed (σ+) polarization light, respectively. The split in Reσxx and the displacement between the absorption of σ+ and σ− are decided by the magnitude of the quadratic term and the magnetic field.