Kerr effect and self-focusing in nodal semimetals in terahertz regime

We determine the Kerr index, associated critical Kerr power, and focal length of nodal semi metals. The focal length is directly relate the dynamical non-linear optical conductivity of the semimetal. In this framework, through the non-linear conductivity, one can directly observe how the Kerr index is altered by intrinsic parameters of the semimetal such as node separation and bandgap, which determine its topological phase. In THz and microwave regime, Kerr index is found to be around 1$0^{15}-10^{20}\text{m}^{2}$/W. Dependence of the Kerr index, critical power and focal length on temperature, chemical potential, band gap and node separation are obtained. Our result shows that the tunability of the non-linear response of a nodal semimetal persists in its focusing phenomenon.