Emergent Nodal Spheres and Weyl Fermions via Spin-Texture Coupled to Thin Film Orbital Dirac Semimetals

Abstract

We consider the minimal coupling of a thin film Dirac semimetal Hamiltonian to a generic spin-texture. 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 novel phenomena arise in such systems. For example, a linear pitch vector leads to the generation of a 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-like transition driven by the exchange coupling. The introduction of a suitable time-dependent pitch vector leads, at the level of the leading-order Floquet effective Hamiltonian, to the emergence of a nodal sphere in momentum space. We further show that, in the full driven problem, a closed quasienergy degeneracy structure persists, continuously connected to this nodal sphere, and constrained by the operator algebra of the Floquet expansion.