Scattering theory and spectral singularities in topological Weyl semimetals

Lasing behavior of optically active planar topological Weyl semimetal (TWS) is investigated in view of the Kerr and Faraday rotations. Robust topological character of TWS is revealed by the presence of Weyl nodes and relevant surface conductivities. We focus our attention on the surfaces where no Fermi arcs are formed, and thus Maxwell equations contain topological terms. We explicitly demonstrate that two distinct lasing modes arise because of the presence of effective refractive indices which lead to the birefringence phenomena. Transfer matrix is constructed in such a way that ref lection and transmission amplitudes involve 2 × 2 matrix-valued components describing the bimodal character of the TWS laser. We provide associated parameters of the topological laser system yielding the optimal impacts. We reveal that gain values corresponding to the lasing threshold display a quantized behavior, which occurs due to topological character of the system. Our proposal is supported by the corresponding graphical demonstrations.