Model For Ferromagnetic Weyl And Nodal Line Semimetals: Topological Invariants, Surface States, Anomalous And Spin Hall Effect

A model based on the Dirac equation allows one to describe topological insulators. In this paper we extend this model by adding a Zeeman term to introduce magnetism. By this means we show that it can be used to describe the electronic properties of ferromagnetic Weyl and nodal line semimetals, which arise for distinct parameters of the model. We confirm the topological nontriviality of the nodal objects by calculating the topological invariants, as well as by demonstrating the existence of topological surface states in the spectral function of the semi-infinite systems. Furthermore, we calculate the anomalous and spin Hall conductivities for various model parameters, which allows us to identify typical signatures of Weyl points and nodal lines in electronic transport.