Energy Symmetry Breaking of Dirac and Weyl Fermions in Magnetized Spinning Conical Geometries

Abstract The dynamics of relativistic fermions are studied in the presence of an out‐of‐plane magnetic field and a spinning point‐like defect, deriving exact solutions. These results show that the defect's spin () breaks the symmetry between fermion and antifermion energy levels around zero energy. This symmetry breaking is influenced by the magnetic field strength () and the conical or anti‐conical geometry. Energy levels are further modified by the fractionalized spin , where denotes the angular deficit or surplus, affecting conical or anti‐conical backgrounds. While fractionalized spin has no effect when , it significantly alters energy levels when . The defect's spin impacts fermion energy levels, leaving antifermion levels unchanged. For large , the defect's spin dominates, minimizing internal quantum effects. In the case of and , Landau levels are recovered. These findings suggest the potential to fine‐tune charge carrier dynamics in magnetized monolayer materials with spinning defects or vortices.