Effect of Spin-Texture Dynamics on Three-Dimensional Orbital Dirac Semimetals

Abstract: We consider the minimal coupling of a Dirac semimetal Hamiltonian to a generic spin-texture in this work. A simple unitary transformation gauges away the spatial dependence in the exchange term, leading to the generation of effective corrections to the Dirac dispersion. A full function's worth of freedom is obtained as a result. Choosing different pitch vectors, we show that many forms of novel phenomena arise in such systems. For example, a linear pitch vector leads to the generation of type-I Weyl semimetal -- we observe the anomalous Hall effect and the chiral magnetic effect. The anomalous Hall coefficient requires a non-zero pitch vector whereas the CME is proportional to the exchange coupling. The band structure of the model in the presence of a magnetic field shows a Lifshitz transition. The introduction of a suitable time dependent pitch vector leads to the formation of nodal spheres in the Sambe space of effective Hamiltonians. This nodal sphere is robust to all orders in van-Vleck perturbation theory as proven explicitly.