Four-wave Mixing of Weyl Semimetals in a Strong Magnetic Field

We theoretically investigate the four-wave mixing process in Weyl semimetals in a strong magnetic field using quantum theory. Weyl semimetals in a strong magnetic field have an extremely high third-order nonlinear optical susceptibility (several orders larger than that of the usual three dimensional materials) originating from the linear energy dispersion near the Weyl points. The third-order response of Weyl semimetal is nearly independent on the Fermi level, which is quite different from the sensitive dependence (on the Fermi level) of the linear response. The unusual polarization dependent selection rules lead to rich nonlinear optical properties, which can be tuned by the polarization of the incident light fields and the magnetic fields.